The major concern of current pagination is to report the doubly stratified medium subject to both magnetized and non-magnetized flow fields. For this purpose both the Newtonian and non-Newtonian liquids are considered in a double stratified medium having magnetic field interaction. To be more specific, a generally accepted rheological liquid around a cylindrical surface having constant radius embedded in magnetized doubly stratified media is taken into account. Additionally, flow field is manifested with various pertinent physical effects. The flow problem statement is defended through generalized formulation via fundamental laws. A computational scheme is executed and stream lines topologies are constructed for the both magnetized and non-magnetized stratified medium to explore the interesting features. It is observed that the Casson fluid velocity towards cylindrical surface is higher in magnitude as compared to flat surface. Such observation is same for the both the magnetized and non-magnetized flow fields. Our general formulation yields some existing attempts in the literature. The variations in local skin friction coefficient (LSFC), local Nusselt number (LNN) and local Sherwood number (LSN) are provided with the aid of tabular forms. It is trusted that the obtain observations via stream lines topologies will serve a clear insight to the said flow problem. Dilatant , Pseudoplastic (when viscosity is decreasing function of shear for instance in ketchup), Thixotropic  and Rheopectic (when viscosity is time dependent increasing function of applied shear like cream and gypsum paste). The movement of electrical conductor (EC) in existing magnetic field results EMF (electromotive force). Such force namely EMF is direct relation with both strength of magnetic field and speed of moving EC. The generated EMF along with applied magnetic field yields a resistive force that opposes the motion of EC. As far as the study of the magnetohydrodynamics (MHD) is concern, the assumed fluid model will play the role of EC. To explore the importance of MHD flows scientists proposed the coupling of applied magnetic field by means of Naviers stokes equations and ultimate results predicts acceptable remarks regarding practical involvements in both industrial and engineering areas like plasma welding, liquid metals subject to casting processes, (EHCs) electrolytic Hall cells, shielding individualities and significant heat transfer characteristics are few examples. Owing the importance of magnetic field involvement various scientist and researchers shared their views like Hua and Walker1 discussed magnetic field interaction via rectangular ducts. In this problem an inclined applied magnetic field is taken into account. The recorded observations were presented with both analytical and numerical approaches. The impact of magnetic field on fluid flow due to flat surface was identified by Chaturvedi2. In this problem viscous fluid is considered as EC along with porous flat surface assumption while the induced magnetic effect is neglected in this attempt. Aldoss3 studied the effects of magnetic field by way of vertical cylinder. The non-Darcian model is assumed in porous medium. He found that both natural and forced convection regime have opposite results against applied magnetic field. The impact of magnetic field on unsteady flow regime is reported by Nanousis4. The incompressibility condition is implemented on viscous fluid being acted as an EC in this study. Moreover, he assumed oscillatory flat surface. Chamkha5 explored the effects of magnetic field subject to vertical surface. In this analysis a surface is considered in thermally stratified medium. Both the Halls and Hartmann impacts are reported numerically. Bhattacharyya and Gupta6 identified magnetic field individualities for stagnation point flow in a three dimensional frame. In this study they also entertained heat transfer properties. A viscous fluid is taken as an EC with arbitrary velocity gradients. The influence of magnetic field and the corresponding involvement namely Joule heating towards microplar fluid was taken by Hakiem et al.7. The micropolar fluid is taken as EC in this study. They found that both the SFC (skin friction coefficient) and HRT (heat transfer rate) reflects decline values for the positive values of magnetic field parameter. Mansour et al.8 addressed the effects of magnetic field in the presence of both heat and mass transfer characteristics. In this study they consider micropolar as an EC by way of circular cylinder. The impact of magnetic field along with variable viscosity was examined by Seddeek9. In this study heat transfer properties are considered in the presence of radiations. They found that the fluid velocity is decreasing function of magnetic field parameter but temperature profile is found to be increasing one. Amin10 considered micropolar fluid as an EC with constant suction assumption. The transverse magnetic field in assumed in this analysis. The impact of magnetic field was provided with the aid of both tables and graphs. The impact of magnetic field on an Oldroyd-B fluid was examined by Hayat et al.11. In this attempt Oldroy-B was taken as an EC and exact solution in this regard was presented. The magnetic interaction towards shrinking surface was discussed by Nadeem et al.12. In this work they considered Casson fluid as an EC and shrinking was exponentially proportional. Adomian decomposition method was utilized to report analytical solution and the outcomes in this regard were offered in terms of both tables and graphs. The Eying-Powell fluid was taken as an EC and magnetic characteristics were reported by Hayat et al.13. They presented series solution and graphical trends are provided to elaborate impact of magnetic field parameter. Since than many attempts were with respect MHD flows. The past and recent developments in this direction can be assessed in refs 31.The fluid flow having interaction with applied magnetic field is termed as magneto-hydrodynamic flow. The engaged fluid can be from Newtonian and non-Newtonian models. The Newtonian fluids possesses linear relation between shear stress and shear rate. This relation is well-known by Newton’s law of viscosity. It is named after Sir Issac Newton. The common examples subject to Newtonian are alcohol, mineral, gasoline and water to mention just a few. The non-Newtonian do not possesses linear relation between shear stress and shear rate. The non-Newtonian class can be explore by dividing into subclasses, namely Section-1 is devoted to skimmed the limited literature survey regarding magneto-hydrodynamic boundary layer flows which includes both Newtonian and non-Newtonians models. The generalized mathematical treatment for Casson fluid model is structured in Section-2. The detail analysis after implementation of computational algorithm is discussed in Section-3. In addition, Section-3 is further divided into sub sections  to facilitate readers. The stream lines patterns for both magnetized and non-magnetized cases are provided as a graphical outcomes in Section-4. The sub cases subject to said problem are retraced and discussed in Section-5. The summary of analysis is offered as an itemized points in Section-6. An adopted procedure is trustful and it can be extended to some useful fluid models like Tangent hyperbolic fluid model, Williamson fluid model, Powell-Eyring fluid model, Jeffrey fluid model etc.The strength of current pagination is generalized mathematical formulation and interpretation in both magnetized and non-magnetized frames. In this article Casson fluid is taken as an EC with doubly stratified medium. The Casson fluid flow regime is further manifested with various physical effects namely stagnation point, applied magnetic field, mixed convetion, thermal radiation, heat generation/absorption, Joule heating, chemical reaction and suspended nanoparticles. It is noticed that the mutual mathematical modelling subject to flow narrating differential equations that is Navier-Stokes equations and Maxwell equations generates complex structures and it seems impossible to obtain exact solutions. Therefore a computational algorithm is developed to report numerical results in terms of both tables and graphs. To be more specific, x-axis and the perpendicular axis to the x-axis is taken as r-axis . Through generally accepted mathematical laws, one can obtained the following flow narrating differential equations:34. One of application of Lie symmetry analysis is order reduction towards differential equations. Ferdows et al.35 carried Lie symmetry approach to find set of similarity transformation for conversion of partial differential equations into ordinary differential system. Some recent trustful attempts subject to similarity transformation can assessed in refs42. Our attention is to solve the system of ordinary differential equations, therefore the widely used set of transformation42 for the cylindrical surface is given asThe flow model for the Casson fluid is mathematically modelled when various effects are taken into account namely, mixed convection, stagnation point, magnetic field, Joule heating, nonlinear radiations, heat generation/absorption, nanoparticles, temperature stratification, concentration stratification and chemical reaction. The fluid flow is achieved due to an inclined stretching cylindrical surface. For clarity the axial cylinder line is supposed to be parallel to s are given as:The involved parameters are defined as below:For the numerical solution the shooting method with Runge-Kutta algorithm is utilized. The complete description in this regard is provided by way of Fig. γ ≠ 0) and non-magnetized (γ = 0) double stratified medium . Figure K = 0) and cylinder geometry (K ≠ 0) while Figs A = 0) but Figs A ≠ 0). In detail, Figs A < 1), (A = 1) and (A > 1) respectively. Lastly, Figs β → ∞). Figures 17–Figures δ1 ≠ 0, δ ≠ 0. FigK), Casson fluid parameter (β), mixed convection parameter (λm), Prandtl number (Pr), heat generation parameter (Q+), temperature stratification parameter (δ1), Schmidt number (Sc), concentration stratification parameter (δ2), chemical reaction parameter (Rc) and Lewis number (Le). To be more specific, Tables Tables rameter δ, Schmidtrameter δ, chemicaγ), curvature parameter (K), velocity ration parameter (A) and Casson fluid parameter (β) are presented. In detail, Figs γ ≠ 0) doubly stratified  medium for both cylindrical (K ≠ 0) and flat (K = 0) surfaces. Particularly, Fig. K = 0.7 and Fig. K = 0.0. Both patterns depicts magnetized stratified medium for Casson fluid and one can observed that the streamlines for γ = 0.5, K = 0.7 are significantly close as compared to γ = 0.5, K = 0.0. This fact is due to cylindrical surface and hence Casson fluid velocity enlarged for the case of cylindrical geometry with respect to flat surface even the fluid flow regime is magnetized. Figures γ ≠ 0) in contrast to non-magnetized stratified medium (γ = 0) In this direction it is observed that the existence of magnetic field is the cause of wider distance between stream lines . The Figs A < 1, when the free stream velocity is lower in strength as compared to stretching rate in both magnetized and non-magnetized stratified medium. One can observed that the for magnetized case γ = 0.5 the stream lines patterns are wider than that of non-magnetized case γ = 0.0 as expected. The case A = 1, when both free stream and stretching velocities are equivalent is examined and observation in this regard is provided by means of Figs A > 1. Figures A > 1 in both magnetized and non-magnetized stratified medium. It can be seen that for A > 1 the impact of magnetic field parameter still remains significant that is the free stream lines patterns depicts larger distance between them as compared to non-magnetized frame which implies the suppress nature of velocity against magnetic flow field. Figures β = 1.3) under the region of stagnation point (A ≠ 0) flow in both magnetized (γ = 0.5) and non-magnetized (γ = 0) stratified medium. It is seen that the Casson fluid particles momentum is significant in non-magnetized (γ = 0) stratified medium than that of magnetized (γ = 0.5). The application of magnetic field brings the resistive role of Lorentz force as results the average velocity of Casson liquid suffers. It can be observed from Eq. (β → ∞) we have viscous fluid via doubly stratified medium having suspended nanoparticles in flow regime. Therefore, Figs γ = 0.5) and non-magnetized (γ = 0) stratified medium. Similar trends are observed for the existing of magnetized stratified medium with that of non-magnetized frame. The viscous fluid momentum is decreasing function of magnetic field parameter. On another hand when the Casson fluid parameter increases the fluid becomes more dense as a result the velocity increases. This fact is validated through stream lines patterns that is for β → 1.3 the distance between stream lines are less as compared to stream lines pattern given in Fig. β → ∞) yields Newtonian fluid model as an especial case.The generalized flow problem for the Casson fluid flow around a cylindrical geometry is controlled by mathematical formulation given in Eqs –6 in ternes Figs  and 4 wifrom Eq. , when Caλm), thermal radiation parameter (RT), temperature stratification parameter (δ1) and chemical reaction parameter (Rc). To be more specific, the impact of mixed convection parameter on fluid velocity is examined and provided by way of Fig. λm = 0.1, 0.3, 0.4 the fluid velocity enhances. Figure RT = 0.1, 0.2, 0.4 the fluid temperature shows an inciting values. Further, it is noticed that the fluid temperature is decreasing function of temperature stratification parameter. Figure δ1 = 0.1, 0.2, 0.3 the fluid temperature reflects decline nature. The effect of chemical reaction parameter on nano-concentration profile is examined and offered by means of Fig. Rc = 0.1, 0.3, 0.4.Additionally, Figs Since an article contains proposed generalized mathematical modelling for the stratified medium towards Casson fluid flow around a cylindrical geometry. The existing literature subject to the Casson flow field via stratified medium becomes over sub-study. The detail in this direction structured through section wise.31. In this problem a magnetohydrodynamic Casson fluid flow towards both flat and cylindrical surfaces via thermally stratified medium. It was concluded that the obtained variations were remarkably enormous for cylindrical geometry as compared to plane surface. The local skin friction coefficient was found as an increasing function of curvature parameter, Casson fluid parameter, Prandtl number and thermal stratification parameter while opposite trends were noticed towards mixed convection parameter and heat generation parameter. The local Nusselt number was an increasing function for greater values of curvature parameter, mixed convection parameter and Prandtl number while inverse values are noticed for Casson fluid parameter, thermal stratification parameter and heat generation parameter. An excellent comparison is noticed with ref.31 for both local skin friction coefficient and local Nusselt number. Tables In the absence of concentration equation and ignoring the stagnation point, thermal radiations, Joule heating and suspended nanoparticles assumptions, the generalized problem reduced to Problem reported in ref.43. In this problem doubly stratified mixed convection flow of Casson fluid due to an inclined cylindrical surface was examined. It was reported that in absolute sense the local skin friction shows an inciting nature towards curvature parameter, Casson fluid parameter, Prandtl number, Schmidt number, thermal stratification parameter while opposite attitude wasobserved for the positive values of mixed convection parameter, solutal stratification parameter and heat generation parameter. It was seen that Nusselt number was decreasing function of Casson fluid parameter, thermal stratification parameter and heat generation parameter but an inverse trends were found for the higher values of mixed convection parameter, curvature parameter and Prandtl number. Additionally, it was observed that Sherwood number reflected an inciting attitude for higher values of curvature parameter, Schmidt number, solutal stratification parameter and chemical reaction parameter. Tables 43. The corresponding mathematical formulation are prearranged as follows:In absence of thermal radiations, Joule heating, suspended nanoparticles and stagnation point assumptions our generalized mathematical formulation meet with formulation reported in ref.44 when we ignore stagnation point, magnetic field, suspended nanoparticles, thermal radiations, heat generation and Joule heating effects along additional condition that is β → ∞. In this problem mixed convection effects towards thermally stratified media were presented. The corresponding mathematical formulation in this problem is as follows:One can confirm from mathematical formulation given by Eqs –12, that45 the impact of Joule heating was ignored. Since our flow problem contains the influence of Joule heating so by ignoring this fact our findings exactly matched with results reported in ref.45. For comparison purpose we have constructed Tables K, and β. On the other hand it shows an opposite trends for the increasing values of λm. Moreover, the local skin friction coefficient in independent of Prandtl number. The negative sign of local skin friction implies the drag forced exerted by cylindrical surface towards Casson fluid particles. It has been observed through the local Nusselt number shows an increasing values for the greater values of K and Pr, however opposite variations are observed for the increasing values of the parameter δ1. The negative sign in local Nusselt number relates the transfer of heat normal to the cylindrical surface. The local Sherwood number depicts an increasing attitude for the increasing values of the parameters K, and Le. On the other hand, it shows a decreasing nature towards δ2. Further, the recent developments on the surface quantities can be assessed in refs47.The effectiveness subject to velocity gradients due to viscous stresses was consider very small therefore in this attemptγ ≠ 0) and non-magnetized (γ = 0) stratified  media is investigated. The stream lines topologies are limited to magnetic field parameter (γ), curvature parameter (K), velocity ratio parameter (A) and Casson fluid parameter (β). The key outcomes are itemized as follows:A generalized mathematical formulation is proposed for the non-Newtonian fluid model.K = 0.7) claims larger momentum values with respect to Casson liquid via flat surface (K = 0.0). This variation is invariant subject to both magnetized and non-magnetized stratified medium.The Casson liquid around cylindrical surface (The flow momentum of Casson liquid found suppress for magnetized stratified medium as compared to non-magnetized medium.β → ∞) and non-Newtonian (β = 1.3) fluids flow reflects decline nature in magnetized (γ ≠ 0) stratified  medium than that of non-magnetized (γ = 0) one.Both Newtonian (The momentum of viscous fluid flow in stratified medium is significantly lower as compared to momentum of Casson fluid flow. Such variation holds in both magnetized and non-magnetized stratified medium.The Casson fluid temperature is increasing function of thermal radiation parameter.The nano-concentration profile is decreasing function of chemical reaction parameter.The LSFC, LNN and LSN are offered in a systematic design via comparison with some interesting existing results.The realistic Casson fluid model via both magnetized (


In the article titled “Genome-Wide Identification of Long Noncoding RNAs in Human Intervertebral Disc Degeneration by RNA Sequencing” , there wThis study was supported by the grants from the National Health and Family Planning Commission (Grant no. 2011-1) and ShaanXi Natural Foundation (Grant no. 2016JM 8136).


Several markers of systemic inflammation, including blood C-reactive protein, platelet lymphocyte ratio (PLR) and neutrophil lymphocyte ratio (NLR) have been identified as independent prognosticators for hepatocellular carcinoma (HCC).To attempt to understand the significance of these markers, they were examined in relation to 4 tumour parameters, namely maximum tumour diameter (MTD), tumour multifocality, portal vein thrombosis (PVT) and blood alpha-fetoprotein (AFP) levels.Using linear and logistic regression models, we found that C-reactive protein and PLR on single variables, were statistically significantly related to the tumour parameters. In a logistic regression final model, CRP was significantly related to MTD, AFP and PVT, and the Glasgow Index significantly related to MTD and AFP. Results of the area under the receiver operating characteristic curves (ROC), showed that the areas for PLR and CRP were statistically significant for high versus low MTD and for presence versus absence of PVT. CRP alone was significant for high versus low AFP.These analyses suggest that the prognostic usefulness of the inflammatory markers PLR and CRP (but not NLR) may be due to their reflection of parameter values for tumour growth and invasiveness. C-reactive protein (CRP) is a recognized part of the acute phase response and is associated with various inflammatory diseases . It is aIn this study, we analysed a database of 424 patients prospectively-accrued HCC patients who had full baseline tumour parameter data, including CT scan information on HCC size, number of tumour nodules and presence or absence of PVT, plasma AFP levels, complete blood count and routine blood liver function tests. Diagnosis was made either through tumour biopsy or according to international guidelines. Database management conformed to legislation on privacy and this study conforms to the ethical guidelines of the Declaration of Helsinki and approval for this retrospective study on de-identified HCC patients was obtained by the Institutional Review Board of each participating institution .The continuous variables including, maximum tumour diameter (MTD), alpha-fetoprotein (AFP) and CRP were divided into two groups with different cut-off values as less than 3 and ≥3, less than 20 and ≥20, and ≤10 and more than 10, respectively. Descriptive statistics for continuous variables, such as the neutrophils-to-lymphocyte ratio (NLR) and the platelet-to-lymphocyte ratio (PLR) for MTD, AFP, multifocality and portal vein thrombosis (PVT) groups were calculated with mean, standard deviation, median, interquartile range, minimum and maximum values. Shapiro-Wilk test was used to check the normality assumption of the continuous variables. In the cases of non-normally distributed data, the Wilcoxon rank-sum (Mann-Whitney U) test was performed to determine whether the difference between the two groups was statistically significant. A linear regression model was constructed to evaluate the associations between PLR on single variables. The univariate logistic regression method was utilized to assess the factors associated with CRP (≤10/>10) and Glasgow index (<2/=2) in single variables, and then multiple logistic regression method was performed. All final multiple logistic regression models were executed with the backward stepwise method. The ability of PLR, NLR and CRP values to predict MTD, AFP, Multifocality and PVT groups in HCC patients were examined by receiver operating characteristic (ROC) curve and their respective areas under the curve. A p-value of less than 0.05 was considered as statistically significant. All statistical analyses were performed using IBM SPSS version 21.0 .The focus of this study was 424 HCC patients with full data including CRP levels. Mean PLR, NLR and CRP were 0.16±0.13, 4.53±4.66 and 18.44±33.24, respectively (data not shown) . summariLinear regression models were then constructed for the association between the PLR ratio and the four tumour parameters, separately . Based oFinal models of logistic regression analysis for independent variables the PLR, NLR ratios and CRP/Glasgow index were then built to evaluate their associations with each of the four tumour parameters . This anA ROC curve analysis was then performed . Our resIn order to better understand their significance, we have examined the associations of 3 commonly used systemic inflammatory markers with each of 4 HCC tumour parameters that reflect HCC aggressiveness. The PLR ratio and the CRP level were each significantly higher in patients with high MTD and positive PVT. Higher CRP levels also significantly associated with higher AFP values. The calculated p-value for the comparison of PLR ratio between multifocal and unifocal patients was near the significance threshold (p<0.05). We thus considered the significance of PLR as a marker to be inconclusive, until more patient data are obtained to accurately elucidate its significance in relation to tumour parameters. The NLR ratio was not found to be a significant marker among the 4 tumour parameters.When the 4 tumour parameters were included separately in the linear regression model, MTD was the only parameter to predict PLR . Our resThe results of AUC for the PLR ratio and CRP were statistically significant in the MTD and PVT groups. CRP alone was significant for high versus low AFP. In our results , CRP hadCRP is a non-specific inflammatory marker that has long been recognized as associated with various inflammatory diseases including coronary artery disease and cancer ,3,31–33.In this context, we addressed in this work the possible mechanisms that might underlie the prognostic usefulness of CRP, PLR and NLR. A working hypothesis that we have tested here, is that each or any of CRP, PLR or NLR might be related to indices of tumour aggressiveness, namely MTD, AFP, PVT and multifocality, as an explanation of their prognostic ability ,36,37. WThese analyses suggest that the prognostic usefulness of the inflammatory markers PLR and CRP (but not NLR) may be due to their reflection of parameter values for tumour growth and invasiveness, but do not explain the mechanisms involved, nor do they address whether CRP and PLR are mechanistically involved in these parameters for tumour aggressiveness, or are just reactive reflections of these tumour behaviours.


Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: (i) a glycolytic phenotype which produces acid that kills stromal cells and (ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby–Gawlinski reaction–diffusion model to derive a system of five coupled reaction–diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: (i) rapidly (matrix-degraders dominate) or (ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated. If the tumour has started to spread, breaching the basement membrane, survival rates are significantly decreased and the tumour is termed malignant (“badly born”). In 90% of patients, the cause of death is not the primary tumour, but the disruption of normal body function caused by metastatic disease , a dense mixture of proteins encapsulating the cells in healthy tissue  such as matrix metalloproteinases  glycolytic, acid-producing cells  have a zero eigenvalue (for details see “Appendix A2”). This corresponds to a perturbation in the ECM density and reflects the fact that, in the absence of M are admissible as steady states. Furthermore, we find that SS2, SS4, and SS6 always have at least one eigenvalue with positive real part for the range of parameters considered  to Eqs. –12) whi whi12) wred Fig. . This imh, and M. The resulting system of ODEs is solved with backwards differentiation formulas (BDF1-BDF5) (Süli and Mayers scipy.integrate.ode class). To improve numerical stability, a stabilisation scheme is used to guide state variables back to zero should they become negative (for details see the provided code). Convergence in space and time for this scheme was checked thoroughly (not shown). The solutions presented are at a resolution of https://github.com/ms234/CooperationInCancerInvasion.We simulate our model using the method of lines by discretising space, and then applying a standard ODE integration scheme in time. We discretise the equations in space using the following central difference scheme:r [as in ], this rr [as in , it provIn Fig. rix Fig. a. Similaoma Fig. b. Plottioma Fig. c.Fig. 4TS and L, and simulated until time Our results in Sect. Figure Furthermore, we observe that the relationship between the invaded distance and the competition parameters is not symmetric about As ion Fig. a. A simueck Fig. b.Similarly, if ced Fig. a. HoweveWhen inter-species competition is stronger than intra-species competition for both populations \documentoma Fig. ? (iii) HWe note that there are a number of potentially important interactions not accounted for in the model. Firstly, we do not model matrix regeneration (e.g. Martin et al. what cells are present but also where are these cells located? Do they live in separate regions or can they spatially mix and, thus, match their traits?To sum up, we have explored cooperation of tumour cells as a mode of tumour invasion. We found that the most invasive tumour emerges when cells coexist in the same region in space as this allows cells to most effectively share their traits. This point is simple but important: to fully understand the implications of tumour heterogeneity, we have to ask not only


The results of our within-subject experimental design revealed that the physiological results varied significantly depending on the type of backpack. Backpacks B and C were superior to Backpack A, resulting in lower physiological responses and higher subjective preferences. Students carrying more weight experienced higher physiological stress; moreover, the use of Backpack C led to the lowest physiological strains and higher subjective preferences.It is important for schoolchildren and their parents (or guardians) to know which backpacks exert the least strain on the cardiorespiratory system. In this study, we investigated the physiological responses of participants while they were walking on a treadmill and wearing one of three different backpacks  under two different load-carrying conditions . The first condition was used as a control and involved walking without a backpack, while the second involved wearing a backpack and carrying a certain weight. Thirty-one male students from King Saud University walked on a treadmill at 0.861 m/s and at a 0% inclination angle, while having their heart rates (beatsmin Students use schoolbags daily to carry educational material  over long distances. Schoolbags are useful for this purpose; however, if improperly worn or overloaded, they may cause pain or injury to the user . The vasThe incidence of lower back pain among young students  is high, varying between 30% and 70%, depending on the type of pain, age, and research study design . Health Previous research involving children has proved that backpacks weighing between 10% and 30% of the user’s body mass cause a significant increase in the contact pressures beneath the backpack shoulder straps . This prSeveral researchers have demonstrated that carrying a heavy backpack results in decreased walking speed  as well The implementation of gait screenings at schools may be useful for the detection of critical conditions exacerbated by load transfer  that may cause discomfort, pain, or decrease the desire of participating in physical activities . SignifiSome school bag designs focus on the harness , which iThirty-one college students from King Saud University volunteered for this study; their characteristics are shown in An informed consent form, approved by the Institutional Review Board of the King Saud University and the College of Medicine  was obtained from each student before the start of the experiment. All procedures and methods were performed in accordance with the guidelines and regulations mentioned in the informed consent form and approved by the IRB. In addition, a specific consent form was obtained from each participant for the publication of their photographs on online open-access publications . AfterwaBackpack A is a popular school backpack, available in the local market, while the other two (B and C) were fabricated for the experiment. Backpack B was similar to the model used in  the Bac. These tA Polar monitor was used to check the participant’s heart rate ; the instrument was covered with a conductive gel and positioned over the subject’s sternum, on clean naked skin. A Moxus Modular Metabolic System using legendary CD-3A and S-3A Gas Analyzers  was used to measure the oxygen uptake and the respiratory rate. The main components of the Moxus Metabolic System included an oxygen analyzer (S-3A/I), a carbon dioxide analyzer (CD-3A), a flow control pump (R-1), a 4.2-L active mixing chamber, a canopy Pump, a canopy Hood, calibration and reference gases, a laptop with an interface software , and a mask worn by the participants (tested for leakage). The mask was connected to the main unit by two flexible pipes. A computer, loaded with software for the recording and analysis of respiratory and heart data, was also connected to the main unit. While the participants were carrying the backpack and walking on a treadmill  , their h−1), VO2 (L·min−1 and mL.kg−1∙min−1), respiratory rate (breaths∙min−1), perceived exertion rate (PER), and backpack preference rating (BPR) represented the dependent variables. The PER was measured referring to the Borg scale, considering values between 6  and 20 . The PER has proved its high reliability in different studies [The backpack type and the load carried were the independent variables of this study. The heart rate  was calculated from those selected by the 31 participants (between 2.9–3.4 km·hr−1) and used during all sessions. The participants were then weighed, their heights measured, the resting heart rate read, and their ages recorded for inclusion in the energy measuring program. The participants were then given an orientation and requested to report any feelings of discomfort, which were resolved before continuing the testing. The backpack’s bottoms were adjusted at the level of each participant’s waist.Before the start of the experiment, all the participants were informed about its purpose and signed consent forms approved by the University Internal Review Board. Then, they were asked to determine the treadmill speed at which they could walk most comfortably while carrying an unloaded backpack. The average speed . During the testing sessions, the participants were dressed in shorts, t-shirt, socks, and sports shoes; additionally, each participant came into the lab at the same time of the day. The test was conducted during the spring semester, at a mean room temperature of 21–22 °C and relative humidity of 50%–60%. The participants were instructed not to eat anything and to avoid exercise and caffeine for at least 4 h beforehand . The results of the reliability analysis, based on the Cronbach coefficient (α), were used to calculate the internal consistency coefficients of the subjective factors, which were satisfactory: 0.836 and 0.751 for the backpack preference and perceived exertion ratings, respectively. Negative linear regression coefficient (p < 0.0001) was found between RPE and BPR with Spearman correlation (−0.915).p < 0.0001, η2 = 0.636), the percent of carried load with respect to the participant’s body mass  = 111.872, p < 0.0001, η2 = 0.789), and the percent of carried load interaction  = 15.866, p < 0.0001, η2 = 0.346). When the carried load corresponded to 10% of the participant’s body mass, the LSD tests revealed that the participant’s heart rate was significantly higher while wearing Backpack A (p < 0.002), rather than Backpacks B and C (p < 0.0001); meanwhile, no significant differences were found for this parameter between Backpacks B and C. When the carried load corresponded to 15% of the participant’s body mass, the LSD tests revealed that the participant’s heart rate was significantly higher in the case of Backpack A (p < 0.0001) compared to Backpacks B and C (p < 0.0001); meanwhile, no significant differences were found between Backpacks B and C  = 52.373,  B and C a.−1 was significantly affected by the backpack type  = 7.313, p < 0.001, η2 = 0.196), the percent of carried load  = 17.027, p < 0.0001, η2 = 0.362), and the percent of carried load interaction  = 2.616, p < 0.039, η2 = 0.08). When the carried load corresponded to 10% of the participant’s body mass, the LSD tests revealed that the participant’s VO2·kg−1 was significantly higher when using Backpack A (p < 0.029), rather than Backpacks B and C (p < 0.016); however, no significant differences were found between Backpacks B and C. When the carried load corresponded to 15% of the participant’s body mass, the LSD tests revealed that the participant’s VO2·kg−1 was significantly higher in the case of Backpack A (p < 0.034) compared to backpacks B and C (p < 0.003); meanwhile, no significant differences were found between Backpacks B and C , the percent of carried load  = 137.363, p < 0.0001, η2 = 0.821), and the percent of carried load interaction  = 14.88, p < 0.0001, and η2 = 0.332). When the carried load corresponded to 10% of the participant’s body mass, the LSD tests revealed that the participant’s respiratory rates were significantly higher when using Backpack A (p < 0.013), rather than Backpacks B and C (p < 0.001); however, no significant differences were found between Backpacks B and C. When the carried load corresponded to 15% of the participant’s body mass, the LSD tests revealed that the participant’s respiratory rates were significantly higher in the case of Backpack A (p < 0.0001) compared to backpacks B and C (p < 0.0001); meanwhile, no significant differences were found between Backpacks B and C  = 28.889,  B and C c.2(2) = 60.612, p < 0.0001; χ2(2) = 62.00, p < 0.0001. When the carried load corresponded to 10% of the participant’s body mass, a post hoc analysis  was conducted, and a Bonferroni correction was applied. We noted a significant reduction of the perceived exertion of Backpack A compared to either Backpack B  or Backpack C ; meanwhile, no significant differences were found between Backpacks B and C concerning the perceived exertion. When the carried load corresponded to 15% of the participant’s body mass, another post hoc analysis  was conducted, and a Bonferroni correction was applied. We noted a significant reduction of the perceived exertion of Backpack A compared to either Backpack B  or Backpack C   . Meanwhi2(2) = 50.596, p < 0.0001) or 15% of the body mass (χ2(2) = 43.676, p < 0.0001). When the carried load corresponded to 10% of the participant’s body mass, a post hoc analysis  was conducted and a Bonferroni correction was applied. We noted a significant reduction of the backpack preference rating of Backpack A compared to either Backpack B  ) or Backpack C ; meanwhile, no significant differences were found between Backpacks B and C concerning the backpack preference rating. When the carried load corresponded to 15% of the participant’s body mass, another post hoc analysis  was conducted, and a Bonferroni correction was applied. We noted a significant increase of the backpack preference rating of Backpack A compared to either Backpack B  or Backpack C  (p < 0.0001)  . In addi 0.0001) .The purpose of this study was to compare the effects of three different backpack designs on the physiological responses and subject measurements of a group of students. Backpack C distributed the carried load on the back (50% of the load) and on the sides (25% of the load on each side), Backpack B distributed it on the back and front (50% of the load on each side), and Backpack A concentrated the carried load only on the back. The results of this study showed the occurrence of significant differences in the physiological responses and backpack preference measurements of students to the three backpack designs. Fewer physiological responses  were associated with wearing Backpack C. Furthermore, the findings in this study are consistent with those of previous researches , demonstIn our study, the students preferred using Backpack C, especially when carrying loads equivalent to 15% of their body mass; meanwhile, the subjective ratings reported in  were notFurther research is required to investigate any variations in the effects of carried loads and backpack designs on both genders, as well as in relation to the transport of backpacks over different periods . A similar study considering a larger sample size may reveal significant differences between distinct school-age groups. Moreover, long-term studies are necessary for determining the long-term effect of wearing backpacks and the load-bearing effect; these would support the establishment of the guidelines for the protection of students from injuries and altered posture.The results of this study indicated significant differences in the physiological responses of a group of students to different backpack designs: Backpacks B and C resulted in a significant reduction of strains on the cardiac and respiratory systems. Additionally, the participants showed a higher preference for Backpacks B and C while carrying loads. Therefore, in order to reduce the negative effects of carrying loads for an extended period of time, we recommend the adoption of these new backpack designs. The results of this study further indicated that, when students carried loaded backpacks exceeding 10% of their body mass, their cardiorespiratory system was significantly more strained, especially while wearing the commercial backpack (A); meanwhile, the same load did not have any adverse effects on the participants while they were wearing the modified backpacks (B and C).The carried weight data of this study were collected in a laboratory environment and, therefore, implied systematic methodological limitations. One of these limitations is that only a limited number of participants could be employed in the experiment; the other is that only male participants were recruited in this study. A prospective study including female participants may elucidate the occurrence of any gender-based differences. Finally, a longitudinal study evaluating the long-term effects of the modified backpacks (B and C) on the cardiorespiratory system could help in identifying the correspondent benefits.


In the original article, we neglected to include the funder NCTN Operations Center Grant U10CA180886  St. Baldrick’s Foundation.The revised “Funding” should read:This work was supported by ARRA grant from the National Institutes of Health, by grant from the Department of Defense (AY) # W81XWH-12-1-0427, by grant from the NIH (AY) #5R01CA164132, the Lou Bridgeman Memorial Fund, the Alex’s Lemonade Stand Foundation (AY), NCTN Operations Center Grant U10CA180886  St. Baldrick’s Foundation and COG SDC grant U10CA180899.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way.The original article has been updated.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


For imaging the activity was normalized to volume and injected activity (68Ga-PSMA at 1 h). For therapy the absorbed dose was calculated for 7.3 ± 0.3 GBq 177Lu-PSMA. The effect of the investigated parameters on therapy were larger compared to imaging. For imaging, the combination of properties leading to the highest tumour uptake was kon = 0.1 L/nmol/min, koff = 0.01 min−1 for typical ligand amounts (1–10 nmol). For therapy, the higher the internalization rate, the larger was the required ligand amount for optimal tumour-to-kidney ratios. The higher the affinity, the more important was the choice of the optimal ligand amount. PBPK modelling provides insight into the pharmacokinetics of PSMA-specific ligands. Further in silico and in vivo studies are required to verify the influence of the analysed parameters.The aim of this work was to investigate the effect of ligand amount, affinity and internalization of prostate-specific membrane antigen (PSMA)-specific ligands on the activity concentrations for PET/CT imaging and on the absorbed doses for therapy. A physiologically-based pharmacokinetic (PBPK) model for PSMA-specific ligands was implemented. Thirteen virtual patients with metastatic castration-resistant prostate cancer were analysed. Simulations were performed for different combinations of association rates  Thus, ideally, theranostic agents can be used for both, imaging and therapy to minimize changes in pharmacokinetics due to different chemical structures. The prostate-specific membrane antigen (PSMA) has received increasing interest for theranostic approaches in prostate cancer4. PSMA-specific ligands are predominantly labelled with 68Ga/177Lu or 18F/177Lu for imaging and therapy5.Theranostics refers to the use of individual patient-level biological information from imaging to determine an optimal therapy for an individual patientkon and koff and the internalization rate λint influence the pharmacokinetics6. The binding affinity is described by the dissociation constant KD = koff/kon7. High affinity (i.e. low KD) is a prerequisite for imaging and therapy especially for small molecules with fast clearance8. However, it is unclear whether ligands optimized for imaging are also ideal candidates for radionuclide therapy, because of different quantities of interest (activity concentrations vs absorbed doses) and different administered ligand amounts9. Basic work on the influence of affinity and ligand amount has been conducted11. However up to now no investigation considering PSMA-targeting small molecules, internalization, different combinations of the association and dissociation rate kon and koff and various tissues for both imaging and therapy concurrently has been performed.Beside important ligand properties like molecular size or lipophilicity, the association and dissociation rate In silico investigations, e.g. by means of simulation and modelling, assist in the development and optimization of theranostics12. Computational approaches, e.g. using physiologically based pharmacokinetic (PBPK) models are important tools for the development of accurate and personalized treatments that are both cost- and time-effective12. PBPK models are increasingly used to systematically investigate pharmacokinetic parameters and absorbed doses16. PBPK models consider the individual patient biokinetics in the organs at risk (OARs) and in tumours17. Recently a whole-body PBPK model has been developed for PSMA radioligand therapy15 based on data from PET/CT imaging with 68Ga-PSMA-11 and peri-therapeutic measurements with 177Lu-PSMA I&T.λint  and dissociation constant KD values .The aim of this work was, to investigate the interconnected effect of affinity, internalization and injected ligand amount of PSMA-specific ligands using a PBPK modelling and simulation approach. For imaging the normalized activity concentrations in tumour, background, and OARs and for therapy the absorbed doses of tumours and the OARs were determined. These quantities were investigated for different combinations of ligand amounts (1–1000 nmol), internalization rates 15 was implemented in Simbiology/MATLAB . The model includes all physiologically and physically relevant mechanisms such as blood flow, plasma protein binding, PSMA-specific binding, internalization and release from the cells, excretion, and physical decay. An effective internalization rate as reported for antibody pharmacokinetic modelling19 was assumed. The number of PSMA receptors (which were estimated in previous work using PSMA-11 and PSMA I&T data) also represent effective values including all receptor subtypes.A recently published PBPK model based on data from PET/CT imaging with PSMA-11 and peri-therapeutic measurements with PSMA I&T15.The competition of labelled and unlabelled peptide (with the same affinity) is described by two separate circulation systems for binding to PSMA and by physical decay. The tumours, kidneys, liver, and the gastrointestinal tract were considered as PSMA-positive tissues. Two tumour lesions were explicitly modelled showing highest uptake and no overlap with other PSMA-positive tissues. All other tumour lesions were merged into tumour REST. The cumulated activity and volume of the tumour REST were obtained by adding all lesions slice by slice using isocontours of 15–20%. To correct the overestimation or underestimation of tumour volume, a correction factor was estimated in the fitting process16. In brief, the model parameters were fitted to time-activity data of thirteen patients including covariates such as age and body weight15. These 13 patient-individualized models  were used in this work as a basis for all simulations. The parameter distributions of the tumour were wide, e.g. total tumour volume  l, receptor densities  nmol/l, blood flows  ml/min/g. Receptor densities in tumour REST were higher and perfusion lower on average compared to the single lesions. The virtual patients account for all these differences. The institutional review board of the Technische Universität München approved all procedures and the compassionate use of 177Lu-PSMA I&T in metastatic castration-resistant prostate cancer patients who had no other therapeutic options. All procedures in this study were performed in accordance with relevant guidelines and regulations. All subjects signed a written informed consent form.For the kidney model, PSMA-specific binding, internalization, release and all mechanisms pertaining to clearance were included. Amino acids were administered to block unspecific uptake as applied in PRRT. Therefore, unspecific uptake in kidney was assumed to be low. The model, its parameters and the fitting methods are described in detail elsewhereKD values of 1, 0.1 and 0.01 nM and ligand amounts of 1–1000 nmol inr of 177Lu-PSMA. The range of the herein used association and dissociation rate kon and koff values were taken from in-house surface plasmon resonance measurements21. For example, for the ligand PSMA-617 dissociation constant KD (koff/kon) was determined to be 0.06 nM. The dissociation rate koff value of 0.0001 min−1 (not measured) was added for a more systematic investigation. Different combinations of association and dissociation rates kon and koff for the same dissociation constant KD value were investigated. To limit the number of possible combinations of association and dissociation rates kon and koff to a reasonable number, two combinations for each dissociation constant KD were investigated for 3 different internalization rate λint values  min−1 , organs at risk OARs , gastrointestinal tract and lung. The normalized activity concentrations ci (t) of each relevant organ i were calculated using (Eq. Ai(t) is the activity in organ i, A0 is the injected activity and Vi is the volume of organ i:The normalized activity concentrations without decay correction 1 h after injections of 177Lu-PSMA radioligand therapy (Activity: (7.3 ± 0.3) GBq) were calculated for therapeutically relevant organs i, i.e. the two tumour lesions, the tumour REST, the kidneys and red marrow, based on the MIRD formalism as follows:Di (T) to organ i (where T = 30000 min), the injected activity A0, the time-integrated activity coefficient i to organ i177Lu for spheres15. For bone marrow the absorbed dose calculation includes other relevant organs and tumours15.The absorbed doses of kon and koff, and internalization rates λint are presented in the supplement  increased the normalized concentration by a factor of 1.2 ± 0.3 for tumour lesions and 1.1 ± 0.1 for tumour REST using the commonly used ligand amount of 10 nmol for imaging : using 32 nmol compared to 1 nmol the normalized activity concentrations increased by a factor of 1.2 ± 0.1 for tumour lesions and 1.18 ± 0.03 for tumour REST .Tumours. Overall the effect of ligand amount (1–32 nmol) is low. However, the effect of the ligand amount is more pronounced for the dissociation constant unt Fig. . The maxKD < 1 nM with an association rate kon = 0.1 L/nmol/min the normalized activity concentrations varied considerably depending on the ligand amount. Otherwise the normalized activity concentrations in OARs and background were similar regardless of the ligand amounts (1–32 nmol)  or by increasing association rate kon from 0.01 to 0.1 min−1 (with a fixed dissociation rate koff = 0.01 L/nmol/min) led to same results: the absorbed dose in tumour increased by a factor of 1.9 ± 0.2 for tumour lesions and 1.7 ± 0.4 for tumour REST  . For affinities KD < 1 nM and with an internalization rate λin = 0.01 min−1, a ligand amount > 32 nmol is required to achieve sufficient absorbed dose in the tumour. Conversely, for the internalization rate λint = 0.0001 min−1, a higher ligand amount led to a lower absorbed dose in the tumour . The internalization rate λint only slightly affects the absorbed dose in red marrow regardless of the ligand amount ,For λint = 0.001 min−1: kon = 0.1 L/nmol/min, koff = 0.1 min−1 with ligand amount of 316 nmol (ratio of 3.8 ± 2.6 for tumour lesions and 4.9 ± 3.2 for tumour REST) andFor λint = 0.0001 min−1: kon = 0.1 L/nmol/min, koff = 0.01 min−1 with ligand amount of 100 nmol (ratio of 3.8 ± 2.6 for tumour lesions and 5.1 ± 3.3 for tumour REST).For The parameter values leading to the highest tumour-to-kidney absorbed dose ratio for different internalization rates nt Table  were:For68Ga-labeled PSMA-specific ligands are effective in the detection of prostate cancer and 177Lu-labeled ligands show great potential in the treatment of metastatic prostate cancer5. For theranostic approaches, efforts are directed to use the same molecule for imaging and therapy with different labelling. This is challenging, as the ligands must be optimized for both at the same time, high tumour activity concentration with low background for imaging and a high tumour-to-OAR absorbed doses ratio. The influence of affinity, internalization and ligand amount on these quantities was investigated in this work based on a validated PBPK model15. The influence of the total tumour volume (tumour sink effect) and normal tissue uptake might be different for varying affinities and ligand amounts22. Different release rates (factor 2) and perfusion (factor 10) of kidneys and of tumour tissue might affect imaging and therapy differently.Currently used 15. A simulation study was therefore conducted using a recently developed PBPK model15 (based on data from PSMA-11 and PSMA I&T) for dissociation constant KD values of 1, 0.1 and 0.01 nM (for each dissociation constant KD two combinations of association and dissociation rates kon and koff were investigated), different internalization rates λint  and ligand amounts (1–1000 nmol). The simulation study yielded three major findings:KD < 1 nM do not substantially increase the uptake in the tumour for commonly used ligand amounts compared to KD = 1 nM as a) a considerable fraction is accumulated in highly perfused PSMA positive normal tissue and b) within one hour post injection differences might be considerably smaller compared to later time points. Therefore higher affinity might have a stronger effect on tumour activity concentration using nuclides with longer half-lives (18F or even 64Cu).For imaging, ligands with KD considerably increases the absorbed dose in all PSMA positive tissue. The differences are the more prominent the higher the perfusion of the tissue and the lower the amount of ligand applied. Higher ligand amounts improve tumour-to-OAR absorbed dose ratios but result in lower absolute values. These results suggest that it is important to optimize the ligand amount and the pertaining activity to maximize efficacy within the dose limits of the OARs.For therapy, a decreasing kon and koff and ligand amount leading to the most favourable tumour-to-kidney ratios are:λint = 0.01 min−1: kon = 0.01 L/nmol/min, koff = 0.01 min−1 with ligand amount of 316 nmolFor λint = 0.001 min−1: kon = 0.1 L/nmol/min, koff = 0.1 min−1 with ligand amount of 316 nmolFor λint = 0.0001 min−1: kon = 0.1 L/nmol/min, koff = 0.01 min−1 with ligand amount of 100 nmolFor The simulations indicate that the combinations of association and dissociation rates A suitable method to systematically and quantitatively investigate these effects in various tissues concurrently is PBPK modellingThe optimal ligand amounts are a consequence of the more rapid saturation of highly perfused PSMA positive normal tissue where PSMA-specific binding is the dominant mechanism in our model.15) represent effective values including all receptor subtypes. In addition, complex internalization and recycling of the ligand and receptor was modelled with one single rate constant as reported for antibody pharmacokinetic modelling19. Although we have recently developed a more complex model for internalization of 68Ga-PSMA-1121, further experiments with different ligands and nuclides are required to integrate this model into the whole-body PBPK structure. The same holds true for salivary gland uptake. More experiments are required to identify the nature of the uptake mechanisms.In our model, all physiologically and physically relevant mechanisms such as perfusion, diffusion, internalization, serum protein binding, PSMA-specific binding are included. The PBPK structure is a trade-off between parsimony and biological reality. For some mechanisms and parameter values detailed knowledge is not available and thus was lumped or fitted. For example, the number of PSMA receptors (which were estimated in previous work using PSMA-11 and PSMA I&T data23. If the unspecific uptake is larger than assumed (not blocked by amino acids and not saturable for high ligand amounts) the ligand amount leading to the optimal tumour-to-kidney absorbed dose ratio will tend to be smaller.The unspecific uptake is assumed to be low given that the specific uptake affinity is high and amino acids were given to block unspecific uptake. For the kidneys, unspecific uptake is reported (and included in the model) but further research is needed to find the non-specific uptake mechanismkon of 108–109 M−1·s−17. However, simply using association rate kon from surface plasmon resonance measurements in this PBPK model might overestimate the actual binding because diffusion in the interstitial space is neglected.In the PBPK model it is assumed that the ligand which is transported over the capillary wall is instantaneously diffused and has access to binding sites. This is a good approximation for flow-limited small molecules as PSMA-11 and PSMA I&T and a maximal, diffusion-limited association rate in vivo systems is challenging. This is especially true for studies where KD is derived at equilibrium whereas in the in vivo system with rapid clearance, binding equilibrium might not be reached. Our results nevertheless confirm that the separate experimental estimation of association and dissociation rates kon and koff and internalization rate λint is important7.In general, the translation of experimental values to Incorporating further information of cell and animal experiments in this whole-body PBPK model is ongoing. In addition, for imaging the effect of using nuclides with a different half-life will be investigated.in silico. According to the simulations, association and dissociation rates that are optimal for therapy also lead to high tumour-to-background activity ratios for imaging. The results indicate that the properties of the ligands currently used are well chosen. Additionally, the simulations suggest that therapy might be considerably improved by choosing optimal activities and pertaining ligand amounts to achieve the highest tumour-to-OAR ratios. Further in silico and in vivo studies are required to verify the influence of the analysed parameters.PBPK modelling proved to be a useful method for theoretically identifying ranges of ligand properties suitable for both imaging and therapy for theranostic applications. For the first time the interplay of important pharmacokinetic parameters for PSMA-specific ligands were investigated Supplementary results


Endometrial cancer (EC) is the most common malignancy of the genital tract among women in developed countries. Recently, a molecular classification of EC has been performed providing a system that, in conjunction with histological observations, reliably improves EC classification and enhances patient management. Patient-derived xenograft models (PDX) represent nowadays a promising tool for translational research, since they closely resemble patient tumour features and retain molecular and histological features. In EC, PDX models have already been used, mainly as an individualized approach to evaluate the efficacy of novel therapies and to identify treatment-response biomarkers; however, their uses in more global or holistic approaches are still missing. As a collaborative effort within the ENITEC network, here we describe one of the most extensive EC PDX cohorts developed from primary tumour and metastasis covering all EC subtypes. Our models are histologically and molecularly characterized and represent an excellent reservoir of EC tumour samples for translational research. This review compiles the information on current methods of EC PDX generation and their utility and provides new perspectives for the exploitation of these valuable tools in order to increase the success ratio for translating results to clinical practice. Establishing suitable models is one of the cornerstones for cancer research. Among the most important and challenging are mouse models, since they have to mimic different steps of the disease and are used as tools for biomarker identification as well as preclinical models for therapy drug screening ,2. In thAs we have mentioned before, some research prefers to use tumour tissue fragments for PDX development, while other research uses a tumour cell suspension as the starting material. Each method has its advantages and disadvantages; tumour fragments retain cell–cell interactions as well as conserve tissue architecture, therefore mimicking better the tumour microenvironment. Alternatively, a single-cell suspension is a more heterogeneous sample that would represent unbiasedly the whole tumour; however, to obtain this type of sample, it is necessary to chemically or mechanically process the tissue, which affects cell viability and has the risk of decreasing engraftment success . Also, tIn summary, the main features and advantages of PDX models are: (1) preservation of the genetic profile of the primary tumour and stability along passages into several animals; (2) retention of the histological and phenotypic features of the tumour, such as its tissue architecture, and the maintenance of stromal and stem cell components, cell-to-cell interactions, and spatial distribution; (3) amplification of tumour tissue biomass to facilitate tumour biology analysis, such as tumour characterization and biomarker identification; and (4) generation of a mice cohort with the same tumour that can be used as a preclinical model to test and predict anticancer drug response .Endometrial cancer (EC) is the most common gynaecological cancer in developed countries and the sixth in mortality among all cancer types in women . The majClassically, EC has been classified into a dualistic model according to its biological, molecular, and clinical features. Type I or endometrioid endometrial carcinomas, comprising 80% of cases, are mainly represented by low-grade and hormone-receptor-positive tumours, while type II or non-endometrioid endometrial carcinomas are represented by papillary serous carcinoma, clear cell carcinoma, and carcinosarcoma, among other minor histologies, and are characterized by high-grade tumours and loss of hormone receptors ,24,25,26Recently, the Cancer Genome Atlas Network (TCGA) performed an integrated genomic, transcriptomic, and proteomic analysis focusing on endometrioid EC and serous histologies, demonstrating that EC is a heterogenic disease. The TCGA identified and classified EC into four distinct molecular subgroups: POLE ultramutated (DNA polymerase epsilon), microsatellite instability hyper mutated, copy-number-low microsatellite stable, and copy-number-high serous-like . InteresConsidering that, researchers and clinicians are now enthusiastic and believe that a combination of both classification systems would be promising to precisely classify EC, thus improving the management of EC patients. However, the road to an ideal scenario should still be paved with a deeper understanding of the ability to predict treatment-response and with an increased variety of effective therapeutic options for the different types of EC. Moreover, inter and intra-tumour genetic heterogeneity represents a challenge that should be faced in the current classification systems as this might have implications for the response to standardized or personalized treatments . In thisEven though PDX development is widely described ,30, seveCabrera et al. was the first to describe the development of orthotopic PDX models using human EC tumour tissue . To deveSimilarly, Haldorsen et al.  reportedLater on, Depreeuw et al.  developeOn the other hand, Unno et al.  establisRecently, Pauli et al.  describeThe ability to monitor disease development is one of the major challenges when using mouse models. Tumour xenografts growing subcutaneously could be followed simply by visual inspection or palpation; however, the monitoring of orthotopic tumour xenografts requires the utilization of imaging techniques to follow-up tumour progression. In this section, we will summarize the most commonly used in vivo imaging techniques that are currently available to monitor tumour growth in PDX models. A full description of these techniques is reviewed by Dall’Ara et al. .Micro-computed tomography is a high image resolution technique with great potential for in vivo use since it could be coupled with other imaging modalities providing three-dimensional (3D) reconstruction of bone and soft tissue. It has been used to study bone metastases  in mice Magnetic resonance imaging (MRI) also offers in-vivo, non-invasive, 3D, and high-resolution images. In recent years, MRI has gained great importance due to the absence of ionizing radiation and its soft tissue contrast. Hence, MRI is used not only for its ability to define lesions with great spatial resolution but also to recover quantitative features that might be able to predict cancer progression.Positron emission tomography (PET) is a highly sensitive and specific imaging technique used to visualize the distribution and concentration of radiolabelled molecules injected into murine models. It is a form of quantitative whole-body imaging used for the in vivo monitoring of biological processes, such as enzymatic reactions, cellular metabolism, and cell proliferation and migration , which mSingle-Photon Emission Computed Tomography is a technique that detects gamma radiation directly emitted by a radionuclide during decay and provides 3D information by acquiring multiple two-dimensional (2D) images while rotating around the imaged object. This technique is frequently used in oncology to visualize neuroendocrine tumours  and thyrUltrasound is an ideal technique for detecting tumour growth in mice since it produces high-resolution images of small structures. It is a non-ionizing radiation technique, portable, easy to use, and quickly generates relevant images.Intravital microscopy is an optical imaging technique that enables highly sensitive in vivo imaging of tissue structure and function at high spatial resolution (cellular and sub-cellular) and temporal resolution. However, a surgical procedure is required to access the tissue/organ of interest for microscopy, having therefore the consequence that immediately after image acquisition the animal must be sacrificed. Intravital microscopy has been reported to be used in studies involving a metastatic process ,47 and tWhole-body optical imaging is a sensitive technique based on fluorochromes excitation by an external light source (fluorescence) or by chemiluminescent enzymatic light emission reactions within the animal (bioluminescence). Despite the poor spatial resolution due to light scattering, this technique enables the integration of the light signal emitted to obtain a 2D planar image. Green fluorescence protein (GFP) has been widely used to measure in vivo tumour growth as well as the effect of metastatic spread and drug treatments on different types of cancer in mouse models ,51.Recently, Haldorsen et al.  describeIn a collaborative effort within the ENITEC consortium, we here describe in detail the PDX mouse cohort developed by the groups in Katholieke Universiteit (KU) Leuven, Haukeland University Hospital Bergen (HUHB), the Institute of biomedical research from Bellvitge–Institute Catalan of Oncology (IDIBELL-ICO), and the Vall d’Hebron Institute of Research (VHIR) in order to compile the information on EC PDX models available within this network. Altogether, we have generated a stable cohort of PDX models from primary tumour and metastasis from 124 EC patients recruited in different centres across Europe. This represents one of the most extensive and best-characterized EC PDX model cohorts available for research and is continuously increasing since we are generating new models from EC patients .We have developed a heterogenous population of PDX covering almost every stage and grade of both EC histological subtypes. In particular, we have 63 endometrioid and 56 non-endometrioid EC PDX models, in which serous and carcinosarcoma histologies are the best represented with 22 and 19 models, respectively. Regarding staging, 62% of the endometrioid EC PDX models are represented by FIGO stage I and classified according to Morice et al.  as low tOur PDX cohort was developed both by heterotopic transplantation of fresh tumour tissue fragments recollected from a surgery room and implanted subcutaneously into athymic nude mice and by orthotopic implantation throughout a laparotomic incision. The engraftment rate of subcutaneous EC PDX varied from 60–80%; however, once the tumour was developed, the engraftment rate increased to nearly 100% in subsequent passages. In addition, PDX models take approximately 3–5 months to engraft and develop the first generation, while subsequent passages take less time to engraft and progress. In contrast, the orthotopic PDX model engraftment rate varies from 75–90% and also takes 2–5 months to develop a palpable and transferable tumour. Additionally, a small cohort of five tumours from EC patients was also injected orthotopically into the left uterine horn of NSG mice. In this case, a primary tumour sample is manually dissociated, filtered, and centrifugated and then a cell suspension is injected by laparotomy in a 1:1 proportion with Matrigel . For thiAll of our models have been histologically characterized by H&E staining . Single-Personalized medicine refers to the discipline focused on treating patients individually with molecular-targeted therapies directed against the altered pathways of their own tumour. This is expected to maximize treatment efficacy and minimize side effects . Based oIn EC, the PI3K/AKT pathway is constitutively active due to mutations, and so this pathway has been an attractive target for therapy in different EC preclinical studies. Winder et al. tested the effect of MK2206, an allosteric inhibitor of AKT, on the growth and invasion of three EC PDX models grafted under the renal capsule of NSG mice. They found that MK2206 treatment inhibited tumour growth as well as decreased invasion into the kidney and spread throughout the peritoneum in the three different types of PDX  . SimilarPten deficiency. This work started with the assessment of palbociclib response in vitro and in a PTEN-deficient GEM model and was finally validated in a PTEN-mutated PDX model of endometrioid EC of FIGO stage IIIC and grade 2. This work evidenced that palbociclib has therapeutic potential as an anticancer drug in the endometrium, since it reduces tumour cell proliferation and disrupts the tumourigenesis process [The use of palbociclib against the cyclin-dependent kinases CDK4 and CDK6 has successfully been used in advanced breast cancer  and it i process .Similarly, Dupreeuw et al.  tested tAll of the above-mentioned studies shared a similar approach to evaluating the efficacy of targeted therapies in EC: all of them relied on the use of PDX to validate a specific treatment which was first assessed in one or more in vitro and/or in vivo models. Moreover, PDX models could also be used to identify pathways responsible for therapy-resistant mechanisms and to identify new approaches to overcome any acquired resistance in EC tumours. Sorafenib, an antiangiogenic drug, has been proposed as a promising targeted therapy for EC, but a multicentre phase II clinical trial demonstrated moderate effects. In a recent work, Eritja et al.  studied HER2 inhibition in serous non-endometrioid EC. The combination of in vitro and in vivo cell-line and PDX models permitted the authors to demonstrate that lapatinib as a single agent and in combination with trastuzumab induced significant tumourstatic effects only in those tumours harboring HER2 gene amplification. In the non-amplified tumour xenografts, a complete lack of response to any administered therapy was seen. Thus, this study unveiled that HER2 gene amplification might be used a biomarker for response to HER2 inhibition in uterine serous carcinoma, as has been shown in breast and gastric carcinomas. Similarly, in another study published by Groeneweg et al. [Equally important is the discovery of biomarkers to predict treatment-response, as this will help to tailor the treatment of EC patients. In this field, Groeneweg et al.  investigg et al. , they deBased on these data, EC PDX models are currently playing an important role in defining new therapeutic options for the different EC subtypes and helping in the selection of populations of patients most likely to be sensitive to a new agent. However, all the studies performed up to date only include from a single to a few EC PDX models; thus, the results are hard to translate into larger populations.There exist interesting avenues for the exploitation of PDX models, which have been explored in other types of cancers but not in the field of EC research. A co-clinical trial is a concept, similar to personalized PDX models, which is based on the development of a PDX from a patient enrolled in a clinical trial and treated in the same way as the patient ,64. ThisAnother interesting approach is the use of PDX panels for preclinical studies as opposed to the traditional methods of assessing drugs in just a few models ,66. ThisMigliardi et al.  was the At present, the cost and resources needed for PDX development and maintenance are a limiting factor for many researchers in order to develop their own models. For this reason, to facilitate working with PDX models, accessible collaborative networks between academic research groups have been established that closely cooperate with the clinic in order to associate preclinical experimentation and clinical activities. Such networks include the EurOPDX Consortium, the U.S. National Cancer Institute (NCI) repository of patient-derived models, the U.S. Pediatric Preclinical Testing Consortium (PPTC), the Children’s Oncology Group (COG) cell culture and xenograft repository, the Public Repository of Xenografts (PRoXe), and the Novartis Institutes for Biomedical Research PDX Encyclopedia (NIBR PDXE) . Some ofBesides academic collaborations, commercial companies have also started to provide PDX models, such as The Jackson Laboratory , Xenopat , CrownBio , Oncotest GmbH , AVEO Oncology , Living Tumour Laboratory , Urolead , Experimental Pharmacology & Oncology Berlin-Buch GmbH , and XenTech  .Although EC PDX models have been established for almost a decade, there are still several challenges that should be faced in the near future. First, immunocompromised mice are used so as to not reject human tumour, meaning that immunologically related aspects cannot be taken into account. Next, human stroma in mice is replaced by murine stroma over different generations. This has been shown for different types of tumours, but also more specifically for EC . Both imTo overcome the lack of tumour microenvironment and immune cell interaction, humanized mice can be used . HumanizOver the last few decades, there has been increasing interest in developing more realistic and clinically relevant mouse models. In this context, PDX emerges as a promising preclinical mouse model mainly because it faithfully retains patient tumour characteristics and behaviour. Importantly, EC PDX models have already been used in an individualized approach to evaluate the efficacy of novel therapies and to identify biomarkers to predict treatment-response. Together with the advances of omics techniques, which allow us to increase our understanding of the molecular alterations of EC tumours and dysregulated EC pathways, EC PDX models are now an untapped source to improve the definition, consecution, and output of preclinical studies to increase the success ratio in further clinical phases. In this review, we compiled the information on EC PDX models that have been described in the literature and highlight the models that have been generated in the ENITEC consortium, from their generation to their use, and identify new perspectives and limitations of those models.


Varicella-zoster virus (VZV) has been known to cause various eye disorders in both immunocompetent and immunocompromised patients. We present a case of a forty-nine-year-old female patient with acquired immunodeficiency syndrome (AIDS) who presented with headache, fever, and blurred vision. Cerebrospinal fluid (CSF) analysis was consistent with VZV meningitis. Magnetic resonance imaging (MRI) of the brain showed enhancement of the right optic nerve indicative of optic neuritis. She responded well to acyclovir and steroids and discharged on the same. Four weeks after discharge, she presented with sudden onset blindness in the left eye. A cerebral angiogram revealed left retinal artery occlusion and was treated with tissue plasminogen activator (tPA). Funduscopic examination showed patchy areas of necrosis in the periphery which were rapidly progressive, diagnostic of posterior outer retinal necrosis (PORN). She was started on ganciclovir and cidofovir and experienced significant improvement in her visual acuity. VZV is one of the most common pathogens affecting the eyes in patients with human immunodeficiency virus (HIV). Initially, it was thought to be a harbinger of AIDS, but now it is being increasingly recognized in every stage of AIDS. VZV can cause a myriad of neurological and ophthalmological complications including meningitis, retinitis, optic neuritis, and retinal artery occlusion . PORN waWe present a case of VZV meningitis, optic neuritis preceding the development of PORN, and CRAO in a HIV patient. To our knowledge, this is the first case of all these rare complications affecting the same patient.A 49-year-old African American female patient with a history of untreated HIV infection presented to the emergency room with a two-week history of left ear pain, headache, fever, and blurred vision. Physical exam was significant for crusted vesicles in the left ear and a vesicular skin rash on the left side of the face consistent with herpes zoster. Ophthalmic examination showed normal visual acuity (VA) in the left eye. VA in the right eye was decreased to 20/100 and an afferent pupillary defect in the right eye was also observed. The fundoscopic examination was unremarkable bilaterally. CSF analysis revealed lymphocytosis consistent with viral meningitis. VZV polymerase chain reaction (PCR) was positive confirming VZV meningitis. She was started on intravenous acyclovir . MRI of Four weeks later, the patient presented to the emergency room with sudden painless loss of vision in her left eye. A cerebral angiogram revealed stenosis of the left ophthalmic artery. tPA was administered which resulted in an improvement in her visual acuity from 20/400 to 20/100 in her left eye. She was started on acyclovir and steroids. Fundoscopic examination revealed the progression of the necrosis ultimately involving the whole retina see . FluoresThe patient responded well to the antiretroviral treatment, her CD4 count six months later was 317 cells/cubic milliliter, and her viral load decreased to 50 copies/ml. Her visual acuity after one year showed significant improvement to 20/40 bilaterally.VZV is a DNA virus belonging to the herpes virus family. Primary infection with VZV results in varicella while secondary reactivation results in herpes zoster. Complications of VZV infection can occur in both the immune competent and immune compromised patients. However, it has been observed that involvement of multiple cranial or cervical dermatomes, extensive skin involvement, and severe pain occur more frequently in the immune compromised population , 6.Herpes zoster ophthalmicus is due to reactivation of the virus in trigeminal ganglion and can result in a variety of ocular manifestations  7]. Opt. Opt7]. VZV retinitis comprises two different entities, acute retinal necrosis (ARN) and PORN. ARN can occur in both immunocompetent and immunocompromised persons and is characterized by vitiris, choroidal vasculitis, and full-thickness retinal necrosis starting peripherally. PORN is seen only in immunocompromised persons and is characterized by multifocal retinal necrosis without granular borders in the deeper retinal layers which start peripherally and rapidly involved the whole retina. PORN is usually seen in severely immunocompromised patients with AIDS and can be confirmed by performing a VZV PCR on the intravitreal fluid . OrmerodRetinal artery occlusion secondary to herpes zoster has been described in nine instances in the literature. The age range of these patients varied between 58 and 77 years, and the incubation period varied between five weeks to two years. The mechanism is similar to herpes zoster associated cerebrovascular accidents, through the formation of granulomatous angiitis. Studies have shown zoster viral particles in the media of the arteries in postmortem biopsies. It has been proposed that the virus travels from the trigeminal ganglion travels to the internal carotid artery and its branches via the sympathetic nerves and can cause CRAO .Franco-Paredes et al. have described eight cases of VZV retrobulbar optic neuritis preceding retinitis in AIDS patients (1). Due to the rarity of these cases, the natural history is not well understood. Steroid use for the treatment of optic neuritis has been implicated in the development of subsequent retinitis .Based on the timeline of development of symptoms in our patient, we suspect that she had viral meningitis and subsequently went on to develop a right optic neuritis (optic nerve), left CRAO , and bilateral PORN (retina) in a contiguous manner. Another plausible explanation is that of the virus causing vasculitis of the posterior ciliary artery and retinal vasculature. CRAO developing approximately a month later after the initiation of HAART  could also be a manifestation of immune reconstitution syndrome. We believe that prompt administration of HAART, aggressive management of CRAO, and administration of both systemic and intraocular ganciclovir and systemic cidofovir were factors responsible for the good visual recovery in our patients. Therefore, we recommend considering therapeutic interventions even in patients with almost complete visual loss.VZV infection can be seen in every stage of HIV. Reactivation of VZV in the trigeminal ganglion can lead to the various ophthalmological manifestations.Sudden onset visual loss in HIV patients could be secondary to optic neuritis, retinitis, or retinal artery occlusion.Optic neuritis is typically seen after herpes zoster skin infection. Clinically, it manifests as loss of visual acuity and afferent pupillary defect. It has been known to precede PORN.PORN occurs in severely immunocompromised patients and is rapidly progressive. It is characterized by rapidly progressive lesions and has an extremely poor prognosis.Retinal artery occlusion can be seen in association with VZV and could be due to either direct invasion or granulomatous angiitis of the arterial wall.Prompt administration of HAART, aggressive management of retinal artery occlusion, and administration of both systemic and intraocular ganciclovir and systemic cidofovir were factors responsible for the good visual recovery in our patient. Therefore, we suggest that even patients with almost complete visual loss should get therapeutic interventions.


Concomitant radiotherapy with immune checkpoint blockade could be synergistic. Out-of-field effects could improve survival by slowing or blocking metastatic spreading. However, not much is known about the optimal size per fraction and inter-fraction time in that new context.The new concept of Immunologically Effective Dose (IED) is proposed: it models an intrinsic immunogenicity of radiotherapy schedules, i.e. the fraction of immunogenicity that results from the choice of the dosing regimen. The IED is defined as the single dose, given in infinitely low dose rate, that produces the same amount of abscopal response as the radiation schedule being considered. The IED uses the classic parameters of the BED formula and adds two parameters for immunogenicity that describe the local availability of immune effectors within the tumor micro-environment. Fundamentally, the IED adds a time dimension in the BED formula and describes an intrinsic immunogenicity level for radiotherapy.The IED is positively related to the intensity of the out-of-field, radiotherapy-mediated, immune effects described in some preclinical data. Examples of numerical simulations are given for various schedules. A web-based calculator is freely available.Out-of-field effects of radiotherapy with immune checkpoint blockers might be better predicted and eventually, radiotherapy schedules with better local and systemic immunogenicity could be proposed.A model for the intrinsic level of immunogenicity of radiotherapy schedules, referred to as the Immunologically Effective Dose (IED), that is independent of the type of immunotherapy. The abscopal effect of radiotherapy describes a rarely observed phenomenon in which one or more metastases located out of the irradiation field regress at some point in time after radiotherapy . DescribThe out-of-field mechanism could initially involve an in-field recruitment of dendritic cells (DC) and other types of Antigen Presenting Cells (APC) in the tumour micro-environment, attracted by radiation-induced inflammation and necrosis. However, these immune effectors have a strong radio-sensitivity: lymphocytes are among the most radiosensitive cells within the body , the average growth delay of the 3 x 8 Gy schedule was 166% of that of the 5 x 6 Gy schedule. Since these two schedules have almost identical EQD2 and BED, the difference in the average out-of-field response, if it is not caused by randomness, can’t be explained by classic radiobiology models alone.is more than twice the IED Efficacy of the 5 x 6 Gy: apparently, it seems strongly associated with the intensity of the out-of-field response. Numerical values are shown in Table Interestingly, the IED Efficacy of 3 x 8 Gy D  and TIR . This can be verified with the online IED calculator: www.smartcalculators.online/ied.Remark 1: this association persists when using a more radiosensitive tumour with α = 0.35 or with varying values of α / β, or with different values of TRemark 2: the definition of EQD2 is standard, i.e. it is the total dose in Gy, that would produce the same cell kill as the schedule of interest, if it was administered in 2 Gy fractions (assuming a linear-quadratic model for cell kill).D) or with long inter-fraction time (> TD + TIR), but this availability is sharply decreased for intermediary inter-fraction values. This is illustrated on Figure The interfraction time is a key factor for the local availability of intra-tumour immune effectors; with the IED model, this availability is increased either with a short inter-fraction time , and greater values for the two hybrid schedules (28% and 67%). These values can be obtained by using the online calculator at The clear positive relationship between IED Efficacy and the intensity of the out-of-field response observed with the data published in  is a strThe model prediction that normofractionated schedules should have lower immunogenicity than shorter schedules with higher doses per fraction seems coherent with some pre-clinical data , 8]. Ho. Ho8]. Hlocal availability of immune effectors inside the tumor micro-environment should be the main driver of anti-tumour immunity for immuno-radiotherapy, which is an idea at the core of the mechanistic approach of this model.The impact of interfraction time is consistent with pre-clinical data that have explored the dynamics of immune-infiltration in the tumor micro-environment after irradiation, such as Frey & al. : with a D and TIR, whose signification is clear, since they control the speed of post-radiotherapy necrosis (TD) and the speed of immune infiltration (TIR) within the TME. Furthermore, thanks to a free access through an online calculator, there is no need to understand the fine details of the formula or to use a mathematical software.The IED model uses only two new “time” parameters TD = 3 days is subject to caution, even though its order of magnitude is in line with some pre-clinical experiments ) sIR: colder (resp. hotter) environment could be associated with higher  values of TIR.Finally, it is undeniable that predicting abscopal response is a difficult task, since it should depend on many parameters that may be patient-, organ-, tumour- or immunotherapy-specific. The IED model should not be misinterpreted as a tentative to replace this multi-dimensional problem by the computation of just one indicator. To give an obvious example, the radiotherapist understands that irradiating a 20g-tumour volume should produce more immune stimulation than the irradiation of a 2g-tumour, all other things being equal. A long list of other confounding factors could be made, whose influence is not in the scope of the proposed model, such as the immune status of the underlying tumor micro-environment (“hot” vs “cold” environment), the intrinsic efficacy of the concomitant immunotherapy, etc. Some of these factors might be added as covariates in the model, especially the state of the tumor micro-environment that could be described with the value of the time parameter TBut even in its simplest form with fixed parameters and no covariate, the IED formula provides a quick rule-of-thumb to assess the relevance of fractionation (from the standpoint of immunogenicity) and, on occasion, avoid the choice of under-performing schedules.In the model, the radiotherapy-mediated anti-tumour immune response is proportional to the fraction of tumour cells killed by irradiation, whose content has been processed by immune effectors before the next irradiation. Hence, depending on the interfraction time, the number of killed tumour cells that contribute to the immune response may be significantly smaller than the total cell kill predicted by the BED.More precisely, each radiation dose kills a certain number of cells, with a surviving fraction described by the two parameters  of a classic linear-quadratic model . Then, lD controls the speed of this antigen release: 50% of the tumour antigens are released after a time TD  controls the speed of this second process: 50% of completion is attained after a time TIR, following tumour antigen release . The IED is interpreted as a measure of the intrinsic contribution of the dosing schedule to immunogenicity.The direct solving of this equation yields a unique IED for any radiotherapy schedule, which is only defined by the dosing schedule and the choice of the radio-sensitivity parameters  and of the parameters that controls the immune response dynamics i-1, the fraction of surviving tumour cells available just before the ith radiation dose, where • Θ is an N by N matrix where: f and g are detailed in Figure •K is a N-by-1 vector whose components are equal to kD;With the above assumptions, for N equal radiation doses of D Gy given at times TE = S Θ K is:For example, with N = 3 doses, Finally, IED is obtained by solving E is named IED Efficacy; it represents the % of tumor volume that is converted into “immunogenic” antigens, hence it is easier to interpret than the crude IED number.The sum of the components of θij coefficients are computed numerically .The θij represents the fraction of immunogenic antigens produced by tumour cells killed by the ith radiation at time Ti but released later between the times Tj and Tj+1; g(x) is the rate of release of tumour antigens per unit of time, after one irradiation (at x = 0); f(x) is the completion rate of the immune activation triggered by the release (at x = 0) of tumour antigens, hence it is a positive number smaller than one. The parameters TD and TIR control the speed of each phenomenon.The integral Θ depends only on the timing of radiation doses and on the time parameters , whereas the vector K and the matrix S depend upon the size of the dose per fraction and the radio-sensitivity parameters .Hence, the matrix E = S Θ K, it is obvious that initial radiation doses contribute to the most part of immunogenic tumour antigens, because of the geometric decrease of the components of S.From The Immunologically Effective Dose (IED) model complements the classic linear-quadratic formula by considering the dynamics of the immune infiltration within the tumor micro-environment. Then, it produces forecasts about the impacts of various radiotherapy schedules on the anti-tumor immune response.Understanding the result of the IED model is easy with the IED Efficacy, which is the percentage of tumour volume that gives “immunogenic” tumour antigens: the closest to one, the better.www.smartcalculators.online/ied. Two parameters are needed: TD and TIR, in addition to the classic parameters  of the linear-quadratic model.Obtaining the IED Efficacy of any radiotherapy schedule can be done with an online calculator that is freely available at It is not recommended to use the model with doses per fraction above 10 Gy, however, an ad-hoc adjustment parameter may be used if necessary.With the IED algorithm, new radiotherapy schedules could be investigated in-silico, before being confirmed by preclinical data or clinical trials.However, the validation of the model on more pre-clinical or clinical data is the next major step.