Understanding untreated tumour growth kinetics and its intrinsic behaviour is interesting and intriguing. The aim of this study is to propose an approximate analytical expression that allows us to simulate changes in surface charge density at the cancer-surrounding healthy tissue interface during the untreated solid tumour growth. For this, the Gompertz and Poisson equations are used. Simulations reveal that the unperturbed solid tumour growth is closely related to changes in the surface charge density over time between the tumour and the surrounding healthy tissue. Furthermore, the unperturbed solid tumour growth is governed by temporal changes in this surface charge density. It is concluded that results corroborate the correspondence between the electrical and physiological parameters in the untreated cancer, which may have an essential role in its growth, progression, metastasis and protection against immune system attack and anti-cancer therapies. In addition, the knowledge of surface charge density changes at the cancer-surrounding healthy tissue interface may be relevant when redesigning the molecules in chemotherapy and immunotherapy taking into account their polarities. This can also be true in the design of completely novel therapies. SeverThe electrical properties and active bioelectricity inherent in cancer and surrounding healthy tissue are experimentally confirmed by means of several techniques, such as: bioelectrical impedance analysis , image tkη, k = 1,2) and electrical permittivities  of the untreated malignant tumour (k = 1) and the surrounding healthy tissue (k = 2) [Several findings have been revealed, such as: 1) differences between electrical conductivities ( (k = 2) ; (2) the (k = 2) ; (3) dif (k = 2) ; 4) the differen the diff (k = 2)  and thei (k = 2) ; (5) the (k = 2) ; (6) the (k = 2) ,18; (7)  (k = 2) –14; (8) Vmem), shape change, pH, heterogeneity, phenotype, metabolism abnormalities, growth signalling, proliferation, tumourigenesis, angiogenesis, invasion and metastasis of the cancer cells, as well as in the plasticity, heterogeneity and cellular networks of cancer [The uneven movement of ions and electrons across the plasma membrane via ion pumps modifies the imbalance of the charge between the intra- and extracellular compartments. This ionic imbalance, gene expression level, glutamate-dependent currents and both ionic and faradic currents explain the active cancer bioelectricity . Furtherf cancer ,16,19–22f cancer . The canf cancer .Biological processes form bioelectric circuits from individual cell behaviours and anatomical information encoded in bioelectrical states to achieve a better control over spatio-temporal biological patterns. Electrically active cancer cells possess bioelectric circuitry that generates resting membrane potential and endogenous electric fields that influence cell functions and communication ,23. EndoVmem are involved in high proliferation (due to the depolarization of their membranes by higher intracellular concentration of sodium ions) and mitosis, depletion of adenosine triphosphate, failure of ionic pumps at the cellular membrane and mechanism of contact inhibition of cancer cells. A depolarized membrane is considered a driving force for the production of Ca2+ and bioelectronic cancer regulator that affect proliferation, migration, invasion and metastasis of cancer cells [Vmem are related to the modulation of local concentrations of signalling molecules and ions, the spatio-temporal regulation of morphogenesis, the interaction with heterogeneous networks  is controlled by spatio-temporal bioelectrical patterns based on electric potentials and currents from steady and oscillatory multicellular states, among others. In turn, these spatio-temporal bioelectrical patterns influence the spatiotemporal distributions of signalling ions and molecules that modulate biochemical pathways in cancer cells, and therefore in growth and regeneration [Alterations in er cells ,12–14. Fneration ,9,25.Vmem may be regulated in different ways, such as: the ion channel expression, the ionic composition of the extracellular environment, and the presence of bioelectronic gradients within cancer [et al. [Vmem should be analysed in two directions: Vmem effect on the cellular function (that contributes to the cancer phenotype) and how Vmem is affected (by the expression of voltage-gated ion channels and cell metabolism). Alterations in the metabolism of cancer cells modify Vmem [n cancer ,20. Therify Vmem ,15,26. Bify Vmem ,26.Σ. This should be taken into consideration because both tissue types have different electrical properties and bioelectrical activities. Therefore, understanding of the bioelectricity in cancer and surrounding healthy tissue constitutes a challenge for researchers.The above-mentioned results corroborate the close relationship between biological and electrical parameters in tissues. Likewise, it confirms that the bioelectrical activity in all cell types (e.g. cancer) is involved in many physiological mechanisms. Nevertheless, bioelectrical pathways are still poorly understood in cancer cells, TGK and σ12) is expected at Σ for the following reasons: firstly, solid tumours have chemical and electrical environments [σ12 is due to synergism between an external volumetric current density (the source of electricity) and the Maxwell-Wagner-Sillars interfacial polarization. The Maxwell-Wagner-Sillars effect is an interfacial relaxation process that occurs for all two-phase multi-systems, in which the electric current must pass an interface between two different loss dielectrics [Σ mainly) is higher than that in the surrounding healthy tissue [It is documented in electrodynamics of media that a surface charge density arises at the interface between two materials in contact with different electrical properties . Thereforonments ,14. Secoronments . Thirdlyronments ,14,29,30ronments ,14. Fourlectrics ,31,32. Ly tissue ,9,14,33.σ12 has been measured in many biological and non-biological heterogeneous materials by means of the surface photovoltage effect, the vibrating probe technique, electrostatic force microscopy, among others [σ12 at Σ has not been experimentally measured nor calculated theoretically in cancer. Estimation of σ12 at Σ presupposes the experimental knowledge of normal components of the flux density vector on both sides of Σ, a procedure that is cumbersome and expensive (in time and resources) in preclinical and clinical studies. Furthermore, an analysis of TGK in terms of kη, kε  and σ12 has not been reported in the literature. σ12 is ignored and cannot be estimated from the vast experimental data available. The aforementioned are the aspects we mainly take into consideration for using the physic-mathematical modelling in our research. Therefore, the aim of this study is to propose an approximate analytical expression that allows us to simulate σ12 at Σ during the untreated tumour growth, in terms of two tumour kinetic parameters, tumour radius and electrical properties of the tumour and its surrounding healthy tissue.g others ,35. Neve. 2. 2.1 1.Σ  is considered as a heterogeneous conducting sphere of radius RT (in m) of constant mean conductivity  and mean permittivity . The surrounding healthy tissue  is supposed to be a heterogeneous infinite medium of constant mean conductivity  and mean permittivity , where η1 > η2 and ε1 > ε2.There is a three-dimensional, conductive, anisotropic and heterogeneous region consisting of two linear, anisotropic and heterogeneous media  separated by an interface Σ . Untreat 2.The source of electricity is neglected because the tumour is unperturbed. 3.Maxwell-Wagner-Sillars effect occurs physiologically between the tumour and the surrounding healthy tissue (see Introduction section). 4.Ef ) depends only on the distance to the tumour centre.In a first approximation, the electromotive force field ( 5.Σ do not significantly contribute to (Ef ).Normal and cancer cells that are at . 2.2η1,η2,η3), where η1, η2 and η3 are electrical conductivities according to these main axes. If these diagonal elements are replaced by their mean value, named η (η = (η1 + η2 + η3)/3) in this approximation, the tensor ηI, where I is the identity matrix of order 3, as in [ε.The first assumption may be approached from the physical point of view. As solid tumour and surrounding healthy tissue are anisotropic and heterogeneous media  ,29,30, wη1 > η2 and ε1 > ε2 have been explained because malignant tumours have a significantly higher water content, higher concentrations of ions and electrons, and altered cellular metabolism compared to those in the surrounding healthy tissue [Although cancer and surrounding healthy tissue are heterogeneous and anisotropic media, most experimental studies report their respective average values of  tensors ,29,36,37y tissue ,16,19,38Σ is the tumour-free margin, according to pathological anatomy reports. This ensures that there is no infiltration of the tumour into the surrounding healthy tissue and there are two well-defined regions instead. In addition, the geometry and border of the tumour (regular or irregular) have no relevance for this tumour-free margin; therefore, the tumour contour may be assumed regular, sharp and smooth. It should be noted that Σ is not chosen as the surgical margin because it does not guarantee that the tumour has infiltrated adjacent normal tissue [Tumour borders play a crucial role in growth, metastasis, aggressiveness and anti-cancer therapy planning ,4,38. Lol tissue .The term ‘infinite healthy tissue’ does not mean an unlimited space but rather refers to an enormous healthy tissue (the limited region free of infiltration and metastasis of cancer cells) in comparison to the tumour.in vitro and in vivo studies). That is why tissue realistic conditions are not considered in this study.A standard pattern of three-dimensional anatomically realistic models  is very unlikely to be established in simulations because it requires precise knowledge of the electric properties  and physiologic characteristics  of both tissues. This becomes even more cumbersome when other characteristics of the tumour are taken into account, such as: histological variety, stage, stiffness, mitotic index, degree of anaplasia, invasiveness and metastasis. In addition, our vast experience in preclinical studies has shown differences in space–time patterns of a same tumour histological variety that grows in several BALB/c/Cenp mice under the same experimental conditions  ,2,4. Thi3) [in vitro models) have been used in cancer research as an intermediate model between in vitro cancer cell line cultures and in vivo tumour. These models have gained popularity in screening environments for better assessment and characterization of anti-cancer therapy efficacy , and identifying potential cancer therapeutics, among others applications. Chemoresistance and radioresistance of cancer may be more marked in spherical tumours than those in non-spherical tumours, according to the results of the simulations reported by Castañeda et al. [in vivo solid tumours and drug screening platforms. Tumour spheroids may contribute to decreased animal experimentation [σ12 at Σ from both experimental and theoretical points of view (unknown effects of the irregular border and changes in σ12 at Σ) are the reasons why we use the tumour spherical shape and symmetry to know σ12 at Σ approximately.The tumour spherical geometry is observed in three-dimensional culture ,42 and f3) ,2,4. Spha et al. , and theentation ,42. The Ef  are neither experimentally nor theoretically known. In this study, Ef  represents the active bioelectricity of unperturbed cancer and due to endogenous electrical biopotentials (ϕ) and/or intrinsic electrical sources in it [et al. [ϕ along axial (z-axis) and radial (r-axis) directions in two tumour types (LLC and fibrosarcoma Sa-1). They report several findings, such as: ϕ is negative in the entire tumour; ϕ is more electronegative in the tumour centre (−160 mV for LLC tumour and −131.5 mV for fibrosarcoma Sa-1); electronegative of ϕ is less negative towards the periphery in LLC and fibrosarcoma Sa-1 tumours; and values of ϕ depend on distance (from tumour centre to its periphery) and not on angular coordinates. It is important to point out that ϕ should not be confused with the electric potential applied to a tissue by means of electrodes [Until now, space–time distributions of es in it –16,19–26 [et al.  measure ectrodes . These aΣ invade the surrounding healthy tissue and do not migrate to the tumour interior. As a result, these cells do not contribute to Ef . As Ef  is only related to the unperturbed cancer active bioelectricity, normal cells at Σ do not contribute to Ef . In addition, normal cells at Σ are replaced in cancer cells during tumour growth. These aspects justify the fifth assumption.Although the tumour border is a marginal zone that contains tumour cells and normal cells from a clinical point of view, cancer cells at . 2.3ϕ and Ef  are related, in a first approximation, by means of the equationThe assumptions in §2.1 and the close relationship between physical and biological aspects in cancer allow us to consider that  studies ,30.Equation (2.1) is obtained by combining the continuity equation D is the induction field (flux density vector). Taking this into account, and assuming that the medium is electrically homogeneous, equation (2.1) has the formAssumptions 2–5 in §2.1 allow us to consider that Therefore,. 2.4η1 and ε1) surrounded by the surrounding healthy tissue , as shown in The region of interest is assumed as a heterogeneous biological tissue formed by the solid tumour  and the surrounding healthy tissue (Jn2) are continuous at ΣAccording to the continuity equation for the static case, the current density normal components of the tumour . The positive normal to the tumour surface is indicated as a unit vector n  drawn from the surrounding healthy tissue (medium 2) into the tumour (medium 1). According to this convention, medium 2 lay on the negative side (n 2 = −n), and medium 1 on the positive side (n 1 = n). Taking this into account as well as the matching boundary condition for D, σ12 the expressionDn1 and Dn2 are the normal components of the flux density vector D in the tumour and the surrounding healthy tissue, respectively.Equation (2.4) is valid if . 2.5ϕ and ∂ϕ/∂nStrictly speaking, the problem to be solved for the calculation of the electric potential is equation (2.3) subject to the matching boundary conditions for ϕ at Σ may be experimentally measured, conditions that may be replaced by a condition of Dirichlet and the work region is only inside the spherical tumour, of radius R, the solution of the problem of Poisson into the tumour in spherical coordinates  is given byϕp1 is a particular solution any of equation (2.3) in the tumour.The tumour spherical model is reported in ,42. As ϕθ and φ, given byAssumption 7 supposes that A and A00 in equation (2.9) are calculated from ϕ0 = ϕ1(r = 0) and sϕ = ϕ1, being ϕ1(r) is given byConstants ϕ0 and sϕ represents the tumour heterogeneity from the electrical point of view. The term (ϕ0-sϕ)/R is interpreted as the linear radial gradient of ϕ1(r).In equation (2.10), the difference between The electric field intensity in the tumour is calculated from σ12, given byEquation (2.11) shows that the electric field is uniformly distributed in the entire tumour volume. If equation (2.11) is substituted in equation (2.6), the following expression is found for σ12 with ϕ0, ϕs, R, kη and kε  for a fixed time after tumour cells are inoculated in the organism. R is any tumour radius higher than and equal to Rm, where Rm is the minimum tumour radius measured in preclinical studies or the first tumour radius detected in clinics [η1/η2−ε1/ε2) represents the difference between the conductive and dielectric ratios of the tumour and the surrounding healthy tissue.Equation 2.12) gives the dependence of 2 gives tR of untreated tumours changes in time t [σ12 is expected to depend on t. For this, CGE is used.Several experimental studies report that n time t –3. As a . 2.6VT(t) represents the tumour volume at a time t after tumour cells are inoculated into the host. The initial tumour volume (VT0) is given by the initial condition V(t = 0) = VT0. The parameter α (α > 0) is the intrinsic growth rate of the tumour. The parameter β (β > 0) is the growth deceleration factor due to the endogenous antiangiogenic process [CGE is given by process .VT(t) in CGE corresponds to the volume of a sphere (RT(t) is the spheroid tumour radius at a time t). As RT(t) and VT(t) depend on t, R in equation (2.12) is replaced by RT(t). As a result, σ12 is a function of t, named σ12(t). Substituting VT(t) in equation (2.13) results inRT0 satisfies the initial condition RT(t = 0) = RT0  = RT0 .σ12 in terms of TR0, ϕ0, ϕs, η1, ε1, η2, ε2, i, i0, α, β and t, unprecedented in the literature. In this study, three graphs for RT  and three graphs for σ12  are analysed, where dRT/dt is the first derivative of RT with regard to t whereas dσ12/dt is the first derivative of σ12 with respect to t. From these six graphs, four graphs are only shown in this study: RT versus t, dRT/dt versus RT, σ12 versus RT, and dσ12/dt versus σ12.The substitution of equation (2.14) in equation (2.12) allows us to express approximately . 2.7α (0.6 days−1) and β (0.2 days−1) corresponding to the fibrosarcoma Sa-37 tumour [RT0 (5.6 mm) and ϕ0 = −160 mV corresponding to the LLC tumour [ϕs (between −15 and −135 mV) and η1/η2−ε1/ε2 (between 1 and 5). For these values of ϕ0 and ϕs, ϕ0−ϕs varies between −145 and −25 mV. In this study, we only show results for ϕ0−ϕs (−145 and −25 mV) and η1/η2−ε1/ε2 . Furthermore, the parameter ε2 in equation (2.12) is calculated by the expression ε2 = εr2ε0, where ε0 (8.85 × 10−12 F/m) is the vacuum permittivity and εr2 (4 × 107) the relative permittivity of the muscle. Muscle is one type of tissue in which tumour cells are more frequently inoculated subcutaneously [For simulations, we use values of 0.6 days− and β  [sϕ depends on the histological variety and size of the tumour, organ/tissue where it grows, type of medium ).The aforementioned range of  tumours . Third,  of view . That is tumour)  for simuη1, η2, ε1 and ε2 values for different tumour histological varieties [η1/η2 and ε1/ε2 ratios for each tumour type and all satisfy that 0 < η1/η2−ε1/ε2 < 5. η1/η2−ε1/ε2 = 0 (η1ε2 = ε1η2) supposes that the tumour and surrounding healthy tissue have the same electrical properties, in contrast with the experiment [η1/η2−ε1/ε2 increases, the conductor properties prevail in both tissues; therefore, they behave as electrical conductors, being marked for the tumour. Contrastingly, the conductor and dielectric properties prevail in these two tissues when η1/η2−ε1/ε2 is small. In this case, both tissues behave as real dielectrics. This may be relevant in the aggressiveness and therapeutic planning of tumours [η1/η2−ε1/ε2 between 1 and 5.Many authors report arieties –12,28,36periment –12,28,36 tumours ,30. ThesA computer program is implemented in the Matlab software  to calculate and simulate the tumour radius, free electric charge surface density and their first derivate in time. These calculations are performed on a PC with an Intel(R) core processor (TM) i7–3770 at 3.40 GHz with a Windows 10 operating system. All calculations take approximately 1 min.. 3RT versus t (a) and dRT/dt versus RT (b). Likewise, σ12 versus RT  and dσ12/dt versus σ12 . The simulations of σ12 versus RT and dσ12/dt versus σ12 are shown for three values of η1/η2−ε1/ε2 above-mentioned and two values of ϕ0−ϕs = −145 mV  and −25 mV .versus t a and dRTersus RT b. Likewiersus RT a,b and drsus σ12 c,d. The  −145 mV a,c and −d −25 mV b,d.FiguRT versus t and σ12 versus t have similar behaviours (figure is not shown). When time elapsed, RT and σ12 grow up to their asymptotic values reached for t = 40 days, called RfT− and σf12−, respectively. The value of σf12− (stationary condition for σ12) is less negative than σ12−0 and its value depends on ϕ0−ϕs and η1/η2−ε1/ε2, where σ12−0 is the value of σ12 at t = 0. Although the graphs of dRT/dt versus t and dσ12/dt versus t are not shown in this study, it can be proved that both graphs evidence similar behaviours. These graphics show that positive values of dRT/dt and dσ12/dt decrease asymptotically to zero when time increases. Figure 2b reveals that dTR/dt decreases nonlinearly to zero when RT increases, while dσ12/dt decreases when σ12 is less negative . In addition, two stages are identified from the results shown in figures RT and σ12 are constant over time).The simulations of negative c,d. In a. 4σ12 at Σ has not been experimentally measured or theoretically calculated for cancer. That is why our simulations have not been experimentally validated (main limitation of this study) nor stochastically. Although stochastic simulation models are used to describe TGK [σ12 at Σ, but do not change its time behaviour. These aspects have made us use deterministic models in this study. And these models are feasible to describe TGK [α, β, TR0, ϕ0, ϕs, η1, η2, ε1 and ε2 (or ε0 and εr2)) which will result in an unique set of outputs (i.e. RT and σ12). In our approach, all random variations are implicitly included in parameters of σ12 .Although endogenous electric potentials and electrical properties of the cancer and surrounding healthy tissue may be measured –14,28, σribe TGK ,46, theyIf ‘realistic simulations' are taken into account ,46, the σ12 at Σ with tumour parameters , tumour electrical properties (η1 and ε1), bioelectrical potential in the tumour , electrical properties of surrounding healthy tissue (η2 and ε2), which is unprecedented in the literature. Likewise, explicit knowledge of σ12 at Σ with α and β allows us to relate σ12 at Σ in terms of Avrami exponent and impingement parameter [RT and σ12 at Σ changes in time without using special software for numerical modelling. That is another reason why we prefer the analytical method. Second, researchers in cancer should take into account our results to increase the effectiveness of anti-cancer therapies, mainly chemotherapy, immunotherapy and physical therapies .This study has two main achievements. First of all, the simple biophysic-mathematical approach proposed in this study that allows us to know an approximated theoretical expression that relates arameter ,5, also σ12 ≠ 0 at Σ is a direct consequence of equation (2.12) if (η1ε2−η2ε1) ≠ 0 and corroborates the existence of a multi-system with two different loss dielectrics in contact: the solid tumour and surrounding healthy tissue. Loss dielectric is a dielectric that has finite electrical conductivity and its induced electrical charges can move but not as freely as they would in a perfect conductor. If σ12 = 0 at Σ (η1ε2−η2ε1 = 0), η1 = η2 and ε1 = ε2, in contrast with the experiment [σ12 at Σ must be considered in cancer and its TGK.The results of this study confirm several findings reported in the literature and suggest others not yet revealed, such as: periment ,14,28–30σ12 ≠ 0 at Σ, there are average current densities J1 , being |J1| > |J2| because η1 > η2 [ϕ, concentrations and mobility of electrical charges) are much higher in the tumour than those in the surrounding healthy tissue [J1 and J2 on both sides of Σ indicate the Maxwell-Wagner-Sillars effect occurs for the tumour-surrounding healthy tissue multi-system. Due to this effect, both free and bound surface charge densities contribute to σ12 . Therefore, the Maxwell-Wagner-Sillars effect must not be ignored in cancer. The motion of electrical charges in both biological tissues involved during the tumour growth happen in different time scales, named relaxation times (τ), τ1 being for the tumour  and τ2 for the surrounding healthy tissue (τ2 = ε2/η2 and it depends on the tissue type). These aspects may suggest that both tissues cannot be perfect conductors (τ1 and τ2 tend to zero because η1 and η2 are infinite) or perfect dielectrics (induced volume charges cannot move), corroborating that these two tissues are loss dielectrics.As  η1 > η2 ,11,14,36y tissue ,9,11,15.J1 < 0), corroborating the tumour electronegativity  [J2 > 0) [entials) –14 and troblem 2.. As ∇∙Ef[J2 > 0) ,14.J1 may create a macroscopic magnetic field in the entire tumour and therefore an endogenous magnetic energy (per unit volume) that grows rapidly with increasing tumour size, in agreement with electric and magnetic fields (static or variable in time) associated with constant and time-varying endogenous electrical currents [r → TR). This corroborates that Σ, due to their higher electrophysiological activity in these regions, as documented in [r = 0, a fact that may explain in part the endogenous central intra-tumour necrosis and migration of tumour cells towards Σ. For this, It should not be ignored that currents –10. All currents ,14,18 anented in ,14,18,33ented in . If Ef=0s growth .σ12 at Σ corresponds to the change from the quick tumour growth phase to asymptotic phase of TGK and follows a sigmoidal behaviour in time, as TGK [σ12 may be explained because η1 and η2 exhibit nonlinear behaviour due to biological tissues being nonlinear systems [ηk, εk , τ1, τ2 and the relaxation time of the interfacial polarization (τp) change in time [ϕo, ϕs and (ϕo−ϕs) may change in time by dynamic self-regulation of σ12 at Σ; nevertheless, we do not explicitly know how. Therefore, we assume as constants these physical parameters in our approximation, being a limitation of our model.The time variation of , as TGK . This no systems , and ηk, in time . Furtherσ12 at Σ must be self-regulated during tumour growth, as TGK [α with respect to β), strong endogenous electrical potential gradient in cancer (greater permissible difference between ϕo and sϕ) and the greater difference is between ratios of electrical properties of the tumour and surrounding healthy tissue . This endogenous electrical potential gradient may explain the altered cancer bioelectricity  [σ12−0 (more negative) to σf12− (less negative) at Σ supposes that negativity of σ12 changes dynamically over time during TGK, being marked for the highest values of ϕ0−ϕs and η1/η2−ε1/ε2. This finding may impact both chemical and electrical environments of the cancer cells and the solid tumour; the hypocellular gap on the tumour-host interface  [pτ, which depends on kη and kε  [Σ [This dynamic change of , as TGK . It is fr cells) ,19. The  tissue) ; τp, whik = 1,2) ,32; and  1,2) [Σ .Σ) and/or the dynamic self-regulation of negativity of σ12 at Σ . This may suggest that dynamical alterations in cancer bioelectricity impact its growth, invasion, metastasis, maximum survival, neutralization of the attack of the immune system and resistance to anti-cancer therapies, as reported in previous studies [σ12 at Σ, ϕ0−ϕs, η1/η2−ε1/ε2 and dynamic change in σ12 at Σ, and electrostatically repels humoral and cellular components of the immune system, mainly those negatively charged  [Σ may avoid that σ12 = 0 at Σ and weaken the electrostatic coupling among cancer cells (negatively charged) in tumour regions near Σ to favour their metastasis. This may explain the acidification of the tumour microenvironment, which is related to the progression, invasion, metastasis, stimulation of many immunosuppressive processes and resistance to anti-cancer therapies [The tumour's electronegativity during its growth  . Consequ others) . This miherapies .σf12− were much more negative than σ12−0 at Σ, the tumour would behave as an isolated system because carriers of negative electrical charges would essentially concentrate at Σ. This interface behaves as an electrical barrier that prevents the entry and exit of different substances through it. If σ12 = 0 at Σ, the cellular elements of the immune system would enter the tumour interior. In both cases, the tumour would completely self-destruct, in contrast to the experiment [σ12 = 0 at Σ and replace the mechanism for which σ12 at Σ changes from σ12–0 to σ12−f as the tumour increases in size. This latter facilitates the migration of cancer cells toward the surrounding healthy tissue and the entry of nutrients into the tumour during its growth because blood is the most conductive tissue in the human body. This may justify why angiogenesis process in cancer emerges due to changes in its electrical and mechanical parameters at Σ, as previously reported in [If periment ,5. Endogorted in .r,θ,φ) in problem (2.8), σ12 would depend on , which means that σ12 is not uniform at the entire Σ. Furthermore, ϕ1(r), E1(r) and J1(r) depend nonlinearly on . As the ellipsoidal geometry of the solid tumour is often observed in the experiment [Although malignant tumours are not generally spherical –4,7, resTR and σ12 at Σ change in time during tumour growth for constant values of α, β, ϕ0, sϕ, η1, η2, ε1, and ε2. These eight parameters as well as ϕ1(r), E1(r), and J1(r) are expected to change in time too due to biological changes in tumour growth, as necrosis , angiogenesis, among others. Nevertheless, there is no relevant experimental/theoretical information available that links these two biological findings with σ12 at Σ. Consequently, it is tedious to propose a biophysic-mathematical approach that involves time dependence of α, β, ϕ0, sϕ, η1, η2, ε1, and ε2 in time changes of TR and σ12 at Σ. With this in mind, a longitudinal study is required to allow each of these eight parameters to be measured in time. It is important to point out that values of ϕ0, sϕ, η1, η2, ε1, and ε2 are reported in transversal studies [The results of this study show that  studies ,36,37,44σ12 at Σ may be explained from equations (2.12) and (2.14). The tumour necrosis leads to an increase of α parameter, whereas tumour angiogenesis brings about an increase of the parameter α and a decrease of the parameter β  in both cases. It should be noted that decrease of β during tumour growth means that the balance between the productions of angiogenic and antiangiogenic molecules is dominated by angiogenic molecules.Tumour necrosis is caused by nutrient and oxygen deprivation, and metabolic stress. The content of necrotic cells enhances angiogenesis and proliferation of endothelial cells, induces vasculature, as well as increasing migration, invasion and cell-cell interaction. Both necrosis and angiogenesis impact directly on cancer promotion and on the tumour microenvironment, as well as on cancer resistance and recurrence ,57. The Tc and GF are the cell cycle average time and tumour growth factor, respectively) [VT0, host and observation period of the study [α and decrease of σ12 at Σ. This may be explained by the following expression obtained by substituting Ncc) leads to an increase of GF  should be carefully analysed in untreated tumours. These CLFs should be small so that the doubling time of the tumour (DT) is short, according to the Steel equation (ctively) . For ins=Tcln2/[−CLFs(1+Ghe study . Short Dα and therefore a decrease of σ12 at Σ. This statement is corroborated from a bioelectric point of view with equation (2.12), as discussed above.When the tumour grows it becomes more heterogeneous, as it demonstrates simulations for its spherical and non-spherical geometries . The tumMT concentric layers, each one of them of radius RiT, average electrical conductivity iη and average electrical permittivity iε; -ϕ0 in the tumour centre; -siϕ in the contour between two adjacent layers (iΣi + 1) and it satisfies −ϕ0 < −sϕ1 < ··· < −sNϕ, keeping in mind [iσi + 1) at iΣi + 1)( < −σi + 1)(i + 2). Furthermore, there is a surface charge density (MσM + 1) at border (MΣM + 1) between the outermost layer of the tumour and surrounding healthy tissue . For this case, the result isThe simulations shown in  suggest  in mind ; and theiσi + 1)( < −σi + 1)(i + 2) supposes that each tumour layer behaves as an electrical shield, with the innermost layer being the most negative, as discussed above. By contrast, the solid tumour is self-destructed, in contrast with the clinics [iσi + 1) may explain that the spherical tumour has well-defined multicentric layers from an electrical point of view, in agreement with well-defined multicentric layers from a biological point of view [TM, TiR, iη, iε, siϕ, iσi + 1)( at iΣi + 1)( at MΣM + 1) are not known neither experimentally nor theoretically. The measurement of these parameters in a multilayer tumour is more cumbersome than in a simple model, as proposed in this study. That is why we do not include a tumour with different concentric layers in the simulations proposed.The condition −σii +  < −σ, angstroms (i.e. single atoms), tens to hundreds of nanometers (i.e. proteins), several microns . Supersystems are referred to tissues, organs and individuals measured in fractions of meters .Large networks of systems in cancer patients allow us to suggest that alterations are not only due to changes at tissue, cellular and molecular levels , but als. 4.1σ12 at Σ are negative to reestablish the bioelectrical states and Vmem of cancer cells within the physiological range, as reported by Cervera et al. [Σ to avoid metastasis of cancer cells when electrochemical therapy is used. This may be explained because anodes generate positively charged carriers (e.g. hydrogen ions) that may intensify electrostatic interactions between negatively charged carriers (e.g. cancer cells) by means of the formation of ionic bridges. Consequently, a possible anti-cancer therapy that inhibits the release of positively charged carriers from the tumour may be suggested. Furthermore, knowledge of shape and orientation of σ12 may be essential to elucidate if anodes should be inserted in regions near Σ with higher or smaller σ12 values to maximize tumour volume destruction with the minimum damage to the surrounding healthy tissue.Many molecules used in chemotherapy and immunotherapy are positively/negatively charged and have not given a definitive solution to the cure for cancer. Our simulations indicate that anti-cancer therapies should take into account that bioelectricity cancer cells and a et al. , who reca et al. ,62. The σ12−0 to σf12− at Σ or does this change lead to the tumour growth? (2) Do biological changes  lead to physical changes  [σ12 at Σ (from surrounding cancer tissue) more easily than the positive ones? (4) Do the negatively charged molecules that cross σ12 at Σ induce the highest antitumour effectiveness than those positively charged? A meta-analysis may be carried out to give answers to these questions and others related to them. The cancer bioelectric handling has been suggested as a useful tool to understand bioelectrical fields that change dynamically during cancer growth and possible anti-cancer therapeutic targets, aspects that remain unclear as yet [σ12 and the tumour contour fractal dimension reported in [σ12 at Σ have during tumour growth? (7) What expression adopts σ12 when a heterogeneous tumour and nonlinear ϕ1 are considered? (8) Can electrochemical therapy with low-level of direct current re-establish physiological bioelectrical disorders that happen in an untreated tumour? (9) How do the endogenous magnetic field and the ellipsoidal geometry influence the untreated tumour growth? (10) How does σ12 relate to other biophysical-chemical processes that occur in the tumour? (11) How does σ12 at Σ change experimentally over time during the growth of untreated and treated solid tumours using any experimental techniques reported in [This study opens new questions that may be essential to understand TGK and how electrophysiological variables of the untreated tumour change during its growth that may be relevant for individualized anti-cancer therapies. Among the possible questions that arise: 1) Does the tumour growth bring about change from perties)  or vice perties) ? We belir as yet ,43. 5)  Does the  Does thorted in ,35 (e.g.On the other hand, the results of this study may contribute to answering to the fourth challenge reported in , related. 5σ12 at Σ may be relevant in the redesign of chemotherapy and immunotherapy that take into account the polarity of the substances or the design of completely novel therapies.In conclusion, results corroborate the correspondence between the electrical and physiological parameters in the untreated cancer, which may have an essential role in its growth, progression, metastasis and protection against immune system attack and anti-cancer therapies. In addition, knowledge of


To simulate the performance of CO2 foam gel fracturing fluid under field operation conditions, the formula of the gel fracturing fluid was obtained through experimental optimization in this paper, and the experimental results show that the viscosity of gel fracturing fluid is 2.5 mPa·s (after gel breaking at a shear rate of 500 s−1), the residue content is 1.3 mg/L, the surface tension is 25.1 mN/m, and the interfacial tension is 1.6 mN/m. The sand-carrying fluid has no settlement in 3 h with a 40% sand ratio of 40–70-mesh quartz sand. The core damage rate of foam gel fracturing fluid is less than 19%, the shear time is 90 min at 170 s−1 and 90 °C, the viscosity of fracturing fluid is >50 mPa·s, and the temperature resistance and shear resistance are excellent. The gel fracturing fluid that was optimized was selected as the base fluid, which was mixed with liquid CO2 to form the CO2 foam fracturing fluid. This paper studied the rheological properties of CO2 foam gel fracturing fluid with different CO2 foam qualities under high temperature (65 °C) and high pressure (30 MPa) and two states of supercooled liquid (unfoamed) and supercritical state (foamed) through indoor pipe flow experiments. The effects of temperature, pressure, shear rate, foam quality, and other factors on the rheological properties of CO2 foam gel fracturing fluid were considered, and it was confirmed that among all the factors, foam quality and temperature are the main influencing factors, which is of great significance for us to better understand and evaluate the flow characteristics of CO2 foam gel fracturing fluid and the design of shale gas reservoir fracturing operations.Foam gel fracturing fluid has the characteristics of low formation damage, strong flowback ability, low fluid loss, high fluid efficiency, proper viscosity, and strong sand-carrying capacity, and it occupies a very important position in fracturing fluid systems. The rheological properties of gel fracturing fluid with different foam qualities of CO Foam gel fracturing fluid is essentially a kind of gas-in-liquid emulsion, and bubbles provide high viscosity and excellent proppant-carrying capacity. Because it has the characteristics of low reservoir damage, strong flowback ability, low fluid loss, high fluid efficiency, proper viscosity, and strong sand-carrying capacity, it occupies a very important position in fracturing fluid systems.The use of foam gel fracturing fluid is a great achievement of liquid technology. Foamed fracturing fluid is formed by dispersing N2 foam fracturing to the present CO2 foam fracturing. In 1986, in the Federal Republic of Germany, 60% CO2 foam gel fracturing fluid was used in the carboniferous gas reservoir in Fez Dolf, which was buried 3400−3650 m underground. The fracturing was successful, and the natural gas production increased by nearly 12 times after fracturing [2 foam fracturing technology [To solve the shortcomings and defects of conventional fracturing technology, researchers began to study foam fracturing technology in the 1970s [2 foam fracturing fluid can also influence the propagation of hydraulic fractures. Several authors reported that the high performance of CO2 foam is attributed to its unique and favorable rheological characteristics [2 foams under reservoir conditions (high temperature and high pressure) for fracturing applications [2 by measuring the viscosity of thickened liquid CO2 in different physical parameters of this prepared thickener and explained the causes of the rheological changes [2 foamed chelating agent, L-glutamic acid-N, N-diacetic acid (GLDA), which was conducted at 100 C, 1000 psi, 3.5 pH level, and various water salinities, resembling harsh reservoir conditions [The characteristics of COeristics ,11,12,13eristics ,16,17,18eristics ,24,25,26eristics . Fu et aications . Li et a changes . Kadafurnditions . Tariq enditions .2 foam gel fracturing fluid is only 2000 psi (13.8 MPa). Under the condition of simulating tubing or formation temperature (30−50 °C), the gas phase of the foam gel fracturing fluid is in a gas state, so the foam gel fracturing fluid in the experiment is in a gas-liquid two-phase flow, while for the actual fracturing technology, the pumping pressure is extremely high, reaching tens of MPa. At the same time, the fluid temperature in the wellbore or formation fracture is also high. For CO2 foam gel fracturing fluid, CO2 is in a supercritical fluid state. The physical property of the supercritical fluid is closer to that of liquid, and the rheological property at this time is closer to that of a liquid–liquid emulsion. Most of the literature has investigated the rheological performance of the CO2 foam gel fracturing fluid unfoamed and ignored the different foam qualities’ effects in the foaming process, and the experimental temperature and pressure are so low that they are unable to simulate actual field fracturing conditions. Therefore, it is very important to study the rheological properties of foam gel fracturing fluid in the two states of supercooled liquid (unfoamed) and supercritical state (foamed) under simulated actual construction conditions—high pressure (tens of MPa) and high shear rate—for the effective implementation of fracturing technology, the selection of reasonable fracturing parameters, more accurate fracturing prediction, and the evaluation of fracturing effects.Presently, the limit pressure of the experimental system for studying the rheological properties of CO2 foam fracturing fluid in the two states of foamed and unfoamed under field operation conditions, the formula of the gel fracturing fluid is obtained through experimental optimization firstly, and the viscosity, static sand setting performance, and rheological performance of the foam gel fracturing fluid are experimentally evaluated. The goal is to obtain a foaming gel fracturing fluid with good performance parameters and which is mixed with liquid CO2. This paper selects the foam fracturing fluid formed by CO2 and gel fracturing fluid and studies the rheological properties of CO2 foam fracturing fluid under high temperature (65 °C) and high pressure (30 MPa), considering the two states of supercooled liquid and supercritical through indoor pipe flow experiments. The effects of temperature (15–90 °C), pressure , shear rate (100–3000 s−1), foam quality , and other factors on the rheological properties of fracturing fluid are investigated, which is of great significance for better understanding and evaluating the flow characteristics of CO2 foam gel fracturing fluid and on-site fracturing construction design.To simulate the rheological performance of CO2 foam gel fracturing fluid changed with the shear rate at 20 MPa, 30 MPa, and 40 MPa, and the temperature changed from 0 to 80 °C.The effects of temperature, pressure, shear rate, and foam quality on the rheological properties of fracturing fluid are considered. In this experiment, the inner diameter of the test instrument pipeline was 12 mm. The effective viscosity of the CO2 is often mixed with guanidine gum and then injected into the formation by tubing for fracturing. As the fracturing fluid enters the formation, the temperature gradually rises, and the high-pressure CO2 completely changes from supercooled liquid to a supercritical state, and the effects of CO2 in the two states on the effective viscosity of CO2 foam gel fracturing fluid are completely different. Therefore, the research on the influence of various factors on the effective viscosity of CO2 foam gel fracturing fluid is divided into two processes for analysis. The CO2 foam fracturing fluid with CO2 in the liquid state is defined as the fracturing fluid system under unfoamed conditions, and the CO2 foam fracturing fluid with CO2 in the supercritical state is defined as the fracturing fluid system under foamed conditions.In actual fracturing construction, high-pressure supercooled liquid CO−1 is other than that when the shear rate is higher than 500 s−1. The shear-thinning characteristics of the foam system in the unfoamed state are mainly due to the influence of shear on the base liquid of the gel fracturing fluid. Linear guanidine gum is a long-chain polymer without a cross-linking structure. Increasing the shear rate will reduce the intermolecular interaction force caused by polymer molecular entanglement and hydrogen bonding, which will lead to a decrease in effective viscosity.2 foam gel fracturing fluid with a shear rate at a pressure of 10 MPa and a temperature of 65 °C. It can be seen from the figure that the effective viscosity of CO2 foam gel fracturing fluid decreases exponentially with the increase in the shear rate at the same pressure, indicating that the CO2 foam gel fracturing fluid system is a typical shear-thinning non-Newtonian fluid, with a changing trend when the shear rate is lower than 1000 s−1. It can be seen from the figure that for CO2 foam gel fracturing fluid during foaming, CO2 is in a supercritical state, and its physical properties are increasingly close to those of gas. At this time, the emulsion formed by guanidine gum solution and supercritical CO2, which are two limited miscible fluids, is closer to the traditional foam system. The weakening effect of shearing on the viscosity of CO2 foam fluid is mainly reflected in two aspects: on the one hand, the shearing mentioned above will reduce the intermolecular interaction force caused by polymer molecular entanglement and hydrogen bonding; on the other hand, it is due to the destruction of the internal-phase CO2 foam structure by shearing.2 volume fraction when the pressure is 10 MPa and the temperature is 20 °C. It can be seen from the figure that the effective viscosity of unfoamed fracturing fluid decreases with the increase in the CO2 volume fraction, and the change range is large. The main reason is that the unfoamed CO2 is in the supercooled liquid form, similar to Newtonian fluid in this mixed system. At this time, CO2 has little significance for the viscosity increase in the whole system. On the contrary, the increase in the CO2 volume fraction will dilute the guanidine gum base liquid. When the volume shares of CO2 increase to a certain extent, the fluid-structure will suddenly change, from the previous guanidine gum base liquid as the continuous phase to the liquid one. When the guanidine gum base liquid changes from the external phase to the internal phase, the continuous phase of the fluid becomes the liquid CO2, which greatly reduces the viscosity of the whole system.2 foam gel fracturing fluid with foam quality under foaming conditions, with a pressure of 10 MPa and temperature of 65 °C. It can be seen from the figure that the change rule of effective viscosity with foam quality is opposite to that without foam. The increase in foam quality makes the effective viscosity of the whole system increase, and the increased range is large. For example, when the shear rate is 834 s−1, the viscosity of foam gel fracturing fluid increases from 26.45 mPa·s to 56.32 mPa·s, with an increasing range of 113%. When the foam mass is 75%, the effective viscosity reaches the maximum value, and when the foam mass is more than 75%, the viscosity of foam gel fracturing fluid decreases obviously. In the research of this system, it can be seen that when the foam mass is more than 55%, with the increase in foam mass, the number of bubbles in the foam system increases, the mutual interference, and deformation among bubbles increase, the bubble structure becomes denser, and the viscosity of the foam system continues to increase.2 foam gel fracturing fluid with a foam mass of 45−75% was tested at elevated temperatures, and the influence of temperature on the effective viscosity of CO2 foam gel fracturing fluid was analyzed. In the experiment, a pipe diameter of 12 mm, a shear rate of 170 s−1, a heating rate of 1 °C/min, and a temperature of 80 °C were selected, and the viscosity−temperature characteristics of CO2 foam gel fracturing fluid under conditions of 10−40 MPa were tested.The effective viscosity of CO2 volume fractions. The temperature ranges from 5 to 25 °C, the shear rate ranges from 503 s−1 to 1500 s−1, and the volume fraction of CO2 from 45 to 75%. It can be seen from the figure that the effective viscosity of unfoamed fluid decreases with the increase in temperature, showing an exponentially decreasing trend. The main reason is the influence of temperature on the rheological properties of the guanidine gum base liquid: with the increase in temperature, the movement activity of guanidine gum molecules increases, and the thermal fracture of the hydrogen bonds of linear guanidine gum in the n liquid system is accelerated, so that the activation energy of guanidine gum base liquid decreases, which comprehensively shows that the effective viscosity of the solution decreases.2 foam gel fracturing fluid with temperature under the foaming condition, with a pressure of 20 MPa, different shear rates, and foam quality. The temperature ranges from 35 to 75 °C, the shear rate ranges from 503 s−1 to 1500 s−1, and the foam mass ranges from 45 to 75%. It can be seen from the figure that the effective viscosity−temperature characteristics of CO2 foam gel fracturing fluid during foaming are consistent with those of unfoamed fracturing fluid, showing an exponentially decreasing trend. At the same time, when the temperature is greater than 55 °C, the variation ranges of the effective viscosity of foam gel fracturing fluid with temperature becomes smaller.2 foam gel fracturing fluid with a shear rate under different pressure conditions and under unfoamed and foamed conditions at 25 °C and 65 °C, respectively. It can be seen from 2 foam gel fracturing fluid with pressure under the conditions of foaming at 65 °C, 55% foam mass, and 10 MPa, 20 MPa, and 30 MPa respectively. Similar to the unfoamed condition, the effective viscosity is less affected by pressure due to the pressure’s influence on bubble size and distribution in the foam gel fracturing fluid. The results show that the diameter of bubbles in the foam system gradually decreases with the increase in pressure, and the higher the pressure, the more uniform the bubble size distribution. On the one hand, the stability of bubbles is increased, while on the other hand, the nonlinear interaction between bubbles is enhanced, and the viscosity of the foam gel fracturing fluid is improved as a whole.2 volume fraction when the temperature is 25 °C and the pressure is 10 MPa, 20 MPa, and 30 MPa, respectively. It can be seen from the figure that, when unfoamed, the flow index gradually increases with the increase in CO2 volume fraction, while the consistency index decreases. Under experimental conditions, the change range of the flow index is 0.37−0.72; the variation range of the consistency index is 0.23−0.39.n of the unfoamed fracturing fluid is less than 1, indicating that the fluid is a shear-thinning non-Newtonian fluid, and the value of n is closer to 1 with the increase in CO2 volume fraction, indicating that the fluid property of the fracturing fluid gradually changes to a Newtonian fluid with the increase in the CO2 volume fraction, which is precise because the unfoamed CO2 exists as a supercooled liquid similar to a Newtonian fluid, and its non-Newtonian property weakens with the increase in the CO2 volume fraction.The flow index is a parameter used to describe the non-Newtonian property of the fluid. It can be seen from the figure that the flow index 2 foam gel fracturing fluid with foam quality when the temperature is 65 °C and the pressure is 10 MPa, 20 MPa, and 30 MPa, respectively. As can be seen from the figure, with the increase in foam quality, the flow index gradually decreases, and the consistency index increases, and from the perspective of the change range, it starts to increase substantially when the foam quality is 55%. This shows that the CO2 foam gel fracturing fluid in the foaming stage still belongs to the shear-thinning non-Newtonian fluid, and with the increase in foam quality, the non-Newtonian fluid properties of the foam gel fracturing fluid gradually increase.2 is 65% without foaming. It can be seen from the figure that with the increase in temperature, the flow index of the fluid increases, and the consistency index decreases.2 foam gel fracturing fluid with temperature when the pressure is 20 MPa and the foam mass is 65%. It can be seen that the change rule of rheological parameters of foamed fracturing fluid with temperature is consistent with that of unfoamed fracturing fluid, which shows that with the increase in temperature, the flow index of fluid increases and the consistency index decreases. From the action mechanism, it is the same as that of the previous temperature on the viscosity characteristics of CO2 foamed fracturing fluid.2 foam gel fracturing fluid changing with pressure when the temperature is 65 °C and the foam quality is 45%, 55%, 65%, and 75% respectively. It can be seen from the figures that with the increase in pressure, the change of fluid flow index and consistency index is very small, which shows that the influence of pressure on the rheological properties of the foam gel fracturing fluid is almost negligible compared with temperature and foam quality. Meanwhile, the influence of pressure on the rheological properties of the foam gel fracturing fluid is negligible.P, are mainly determined by n factors a = {a1, a2, …, an} and P = f . In a certain reference state, a* = {a1*, a2*, …, an*}, the system characteristic is P*. Let each factor change within its possible range, and analyze the trend and degree of the deviation of the system characteristic P from the benchmark state P* due to these factors. This analysis method is called sensitivity analysis.Sensitivity analysis is a method to analyze system stability in system analysis. There is a system, and its system characteristics, P to the relative error of the parameter ka is defined as the sensitivity function kS(ka) of the parameter ka.We define the dimensionless sensitivity function and sensitivity factor. That is, the ratio of the relative error of the system characteristic kS(ka) can be approximately expressed as:When kS*, k = 1, 2, …, n, is a set of dimensionless non-negative real numbers. The larger the kS* value, the more sensitive P is to ka in the reference state. Through the comparison of kS*, the sensitivity of system characteristics to various factors can be compared and evaluated.2 foam gel fracturing can be mainly regulated by the two parameters, which is helpful for application in shale gas reservoir fracturing.To understand the sensitivity of the rheological properties of foam gel fracturing fluid to various factors, the above sensitivity analysis method was used to analyze the main factors affecting the rheological properties of foam gel fracturing fluid, and the sensitivity of each factor was compared. The characteristics of the system, that is, the rheological characteristics of foam gel fracturing fluid, are characterized by the effective viscosity of the system. The parameters for sensitivity analysis are shear rate, pressure, foam quality, and temperature. Observe the shape of the rheological curve and establish the functional relationship between effective viscosity and shear rate, temperature, and other parameters to obtain the sensitivity function, and then calculate the sensitivity factor. After analysis, the sensitivity values of each parameter are obtained , which a−1 and 90 °C, and the viscosity of the fracturing fluid is >50 mPa·s.The formula of the gel fracturing fluid was obtained through experimental optimization, which evaluated experimentally the viscosity, residue, surface tension, sand-carrying capacity, and interfacial tension of the gel fracturing fluid. The core damage rate of the gel fracturing fluid is less than 19%, the shear time is 90 min at 170 s2 foam gel fracturing fluid and its influencing factors were studied experimentally. For the foam gel fracturing fluid with CO2 in supercooled liquid and at a supercritical state, the effects of temperature, pressure, shear rate, and foam quality on the rheological properties of the gel fracturing fluid were considered. The main conclusions are as follows:The rheological properties of CO2 volume fraction, and the effective viscosity of fluid decreases with the increase in temperature. The effective viscosity is little affected by pressure. In the foaming state, the change rule of effective viscosity with shear rate is the same as that without foaming, the change rule with foam quality is opposite to that without foaming, and the effective viscosity−temperature characteristics of fluid are the same as that without foaming.In the unfoamed state, the effective viscosity of foam gel fluid decreases exponentially with the increase in shear rate, gradually decreases with the increase in COWithout foaming, the foam quality increases, the flow index gradually increases, and the consistency index decreases. With the increase in temperature, the flow index of fluid increases, and the consistency index decreases. When foaming, the foam quality increases, the flow index gradually decreases, and the consistency index increases. When the foam quality is about 50%, a sudden change begins. With the increase in temperature, the flow index of fluid increases, and the consistency index decreases. With the increase in pressure, the flow index and consistency index of fluid change very little.2 foam gel fracturing fluid are foam quality, temperature, shear rate, and pressure, in turn, which provides a theoretical basis for CO2 foam fracturing technology.Based on the sensitivity analysis method, the influencing factors of the rheological behavior of CO2 foam gel fracturing fluid system, which has been applied successfully to reservoir stimulations, is a cross-linked fracturing fluid system with guanidine gum as the thickener.In recent years, the CO2 in this research is formed. According to the characteristics of foam gel fracturing fluid, the high-speed mixing method (Waring Blender method) was selected to evaluate the foaming ability and foam stability of the foaming agent.The commonly used foam sealing and channeling systems are mainly composed of a foaming agent, foam stabilizer, and gas phase ,33. Ther(1)Thickener optimizationTo select a liquid that can form foam with good stability at a low dosage, the frequently used thickeners were evaluated and optimized by experiments, including CT5-7, CT5-7WⅠ, hydroxypropyl guar gum (CMHPG), instant carboxymethyl cellulose (CMC), and polyanionic cellulose (PAC), and the results of the thickeners’ foam stability are shown in The CT5-7 is a thickener, which is prepared from acrylamide, vinylpyrrolidone, maleic acid, anionic functional monomer, initiator, inorganic salt, etc. It includes acrylamide 25~30%, vinylpyrrolidone 3~5%, maleic acid 4~6%, anionic functional monomer 5~7%, initiator 0.08~0.15%, potassium hydroxide 1~8%, inorganic salt 5~10%, and the rest is water.(2)Foaming agent optimizationΓ is:0 is the volume of gel fracturing fluid, mL.The foaming ability and foam half-life of 0.3% CT5-7B, CT5-7S, sodium dodecylbenzene sulfonate (ABS), alkyl betaine (DSB), CT5-7C and other foaming agents in CT5-7 thickener solution were experimentally evaluated. These are the foaming agent, and their main component is alcohols; CT5-7B is fusel, CT5-7S is methyl isobutyl methanol, and CT5-7C is triethoxybutane. The results are shown in The foaming power and foam stability data of five foaming agents were analyzed, and CT5-7S with good foaming power and foam stability was selected as the foaming agent of the foam gel fracturing fluid formula.(1)Thickener dosageTo optimize the amount of thickener in gel fracturing fluid, an experimental evaluation was carried out on the sand suspension (settling velocity of 40–70 mesh quartz sand) of fracturing fluid with 0.2, 0.3, 0.4, and 0.5% of thickener at 30~90 °C, and the experimental results are shown in The experimental results show that the sedimentation rate of quartz sand in the gel fracturing fluid increases with the increase in temperature. When the amount of CT5-7 is 0.2% and 90 °C, the suspension capacity of quartz sand is poor. When the amount is 0.3–0.4%, the sedimentation rate of quartz sand is 1–10 mm/s at 90 °C, but when the amount is increased to 0.5%, the quartz sand hardly sinks.The analysis shows that after the gel fracturing fluid forms foam, its apparent viscosity increases, and the ability to suspend and carry solid particles increases significantly.(2)Stability of foam with different thickener dosageThe stability  of gel fracturing fluid with thickener dosages of 0.2, 0.3, 0.4%, and 0.5% was experimentally evaluated at room temperature and up to 90 °C The dosage of 0.3% CT5-7S foaming agent was 0.3%, as shown in Based on the experimental data on viscosity, sand suspension, and the half-life of foam in gel fracturing fluid, the thickener dosage of gel fracturing fluid with a foam formula is determined to be 0.5%.(3)Determination of Foaming agent dosageTo determine the dosage of the foaming agent, the half-life of foam when the dosage of CT5-7S foaming agent is 0.1, 0.3, and 0.5%, the experimental temperature is 30 °C, and the experimental data are shown in Through the experimental evaluation of the single agent of gel fracturing fluid with foam such as foaming agent and thickener, the experimental evaluation data analysis of foam half-life, foam quality, and the viscosity of gel fracturing fluid is carried out, and the formula of gel fracturing fluid is determined: 0.5% CT5-7 thickener + 0.3% CT5-7S foaming agent + 0.3% CT5-7D high-temperature stabilizer + 0.3% CT5-7U regulator.The gel fracturing fluid volume of 1000 mL was prepared in the mixer, and then the 600 ppm gel breaker (ammonium persulfate) was added, which may break the gel fracturing fluid at 90 °C. The gel fracturing fluid after the gel was broken was centrifuged and dried with the separated residue at 105 °C ± 1 °C. Then, the residue content in the gel fracturing fluid was determined. The results are shown in The residue content in the gel breaker is calculated according to the following formula:It is necessary to test the sand carrying performance of gel fracturing fluid by a static suspended sand experiment. The gel fracturing fluid with foam quality (Q = 65%) was prepared according to the liquid formula and 200 mL of fluid was poured into the beaker and then placed in a 90 °C water bath at a constant temperature for 20 min. Then, the liquid was poured into the mixer, and 40−70 mesh quartz sand was added according to the 40% sand ratio and stirred evenly. Then, the mixed liquid with sand was poured into a 250 mL measuring cylinder and put into an oven at 90 °C . The volume of clear liquid separated from the upper layer was recorded at regular intervals. The static suspended sand test results of the gel fracturing fluid are shown in The core of the shale reservoir is used to evaluate the damage performance of gel fracturing fluid. The test results are shown in v/v), adjust the pH value of the liquid to 5.8, then add foaming agent according to the design proportion, mix it evenly, transfer it to the closed system of the RS6000 high-temperature rheometer, connect the CO2 gas source to pressurize 10 bar and ensure that the gel fracturing fluid is in the CO2-saturated state, and test the temperature resistance and shear resistance of the fracturing fluid. The experimental results show that the fracturing fluid can still maintain a high apparent viscosity after a long time of shearing at 90 °C at a shear rate of 170 s−1 and the apparent viscosity is greater than 50 mPa·s, indicating that it has excellent temperature and shear resistance.Evaluation method: take 70 mL of gel fracturing fluid, add regulator according to the proportion of 0.3% (−1), the residue content is 1.3 mg/L, the surface tension is 25.1 mN/m, and the interfacial tension is 1.6 mN/m. The 40−70 mesh quartz sand commonly used in shale gas fracturing is used for static sand setting experiments and the sand ratio is 40%. The static sand carrying experiment was carried out. The sand-carrying fluid had good flow performance, and the proppant showed no settlement in 3 h. The core of the shale reservoir was selected for the damage evaluation experiment of the foam gel fracturing fluid. The test results are shown in −1 and 90 °C, and the viscosity of the fracturing fluid is >50 mPa·s, and the temperature resistance and shear resistance are excellent.The formula of the gel fracturing fluid is obtained through experimental optimization, and the viscosity, static sand setting performance, and rheological performance of the foam gel fracturing fluid are experimentally evaluated. The experimental results show that the viscosity of the fracturing fluid is 2.5 mPa·s  into Formula (7):Formula (7) is the basic formula for the rheometer.For power-law fluid, the constitutive formula is:Substituting Formula (8) into Formula (7) of tube rheometer to obtain Formula (9):Integrate the above formula to obtain Formula (10):Take the logarithm on both sides of the formula and obtain Formula (11):Type, the wall shear stress Q is measured, and the relationship curve B of the straight line, the rheological characteristic parameters n and k of the power-law fluid can be determined.After the pressure drop and flow,


Severe COVID-19 infection is characterized by a dysregulated hyperinflammatory state that contributes to morbidity and mortality. Immunomodulatory therapy has been shown to improve outcomes. We investigated if abatacept, CTLA-4-Ig, a selective costimulation modulator, provides additional benefit when added to standard of care.We conducted a double-blind, randomized, placebo-controlled trial evaluating abatacept  compared to standard of care (including remdesivir and dexamethasone) in patients hospitalized with COVID-19 pneumonia. The primary outcome was median time to recovery by day 29. Key secondary endpoints included 28-day mortality.A total of 1019 patients received an infusion (509 assigned to abatacept and 510 to placebo), constituting the analyzed modified intention-to-treat cohort. The mean age 54.9 years (SD 14.65), 60.5% were male, 44.2% Hispanic or Latino and 13.7% black. Patients were evenly matched in terms of severity of illness, and comorbidities. Participants randomized to abatacept did not show a statistically significant difference in the primary endpoint with a recovery rate ratio of 1.135  compared to placebo. The median (IQR) time to recovery was 9 days  for both groups. The 28-day mortality in the abatacept arm was 11.0% and in control arm 15.0% ), with a 37.8% lower odds of dying in patients receiving abatacept. The improvement in mortality was demonstrated for patients requiring low or high flow O2 at baseline but was not seen in patients who required mechanical ventilation or ECMO at time of randomization. Subgroup analysis identified the strongest effect in those with baseline CRP >75mg/L, age >65 and diabetics. Safety data demonstrated slightly lower risk of adverse events. Rates of secondary infections were similar (abatacept 16.1% and placebo 14.3%).Although single-dose IV abatacept did not demonstrate statistically significant improvement in time to recovery, it did show a substantial reduction in 28-day mortality compared to standard of care.Reynold Panettieri, Jr., MD, AstraZeneca: Advisor/Consultant|AstraZeneca: Grant/Research Support|AstraZeneca: Honoraria|Equillium: Grant/Research Support|Genentech: Advisor/Consultant|Genentech: Grant/Research Support|Janssen: Grant/Research Support|MedImmune: Grant/Research Support|Merck: Honoraria|Novartis: Grant/Research Support|Origo: Grant/Research Support|RIFM: Advisor/Consultant|RIFM: Grant/Research Support|Sanofi: Honoraria|Vault Health: Grant/Research Support Jane A. O'Halloran, MD PhD, Janssen Scientific Affairs, LLC: Grant/Research Support Michael A. Maldonado, MD, Bristol Myers Squibb: Employee|Bristol Myers Squibb: Stocks/Bonds William G. Powderly, MD, Merck: Advisor/Consultant.


Detecting residual nasopharyngeal carcinoma (rNPC) can be difficult because of the coexistence of occult tumours and post-chemoradiation changes, which poses a challenge for both radiologists and surgeons using current imaging methods. Currently, molecular imaging that precisely targets and visualises particular biomarkers in tumours may exceed the specificity and sensitivity of traditional imaging techniques, providing the potential to distinguish tumours from non-neoplastic lesions. Here, we synthesised a HER2/SR-BI-targeted tracer to efficiently position NPC and guide surgery in living mice. This bispecific tracer contained the following two parts: IRDye 800 CW, as an imaging reagent for both optical and optoacoustic imaging, and a fusion peptide (FY-35), as the targeting reagent. Both in vitro and in vivo tests demonstrated that the tracer had higher accumulation and longer retention (up to 48 h) in tumours than a single-targeted probe, and realised sensitive detection of tumours with a minimum size of 3.9 mm. By visualising the vascular network via a customised handheld optoacoustic scan, our intraoperative fluorescence molecular imaging system provides accurate guidance for intraoperative tumour resection. Integrating the advantages of both optical and optoacoustic scanning in an intraoperative image-guided system, this method holds promise for depicting rNPC and guiding salvage surgery. Nasopharyngeal carcinoma (NPC) is an epithelial malignancy characterised by a distinct geographical distribution . Up to 9Recent advances in optical molecular imaging have the potential to exceed the specificity and sensitivity of conventional techniques for effective detection of small tumour foci both preoperatively and intraoperatively . OpticalTo achieve effective targeting, a single molecular target may not be sufficient. Recently, scavenger receptor class B type I (SR-BI), a receptor that selectively binds to high-density lipoprotein (HDL) and functions in lipoprotein metabolism, was reported to be overexpressed in all investigated NPC cell lines and 75% of NPC biopsies, demonstrating its promise in NPC imaging . Thus, aFluorescence-guided surgery is an optical imaging strategy that allows real-time guidance for detecting and resecting tumours intraoperatively with higher sensitivity than direct visual inspection and palpation . Tumour-In this study, a bispecific peptide (FY-35) was labelled with IRDye 800CW (IR800-FY-35) and evaluated for its ex vivo and in vivo targeting efficacy . A singlN, N-dimethylformamide (DMF), (II) DMF washings, (III) coupling, and (IV) DMF washings. The resin was treated with 2 mL dichloromethane (DCM) for 5 min three times and 2 mL DMF for 5 min three times before it was used. The resin was washed thoroughly before it was incubated with HBTU-preactivated amino acid, or commercially-available fluorophores (FITC/IRDye800 CW) activated ester. Cleavage from the solid support was performed with trifluoroacetic acid (TFA)/water/triisopropylsilane  over 3 h at room temperature. All products were purified by high-performance liquid chromatography (HPLC) using a Gemini-NX 10μ C18 4.6 × 250 mm column  on a Shimadzu LC-2010A HPLC System . Mass spectroscopy was used to characterise the probes. The FITC-labelled probes were used for in vitro cell-binding assays.The dual-targeted peptide FY-35  and a single-targeted peptide FL-35  were obtained by solid-phase peptide synthesis in Apeptide Co., Ltd. . The synthesis cycle consisted of the following: (I) Fmoc cleavage: 20% piperidine in 2 at 37 °C. The cells were harvested at 80% confluence and maintained in the exponential growth phase. Cell density was calculated using a haemocytometer and performed before any experiments.Human NPC cells 5-8F were transfected with firefly luciferase for in vivo imaging. Transfected cells (5-8F-fLuc) and non-transfected cells (5-8F) were cultured in high-glucose Dulbecco’s modified Eagle’s medium (DMEM), containing 10% foetal bovine serum, 1% penicillin, and streptomycin in a humidified atmosphere of 5% CO2 cells) for 24 h at 37 °C and then co-incubated with FITC-FY-35 or FITC-FL-35 (1.5 μM) for 1 h. The cells were then washed three times with phosphate-buffered saline (PBS) and fixed with 4% paraformaldehyde (PFA) for 8 min. Then, 4,6-diamidino-2-phenylindole and rhodamine B were used to stain the cellular nuclei and cytoskeleton, respectively. Immunofluorescence staining was performed using SR-BI and HER2 antibodies. The cells were fixed with 4% PFA for 8 min, permeabilised with 0.1% Triton™ X-100 for 15 min, and blocked with 2% bovine serum albumin (BSA) for 1 h at room temperature. The cells were then co-incubated with the SR-BI antibody  or HER2 antibody  overnight at 4 °C. After the standard washing process, the cells were co-incubated with rabbit anti-goat IgG H&L (ab150141) at a dilution of 1:1000 for 45 min at room temperature. All the above-mentioned staining processes were conducted away from light. Confocal images were acquired using a confocal laser scanning microscope . Imaging was performed using ZEN 2.3 lite . Quantification of mean fluorescence intensity (MFI) was conducted using Image J 2.X .Confocal imaging was performed to explore the targeting efficiencies of FY-35 and FL-35. The 5-8F cells were cultured on confocal plates (500 μL of DMEM containing 5 × 103 cells/mL) for 24 h at 37 °C. When the cells reached the desired density, cells in the six plates were co-incubated with FITC labelled FY-35 or FL-35 at six concentrations  for 1 h. Before flow cytometry analysis, the cells were washed three times with PBS, dissociated from the wells with trypsin–ethylenediaminetetraacetic acid (EDTA), and then resuspended in PBS. Cell counting was conducted using a flow cytometer  with an excitation wavelength of 488 nm for FITC (525/30 emission filter). The data were analysed using FlowJo software .The 5-8F cells were cultured in 6-well plates (1.2 × 106 in 200 μL PBS) in the lower right flank. Experiments were started 10–14 days after tumour implantation, when the tumour diameter was 6–8 mm. Tumour volumes were measured using a Vernier calliper and calculated using the formula for a hemiellipsoid (volume = 0.5236 × length × width2), as this form best approximated the tumour shape [5 5-8F-fLuc cells into the nasopharynx using a 28-gauge needle, as previously reported [® Spectrum In Vivo Imaging System . Specifically, mice received an intraperitoneal injection of 3 mg/mL luciferin bioluminescent substrate  4 min before imaging.Animal experiments were performed in accordance with the approval of Animal Welfare and Ethics Committee of Jinan University . Four-week-old BALB/c nude mice were purchased from the Beijing Vital River Laboratory Animal Technology Co., Ltd. . Subcutaneous tumour models received a subcutaneous injection of 5-8F (5.0 × 10ur shape . For ortreported . Mice wen = 3 per group). The three groups received intravenous (i.v.) injection with 12 μM FY-35 , 12 μM FL-35 (single-target dye), and equimolar quantities of free dye, respectively. Fluorescence images were acquired pre-, 2 h, 6 h, 10 h, and 24 h post-injection. The mice in each group were euthanised. The heart, lung, liver, pancreas, spleen, kidney, intestine, and tumour tissues were collected for ex vivo imaging. The MFI was analysed to determine organ biodistribution and tumour selectivity in the three groups. The TBR was calculated by drawing regions of interest within the tumour region and ipsilateral auricle of each mouse.Mice with subcutaneous 5-8F tumours were randomly divided into three groups (n = 8) were injected with 12 μM FY-35, and imaged at 24 h post-injection to measure MFI in the tumour region. A linear regression model was used to demonstrate a linear relationship between tumour volume and MFI. To confirm the feasibility of IR800-FY-35 for detecting residual tumours, mice with orthotopic tumours (n = 5) were intravenously injected with 12 μM IR800-FY-35. Fluorescent images at various time points  were acquired with a 745-nm excitation wavelength and 800-nm filter using the IVIS® Spectrum In Vivo Imaging System . After 48 h post-injection, the mice were sacrificed. The orthotopic tumours and main organs were imaged ex vivo. To simulate salvage surgery in patients with NPC, we performed tumour resection on the sacrificed mice. Repeated imaging was performed to identify residual signals. The resected tumours were embedded in optimal cutting temperature (OCT) and stored at −80 °C. Serial sections were cut at a thickness of 10 μm for fluorescence imaging using an inverted microscope , and 4 μm for haematoxylin–eosin (H&E) staining.To identify the minimal size of detectable tumours, subcutaneous tumours of different sizes  and IRDye800 CW, which are the two major contributors of the photoacoustic signal.Three-dimensional (3D) volumetric optoacoustic imaging  was performed using a 384 ultrasound transducer with a centre frequency of 10 MHz organised in a hemispherical array with a radius of curvature of 4 cm. During the entire scanning, the mice were anaesthetised with an isoflurane-oxygen mixed gas . Tumours were imaged at multiple wavelengths . Raw data were reconstructed using the ViewMSOT software . We implemented spectral unmixing to resolve oxyhaemoglobin  with the advantage of convenient operation. The FMI intraoperative system is a dual-mode imager that combines the following two systems: NIR fluorescent imaging to detect targeted cancer cells, and visible-light reflectance imaging to observe the contours of the tissue itself. This system improves the image quality via feature point algorithms and allows rapid and precise imaging fusion for two cameras . Surgicat-test or a chi-square test. Simple linear regression was used to estimate the relationship between two quantitative variables. Here, p < 0.05 was considered significant.Statistical analysis was conducted using GraphPad Prism . Data are reported as mean ± standard deviation. Comparative analysis was performed using an independent two-sample p = 0.0001). Immunofluorescence staining demonstrated stable co-expression of SR-BI and HER2 in 5-8F cells, providing the basis for effective targeting of the two tracers. The flow cytometry results further validated the findings of confocal imaging  with equal average tumour burden  of different sizes (1–7 mm) were injected with equivalent IR800-FY-35 and imaged at several time points. The MFI in the tumour region at the 24 h time point was recorded in each mouse, and then a linear regression model was performed to exhibit a linear relationship between the tumour volumes and MFI. We observed a linear relationship between these two variables (Y = 7.178 × X-41.31)  . The MFIs 3.9 mm a.n = 5) was constructed by injecting 5-8F-fLuc cells into the nasopharynx and experimented when the bioluminescent signal reached 108. Considering that the parotid gland presented apparent probe uptake  was IV injected with IR800-FY-35, and image-guided resection was conducted using both photoacoustic and fluorescence imaging. The 3D volumetric optoacoustic imaging was performed to clearly visualise the tumour vessels at 24 h after administration  that targeted HER2/SR-BI, and confirmed its superior targeting efficiency and longer retention in NPCs, with the contrast being improved 2.3-fold at 24 h post-injection and the retention time extended up to 48 h, when compared to a single-targeted tracer (IR800-FL-35). These results reveal the potential for IR800-FY-35 to be utilised for preoperative detection and to guide intraoperative resection of NPCs. Although it is not technically feasible to perform salvage surgery in live mice with orthotopic NPC, resection surgery on the executed mice with orthotopic tumours simulated the difficulty of residual tumour visualisation under white light and identified the feasibility of IR800-FY-35 in detecting minimal residual tumours. Moreover, with the good performance of vascular network mapping by 3D volumetric optoacoustic imaging, surgical excision of subcutaneous NPC tumours was successfully achieved with the guidance of our intraoperative FMI system.Despite advancements in NPC therapy, approximately 10% of patients develop residual or recurrent disease; the genomic landscape of rNPC is complex, with enriched mutations leading to enhanced tumour heterogeneity . The duaExcept for superior targeting efficiency, longer retention in the tumour region can provide a one to two day window that offers flexibility in scheduling surgical procedures. There are many platforms for tumour-targeted fluorescent probes . BesidesThe imaging strategy used in our study has the potential for translation into clinical practice. First, both fluorescent and optoacoustic imaging systems were approved by the US Food and Drug Administration. Second, a fibre-delivered optoacoustic guide was previously reported, which mimicked the traditional guide wire and allowed intraoperative placement into the tumour mass to visualise the tumour with sub-millimetre variance . ConsideThere are several limitations in our study. Firstly, we only selected the peptide FL-35 that had the same molecular weight as FY-35, but only targeted SR-BI as a single-target control. To evaluate both, two separate peptides as control would be more persuasive. Secondly, while we successfully performed tumour resection under fluorescent and optoacoustic imaging guidance, there was a lack of analysis concerning the volume of intraoperative bleeding, which would be worthy of testing in our future study.Our data demonstrated the power of the dual-targeted tracer for optoacoustic and fluorescence-guided surgery. Utilisation of this method enables the detection of residual tumours and tumour delineation in NPC in vivo, providing a basis for image-guided surgery. Combining the advantages of optical imaging  with optoacoustic scanning , this method holds promise in guiding salvage surgery for rNPC, which might reduce reoperation rates and shorten surgery time.


Formulating sophisticated fluid therapy plans can be complicated and time consuming. Consequently, veterinarians in the field who lack experience, time, or confidence may formulate suboptimal fluid therapy plans.Compare conventional and app‐guided fluid therapy plans for simulated cases of neonatal calf diarrhea.Third and fourth year veterinary students (n = 55) from The University of Sydney.http://calfaid.com) that was evaluated in a randomized case simulation trial. Participants were instructed to perform fluid therapy calculations and formulate an integrated fluid therapy plan for case scenarios using conventional methods and using the fluid therapy app. Responses were scored by a blinded study investigator using an a priori scoring guide and groups  were compared using linear mixed models.We developed a web app to assist fluid therapy formulation  than calculations completed using the conventional method . On average, total scores for app‐guided integrated fluid therapy plans were 14.2% points higher . Eighty percent of respondents indicated they would prefer to use the app‐guided method over the conventional method.Our findings suggest that fluid therapy plans can be improved using apps. In many cases, affected animals can develop dehydration, metabolic acidosis, and electrolyte imbalances, which can be corrected with fluid therapy. However, the beneficial effects of fluid therapy require that the fluid plan be appropriately designed. For example, a recent studyAfter patient assessment, numerous additional calculations are required to design a fluid therapy plan that includes appropriate fluid types, routes and rates of administration, and additives to facilitate rapid recovery. Consequently, designing an appropriate fluid therapy plan can be challenging and time‐consuming for clinicians with limited experience, and in some situations may lead to the adoption of generic  fluid plans or fluid plans based on erroneous calculations. To simplify the process, treatment guides (flowcharts and tables) have been developed and are found in most veterinary medicine textbooks.Smart phone apps have been developed and validated to assist calculations in clinical environments in human medicine. For example, a recent clinical trial found that Swiss paramedics were 66.5% less likely to make medication errors when using an app to calculate doses of epinephrine, midazolam, 10% dextrose, and sodium bicarbonate for a simulated cardiopulmonary resuscitation scenario for an 18‐month‐old child.2A randomized trial was conducted using an online questionnaire to compare fluid therapy plans formulated using conventional and app‐guided methods. All procedures in the study were conducted in accordance with The University of Sydney Research Ethics Committee (Protocol # 2021/140). Informed consent was obtained from the participants and the questionnaire was voluntary, anonymous, and untimed. It was originally estimated that 50 students would be necessary to demonstrate a 20% point difference in scores for app‐guided (80%) and conventional (60%) fluid therapy plans, assuming a SD of 30%, alpha of 0.05, and power of 0.80.2.1Participants were veterinary students at The University of Sydney in 2021. Students in their fourth year of study  were invited to participate during their livestock medicine rotation  and the third year students  were invited on August 2, 2021 after having completed lectures and examinations in the topic of large animal fluid therapy. The online questionnaire was closed on October 5, 2021. At the time of the study, veterinary students from both cohorts had 1 lecture that was focused on livestock fluid therapy in third year where they learn about fluid types and routes and rates of administration. Students were also taught a systematic approach to performing fluid therapy for calves, including estimation of clinical variables  and a guide to performing calculations . During the clinical rotation in the fourth year, students did not receive structured learning activities in the topic of fluid therapy, but participated in treating clinical cases that presented to the Livestock Veterinary Services at The University of Sydney. The livestock courses and clinical rotations were compulsory for all students, because “tracking” in a specific discipline of veterinary medicine is not available in veterinary schools in Australia.2.2http://calfaid.com) was developed by our group in R.A Shiny web app that helps users formulate fluid therapy plans for dehydrated calves , participants were instructed to perform calculations and to formulate their integrated fluid plan using a “conventional” approach, which included the use of lecture material and textbooks. To facilitate doing so, students were provided with a link to download the lecture slides from their DVM curriculum that provided instructions on formulating fluid therapy plans for calves with diarrhea. For the second case (A or B), students were provided a link to the fluid therapy app and instructed to use it to complete the same tasks that were done for the previous case. No instructions were provided on how to use the app. Case scenarios were designed such that students had the sufficient information in the lecture notes and in the app to score 100% for all questions Figure .After the completion of both cases, participants were asked the following questions with Likert scale responses: “Describe your level of confidence in the accuracy of your calculations for the case that was completed using the conventional method” and “How user‐friendly was the interface for the app?” Students also were asked: “If you were expected to design a fluid therapy plan for a sick calf in the field, which method would be your preference?”2.4The responses from the survey were collated and recorded in Qualtrics and imported into Microsoft Excel  at the end of the study. Participants who did not attempt to answer the questions relating to the case scenarios were excluded from analysis. Scoring guides were created to determine the accuracy of fluid calculations and integrated fluid plans. The investigator who scored responses was blinded to the method used by the participant . Scoring of fluid therapy calculations evaluated the participants' ability to estimate fluid deficits, ongoing losses, maintenance requirements and base deficits. Each component was scored out of a total of 2, with a value of 2 being assigned to responses that were within an a priori range that we deemed to be acceptable, based on our subjective assessment for how effective the fluid therapy plan would be based on calculated outcomes. A value of 1 was given if the response was outside of the acceptable range, but close enough to demonstrate some accuracy in the calculation. A score of 0 was given if the response was outside of the ranges for scores 1 or 2. All ranges were established before data analysis was conducted and are shown in Table Scoring of responses for the integrated fluid therapy plan was done in a similar way to scoring of fluid calculations, except that each component (n = 6) was assigned a score of 0 or 1 Table . The 6 c2.5The 2 major quantitative outcomes in our study were (a) total score for fluid therapy calculations (sum of the 4 components) and (b) total score for integrated fluid therapy plan (sum of 6 components). Total scores were expressed as percentages. For example, a response with the following component scores for fluid deficit (1/2), ongoing losses (2/2), maintenance (2/2), and base deficit (2/2) would have a total score for fluid therapy calculations of 87.5% (7 out of 8).2.6https://rpubs.com/samrowe/fluid_app_2022.Analysis was conducted in R.33.1Fifty‐eight questionnaire responses were returned between March 22 and October 5, 2021, of which 55 were eligible for inclusion into the final dataset. On average, participants were 26.7 years of age at the time of enrollment , 37 (67.3%) were female, and 18 (32.7%) were male. Twenty‐one (38.2%) students were in the third year of their veterinary degree, and 34 (61.8%) were in their fourth year. The response rates from DVM3 and DVM4 students were 17.5% (21/120) and 30.9% (34/110), respectively. Thirty‐three (60%) students indicated that they used apps as part of their study routine. The number of participants who were randomized to complete Case A using the conventional method and Case B using the app‐guided method was 30 (55.5%). The remaining 25 (45.5%) participants completed Case B using the conventional method before completing Case A using the app‐guided method.3.23.2.1Crude average scores for fluid therapy calculations and model‐estimated differences between app‐guided and conventional methods are shown in Table 3.3Crude average scores for integrated fluid therapy plans and model‐estimated differences between app‐guided and conventional methods are shown in Table 3.4When asked “Describe your level of confidence in the accuracy of your calculations” for the case that was completed using the conventional method, participants responded with very high (0%), high (3.8%), moderate (45.3%), low (39.6%), and very low (11.3%). When asked “How user friendly was the interface for the app?,” the responses were very easy to use (34.5%), easy to use (49.1%), neutral (10.9%), hard to use (1.8%), and very hard to use (0%). When asked “If you were expected to design a fluid therapy plan for a sick calf in the field, which method would be your preference?,” 80.0% of respondents indicated they would prefer to use the app‐guided method, 10.9% indicated that they would use a combination of the app‐guided and conventional methods, 3.6% indicated that they would prefer to use the conventional method, and 5.5% of students did not respond.44.1In this randomized trial we found that the use of an app improved the accuracy of fluid therapy calculations and enabled veterinary students to formulate integrated fluid plans that were more closely aligned with best practice, as evidenced by higher scores for fluid therapy calculations  and integrated fluid therapy plans . We are not aware of other studies that have quantitatively evaluated the use of apps to guide fluid therapy in veterinary medicine. However, findings from studies in human medicine are consistent with ours. For example, a recent clinical trialIn our study, the higher score for fluid therapy calculations resulted from higher accuracy when estimating fluid deficits (+25.5%), ongoing losses (+20.9%), maintenance requirements +17.3%), and base deficits  because we could not restrict access to the app once it was provided. It is also important to acknowledge the limitations of using an online questionnaire of simulated cases that was completed by third and fourth year veterinary students as a proxy for fluid therapy plans conducted in the field. First, it is unknown how representative veterinary students are of practicing cattle veterinarians, because veterinary students have considerably less experience. Second, it is possible that written responses to case simulations may differ from how participants would respond if faced with a real case in the field, because it lacks the practical factors that often are present in the clinical context, such as limited time and intrinsic and extrinsic motivations to help the patient and client. Finally, the a priori scoring scheme that we used is likely to be an imperfect quantitative measure of fluid therapy efficacy in the field. For example, it cannot be assumed that a fluid therapy plan that has a score 2 times higher than another plan is going to be 2 times more likely to prevent death in a patient.4.4Field‐based intervention studies should be conducted with practicing veterinarians to see if app‐guided fluid therapy can improve health outcomes and decrease time spent formulating fluid plans. Furthermore, we believe that fluid therapy apps could be developed to incorporate machine learning algorithms to predict base deficits from clinical signs.5In our randomized trial, we found that app‐guided fluid therapy plans were more closely aligned with best practice, as evidenced by higher scores for fluid therapy calculations and integrated fluid therapy plans. Therefore, additional studies are needed to determine if outcomes for calves with diarrhea can be improved using an app‐guided method.The authors developed the app evaluated in this study, but have not, and will not, benefit financially from its use.Authors declare no off‐label use of antimicrobials.Approved by the University of Sydney Human Research Ethics Committee (Protocol # 2021/140).Authors declare human ethics approval was not needed for this study.Data S1 Supporting Information.Click here for additional data file.