Since therapeutic peptides and oligonucleotides are gathering interests as active pharmaceutical ingredients (APIs), nanoparticulate drug delivery systems are becoming of great importance. Thereby, the possibility to design drug delivery systems according to the therapeutic needs of APIs enhances clinical implementation. Over the last years, the focus of our group was laid on protamine-oligonucleotide-nanoparticles , however, the possibility to modify the size, zeta potential or loading efficiencies was limited. Therefore, at the present study we integrated a stepwise addition of protamine (titration) into the formation process of proticles loaded with the angiogenic neuropeptide secretoneurin (SN). A particle size around 130 nm was determined when proticles were assembled by the commonly used protamine addition at once. Through application of the protamine titration process it was possible to modify and adjust the particle size between approx. 120 and 1200 nm (dependent on mass ratio) without influencing the SN loading capacity. Dynamic light scattering pointed out that the difference in particle size was most probably the result of a secondary aggregation. Initially-formed particles of early stages in the titration process aggregated towards bigger assemblies. Atomic-force-microscopy images also revealed differences in morphology along with different particle size. In contrast, the SN loading was only influenced by the applied mass ratio, where a slight saturation effect was observable. Up to 65% of deployed SN could be imbedded into the proticle matrix. An in-vivo biodistribution study (i.m.) showed a retarded distribution of SN from the site of injection after the application of a SN-proticle formulation. Further, it was demonstrated that SN loaded proticles can be successfully freeze-dried and resuspended afterwards. To conclude, the integration of the protamine titration process offers new possibilities for the formulation of proticles in order to address key parameters of drug delivery systems as size, API loading or modified drug release. The formulation of an effective nanoparticulate drug delivery system requires consideration of various physicochemical properties. The therapeutic effect of an active pharmaceutical ingredient (API) is strongly influenced by the size and the surface charge of the delivery system , 2 as weOver the last 15 years, the focus of our group was laid on the formulation of nanoparticulate drug delivery systems based on protamine and oligonucleotides (ODNs), so called proticles . So far,Secretoneurin is a direct angiogenic cytokine consisting of 33 amino acids, which was described first by Kirchmair et al. in 1993 . The actWithin the last years, several drug delivery systems were described for the application of angiogenic compounds. Thereby, different types of nanoparticles were investigated, e.g. protamine/heparin nanoparticles for delivery of FGF growth factor , 17 or cAlthough there have been studies on SN gene therapy , 15, 22,One of the major advantages of proticles is their simple formation process through a self-assembly process based on ODN condensation by the arginine rich protamine . TherefoAt the present study, on the one hand we aimed to successfully imbed SN into the matrix of proticles in order to provide a delivery system for the peptide. Otherwise, we wanted to investigate if the dependency of mass ratio on particle size and surface charge can be minimized. Thus, the approach of a stepwise protamine titration process was introduced to achieve a more controlled proticle assembly and to offer new possibilities in the development of peptide loaded proticle formulations. To sum up, we succeeded the embedding of SN into proticles and were able to show that a stepwise protamine addition can modify the size of proticles without influencing the SN loading capacity of the delivery system. Results pointed out that the alteration in particle size is due to a secondary aggregation of initially-formed particles within the titration process.Secretoneurin (SN) and Alexa Fluor® 647 labeled SN were synthesized and purified by piChem  and provided as freeze-dried product. Full length SN sequence was used as reported by Fischer-Colbire et al: TNE IVE EQY TPQ SLA TLE SVF QEL GKL TGP NNQ . Single Stock solutions for each component were prepared in Milli-Q (MQ) water and stored at -24°C. MQ water (ultra-pure water) was provided by a Milli-Q-Gradient system . In addition, the water was sterilized before usage at 121°C for 20 min.For HPLC measurements, acetonitrile (HPLC gradient grade) was obtained from VWR  and trifluoroacetic acid from Merck . Mannitol was purchased from Carl Roth  and was used as cryoprotectant for lyophilization.The formation of proticles occurs through a self-assembly process based on oligonucleotide condensation by the arginine rich protamine (up to 70% arginine residues ). CondenInitially, SN was added to the ODN dilution and mixed accurately. After 10 min incubation time at room temperature the protamine dilution was added at once or by a seven step titration process. Therefore, the protamine dilution was divided into 7 equal parts and added separately after an incubation time of 10 min. Pre-studies revealed that splitting the protamine solution in more than 7 aliquots will not change the properties of the resulting nanoparticles. When the protamine dilution was added by a single addition the particle characterization was done consequently after incubation of 10 min.The concentration of ODNs in the final particle dispersion was set to 100 μg/ml throughout all proticle formulations. SN and protamine concentrations varied according to the declared mass ratios, given in consecutive order of addition as ODN:SN:protamine. SN varied between 25, 50, 75, and 100 μg/ml in the final particle dispersion and protamine was used in concentrations of either 150 or 300 μg/ml.The lyophilization of the nanoparticles was carried out using a Virtis Sentry freeze-drying unit and 1% (m/m) mannitol as cryoprotectant in order to achieve redispersability of the dried nanoparticles. Briefly, 150 μl of particle dispersion was transferred into 2R crimp vials , followed by freezing in liquid nitrogen at atmospheric pressure and sublimation of water in vacuum below 6 mbar over 24 hrs. Freeze-dried particles were resuspended in 150 μl MQ water to achieve the same particle concentration as before the lyophilization process.The mean particle size , the particle size distribution  as well as the derived count rate (DCR) of particles were determined by dynamic light scattering (DLS), using a Zetasizer Nano ZS  equipped with a green laser (532 nm). The size measurements were performed in a micro cuvette  by non-invasive back scatter mode (automatic mode), detecting the scattered light at 173°. The sample temperature was set to 25°C, and each measurement (including up to 20 sub-runs) was performed at least in duplicate. Results of the size measurements are always given as mean values of the hydrodynamic diameter in nanometer scale. To enable particle characterization throughout the titration process the DLS measurement was started 5 min after the protamine addition to achieve a total incubation time of 10 min between the several titration steps (see above).Further, also the DCR of size measurements was evaluated. The DCR refers to the total intensity of scattered light without attenuation of the light source. As the attenuation factor of the measurement system is included in the DCR, it is calculated from the measured count rate at the detector and the applied attenuation factor , shown iFor zeta potential measurements the samples were diluted 1:5 in MQ water and transferred into a clear folded capillary cell . Primarily, the electrophoretic mobility of the particles was determined by the Zetasizer using Laser Doppler Velocimetry. Afterwards, the zeta potential was calculated from the electrophoretic mobility applying the Henry equation . For allSecretoneurin and protamine loading efficiencies were determined by an indirect quantification method using reversed phase high performance liquid chromatography (RP-HPLC). The particle dispersions were centrifuged immediately after the DLS measurements at 20817 rcf, at 4°C for 2 hrs . Subsequently, the supernatants were transferred and centrifuged again for 2 hrs. SN and protamine concentration in the obtained supernatants were determined using external standards. For each HPLC series at least four different SN and protamine concentrations were prepared as external standards. Thereby, for each concentration two samples were prepared independently and injected twice (at the beginning and at the end of the series). The mean values of the four measurements were used in the calibration line for further determination.A) and the determined unbound concentration in the supernatant (CS).As shown in Our inert HPLC system (Merck Hitachi) was equipped with a D-7000 Interface, L7200 autosampler, L-7120 pump and L-7300 column oven. The column temperature was set to 30°C using a Zorbax Extend C18 column for separation . The elution of the compounds was carried out by a water/acetonitrile gradient (96.5:3.5 to 33.5:66.5 within 15 min) with a constant flow rate of 1 ml/min. To avoid peak tailing 0.075% (v/v) trifluoroacetic acid was added to the mobile phase. Detection was carried out at 215 nm using an L-7400 UV-detector.HPLC pre-tests pointed out that SN was partly remaining in the system at higher concentrations, and eluted with the following injection (carry-over). The same behavior was observed with a modified HPLC method reaching 98% acetonitrile at the end of the gradient. However, carry-over was especially observed when no or low concentrations of protamine were present in the measured sample. Therefore, all samples as well as the external standards were spiked with 75 μg/ml protamine to avoid undesired carry-over of SN and to achieve equal sample preparation. The positive effect of the protamine addition is most probably referred to an ion-pair formation of the positively charged protamine and negatively charged SN. However, the mixture of 75 μg/ml protamine and different SN concentrations did not show turbidity or aggregation, and the single peptides were well-separated by the applied method.Before the AFM measurements the particle dispersions were diluted 1:10 in MQ-water in order to enable the detection of single nanoparticles. The diluted dispersions were dropped on a silicon wafer  and dried overnight at room temperature. To guarantee suitable wafer coating AFM test measurements were performed. Consequently, the wafer was dried again for 2 days under vacuum at room temperature to remove remaining water.AFM images were recorded using a Nanosurf AFM with an Easyscan 2 controller . All measurements were performed at non-contact mode with a Tap190Al-G cantilever . Further, image analysis and determination of particle dimensions was accomplished using Imaris 7.3.0  and compared to results from DLS measurements.For the in vivo biodistribution scan SN was labeled with fluorescent dye Alexa Fluor® 647 and applied either in solution or assembled into the proticle matrix. Alexa Fluor® 647 is known for unusually low fluorescence quenching upon protein conjugation , and wasHydrodynamic diameters from proticles assembled by different preparation methods were analyzed by one-way ANOVA  to verify statistical significance. F-test was performed whether equal or unequal variances had to be assumed followed by a student’s t-test (two-tailed) to compare mean values. A p value < 0.05 was considered to be statistically significant different.The characterization of the SN-proticle formulations focused on the mean particle size , the particle size distribution  and SN loading. Various mass ratios were applied by adding protamine in a single step or by a stepwise titration process in order to verify the effect of the manufacturing process and the mass ratio on size and loading efficiencies.Mean hydrodynamic diameters around 120 nm were recorded when 300 μg/ml protamine was applied by a single addition  was measured for formulations with 25 μg/ml and 100 μg/ml SN assembled by single protamine addition to cover the highest and lowest SN concentration. Our nanoparticles showed ZPs higher than +40 mV pointing out a highly positive surface charge. For comparison of the different preparation methods, ZPs were also determined for particles with 100 μg/ml SN assembled by protamine titration. Thereby, even slightly higher ZP values were recorded.Proticles without SN were prepared in order to investigate the self-assembly and especially the titration process regardless of a third component. Applying 150 μg/ml protamine, no significant difference in size was obtained, whether protamine was added by a titration process (224 ± 5 nm) or a single addition (233 ± 2 nm). However, formulations with 300 μg/ml protamine showed a different performance. Now, a single protamine addition resulted into smaller nanoparticles with a ZAve of 140 ± 4 nm, whereas particles prepared by titration showed much higher values of 476 ± 103 nm. Recorded PdI values around 0.2 were similar to particles with SN, but after titration of 300 μg/ml protamine higher values of 0.47 ± 0.06 were observed.Generally, particle formation only occurred when protamine and ODN were present in the formulation. A mixture of 100 μg/ml SN and 300 μg/ml protamine did not result in turbidity and showed a low DCR of 1,183 ± 592 kcps. Similar values were recorded for mixtures of ODN and SN, which are presented in later sections.In general, the preparation method showed no influence on the SN loading of the proticles. In contrast to the particle size measurements mentioned above, all mass ratios showed similar loading efficiencies whether protamine was added at once or by a stepwise titration process . FurtherThe highest SN loading efficiency was determined at the mass ratio of 1:0.25:1.5 (ODN:SN:protamine). Using the titration process 69 ± 1.5% of SN was imbedded into the particle matrix and 61 ± 6% when protamine was added in a single step . HoweverThe same influence of SN concentration was observed for particles with 300 μg/ml protamine , howeverThe evaluation of the protamine loading efficiency pointed out that around 35% of the deployed protamine was incorporated at formulations with 300 μg/ml protamine. With a protamine concentration of 150 μg/ml, a protamine loading around 76% was determined. This again indicated a saturation of peptide loading, which is comparable to SN. Remarkably, the protamine loading into the proticles was influenced by neither the assembly method nor the SN concentration. Even without SN a similar amount of protamine was assembled when 150 μg/ml were applied.As already shown above, the stepwise titration process resulted in larger mean particle sizes compared to a single protamine addition. Therefore, the progression of the particle size along with consecutive titration steps was investigated in detail. Our results indicated a correlation between the mean particle size and the derived count rate (DCR) of DLS measurements . As the In our study we determined the nanoparticle assembly  already after the first titration step, regardless of protamine or SN concentration. The initial mixture of ODN and SN did not result in any kind of nanoparticulate formation, indicated by a lack of turbidity and a very low DCR see . FurtherBy titration of 150 μg/ml protamine in total, the particle size remained constant within the first three steps  the biodistribution of the peptide was observed in vivo. Therefore, SN was applied in solution as well as assembled within proticles. The proticle formulation with mass ratio 1:0.25:1.5 prepared by protamine single addition was chosen because of the highest SN loading efficiency. Therefore, only a low amount of unbound SN should be present and misinterpretation of non-assembled signal emitting peptides was minimized. Because of the low injection volume for i.m. administration in mice, the concentration of SN was set to 50 μg/ml in order to generate a sufficient fluorescent signal (ODN and protamine was adjusted according to given mass ratio). These particles showed ZAve values of 657 ± 78 nm with a narrow size distribution, indicated by PdI of 0.05 ± 0.02. Basically higher ZAve values were recorded compared to particles without the fluorescent dye. This difference in particle size can be the result of the employed fluorescent dye, but also from the higher concentration of the components. However, the difference is only less important for the obtained results of the biodistribution scan, because SN in solution is generally compared to a nanoparticulate formulation and not to a certain particle size. For each picture a second mouse was used as blank signal to monitor possible auto-fluorescence.The biodistribution scan pointed out that SN was remaining longer at the site of injection when assembled within proticles, whereas the application of SN in solution resulted in a more diffusive pattern  or higher, regardless of a phosphate or phosphorothioate backbone . At presThe difference in particle size between the two preparation methods was most probably due to secondary aggregation during the stepwise addition of protamine (titration). The correlation which was found between the hydrodynamic diameter and the derived count rate pointed out that the initially-formed particles within the first titration steps were aggregating towards bigger assemblies.DLS measurements revealed that particles were assembled even at very low protamine concentration, also visualized by turbidity. The particle formation already occurred after the first protamine addition when 150 μg/ml protamine were added by titration, which corresponds to a mass ratio of 1:0.21 (ODN:protamine). This mass ratio pointed out that particle assembly was possible even at lower mass ratios than previously described , 38. By In detail, not all ODN molecules were condensed into nanoparticles after the first titration step and were compacted by further protamine addition. This was also supported by findings of previous studies, where it was shown that unbound ODNs were present at a mass ratio of 1:0.5 (ODN:protamine). Further, zeta potential remained constantly negatively charged until secondary aggregation occurred. A negative surface charge of the nanoparticles is in line with previous studies on proticles assembled with an excess of ODN over protamine , 38. DurThe formation of secondary assemblies was related to a calculated n/p (+/-) ratio of 1.48. Thereby, the molecular weight of the components was considered as well as 21 arginine residues per protamine molecule  and 18 pIn our study, the particle size of the secondary assemblies was mainly influenced by the applied SN and protamine concentrations. Higher concentrations of SN showed a more evident increase in particle size and protamine concentration of 300 μg/ml also resulted in a higher particle size than 150 μg/ml. In addition, this was also shown for a stepwise addition of protamine to ODN (without SN). The amount of unbound biomolecules probably regulated the growth of the secondary assemblies by acting as a linker between the initially-formed particles. The protamine titration process enabled the modification of the particle size through a more controlled proticle assembly. The protamine addition in a single step basically showed similar ZAve values at all mass ratios (except 1:1:1.5). However, the titration process showed a slight increase in particle size (170–280 nm), as well as intermediate (480–650 nm) and high particle sizes (> 1000 nm).The secondary aggregation of pre-formed particles was also indicated by the extensive decrease in the DCR. As the DCR was compared between different particle sizes, scattering theories had to be considered. Generally, Mie theory describes the relation between the total scattering intensity and particle size, which is roughly equivalent to the wavelength of the light source. Thereby, the scattering intensity increases less with particle size  and is also dependent on the applied wavelength, the scattering angle and the refractive index . Mie theLyophilization studies pointed out that SN-proticle formulations showed both, an increase in mean particle size after resuspension, as well as smaller particles. Thereby, particles around 125 nm tend to increase in particle size after resuspension. This is in line with results from other research groups, which also showed that the particle size could be reduced by sonication afterwards , 44. SadOn the other hand, SN-proticle formulations about 1030 nm showed a decrease in mean particle size after resuspension and high polydispersity. This indicates that the secondary aggregates, which were formed during the titration process, partly disassembled (most probably during resuspension). In both cases, the loading efficiencies of the components were similar to values before lyophilization. This again indicated that the loading efficiencies are mostly dependent on the mass ratio, as already discussed.Concerning a favoured depot effect, in vivo images of SN-proticle formulations showed a closer and more retarded distribution pattern of SN than the control solutions. After 3 hours, there was still a detectable amount of fluorescently labeled SN at the site of injection when a SN-proticle formulation was applied. At the same time, no signal could be recorded after the administration of labeled SN in solution (control). However, the observed depot effect (i.m.) was not as obvious as in one of our previous distribution study after subcutaneous (s.c.) injection of peanut allergen Ara h 2 . The difTo conclude, the integration of the protamine titration process into the assembling of proticles demonstrated that the size of the resulting particles can be adjusted without influencing the loading efficiencies of secretoneurin. The particle size was mainly influenced by the applied formation method, but SN loading was only depending on the mass ratio of the components. Up to 65% of deployed SN could be successfully assembled into the proticle matrix and a basic approach of a depot effect in vivo was observable. In addition, lyophilization of proticles was shown for the first time. Due to the possible modification of the physicochemical properties various pharmacokinetic aspects like initial dose and modified drug release can be considered for the application of SN-proticle formulations.S1 Fig(PDF)Click here for additional data file.S2 Fig(PDF)Click here for additional data file.


The Funding statement is incorrect. The correct statement is: This work was supported by Ministry of Higher Education FRGS grant (FP012-2015A) and University of Malaya Prototype Research Grant Scheme (PR002-2015B).


Underwater ultrasonic transmissions for fluid-solid and air-solid phononic brass plates are reported in this work. Although the structure is roughly the same, experimental results show very different behaviour between fluid-solid and air-solid phononic plates, due to most of the properties of the fluid-solid perforated plates rely on Fabry-Perot resonances, Wood anomalies and Lamb modes. In air-solid phononic plates Fabry-Perot resonance is highly attenuated due to impedances difference between air and water, and therefore some transmission modes are now distinguishable due to surface modes coupling. S0) Lamb wave mode thanks to strong reflection in acoustic band gaps [At the end of the 19th century Lord Rayleigh ,3. Conceand gaps .On the other hand, a periodically perforated plate structure has been brought into focus while researching on the acoustic counterpart of Extraordinary Optical Transmission ,12. ResoIn this letter we provide experimental results for fluid loaded fluid-solid and air-solid phononic plates. Angle resolved transmission measurements of underwater ultrasound reveal key aspects of the different behaviour of phononic plates having fluid or air inclusions.Underwater ultrasound has been chosen to measure the acoustic transmission through perforated plates. The geometrical parameters to describe perforated plates are the diameter of the hole d, the array periodicity a and the plate thickness h. The experimental setup is based on the well-known ultrasonic immersion transmission technique. This technique makes use of a couple of transmitter/receiver ultrasonic transducers. Two different couples of transducers were used: one couple with a center frequency of 250 kHz and a frequency range between 155–350 kHz and the other couple with center frequency of 500 kHz and a frequency range between 350 and 650 kHz. Each transducer was located at a distance larger than that of its nearfield distance (43 mm) from the plate and aligned with respect to the plate. A pulse is launched by the emitter piston transducer through the inspected plate. Then, the signal is detected by the receiving piston transducer and acquired by the pulser/receiver, post amplified and digitized by a digital PC oscilloscope . Time domain data is finally analyzed after averaging 100 different measures and deleting unwanted reflections by means of a time window. The transmission spectrum is then calculated from the power spectrum of the signal normalized with the reference signal power spectrum measured without the sample plate. Typically, angle dependent measurements were done in angle steps of 1° and comprising from 0° to 60°.3, cl = 5670 m/s, tc = 3230 m/s) and 2 mm thickness, immersed in water .The measurements were made using brass plates with 350 mm in width and 450 mm in length  the Fabry-Perot full transmission at k0·a/π = 1.2 and Wood anomaly can be clearly seen both thickness at k0·a/π ≈ 2. However, the modes appearing from the bottom of the figures are not predicted by the Wood anomaly and are related to leaky surface modes. These surface modes are leaky Lamb modes observed in the homogeneous plate  with respect to the forward direction of the plane wave. Clearly these eigenmodes produce poor fluid-solid coupling and lead to non-radiative bands, while symmetric eigenmodes  produce defined transmission lines.To analyze this fact, we calculate the displacement of the unit cell in the The results presented in this letter give a wide description of the phenomena involved in phononic plates as they also includes the coupling with the surrounding fluid. The fluid-solid phononic plates behavior is mainly governed by holes resonances and coherent diffraction effects which interact with Lamb-like modes. However, in air-solid phononic plates, zero order Lamb modes, Scholte-Stoneley mode near grazing incidence, Wood anomalies and new transmission modes are clearly distinguishable while the Fabry-Perot resonance was highly attenuated due to the impedance difference between water and air. It has been reported here that these differences are due to antisymmetric eigenmodes produce poor fluid-solid coupling and lead to non-radiative modes, while symmetric eigenmodes has high fluid-solid coupling and lead radiative modes.


Explore the heterogeneity in dynamics of tumour response to vemurafenib, dabrafenib and trametinib using routinely collected clinical trial imaging data.Time-series imaging data from the phase III studies of vemurafenib, dabrafenib and trametinib were collected through a data repository. A mathematical model based on basic mechanisms of tumour growth was placed within a statistical modelling framework to analyse the data.The analysis revealed: (1) existence of homogeneity in drug response and resistance development within a patient; (2) tumour shrinkage rate does not relate to rate of resistance development; (3) vemurafenib and dabrafenib, two BRAF inhibitors, have different variability in tumour shrinkage rates.Overall these results show how analysis of the dynamics of individual lesions can shed light on the within and between patient differences in tumour shrinkage and resistance rates, which could be used to gain a macroscopic understanding of tumour heterogeneity.The online version of this article (10.1007/s00280-017-3486-3) contains supplementary material, which is available to authorized users. Tumour heterogeneity at the molecular level is known to exist not only between patients but also between lesions within a patient and within an individual lesion –3. At thIn most cancers, the response of a tumour to treatment is predominantly measured through quantifying images taken of it over time. A standardised methodology to quantify patient response to a treatment that is routinely applied in clinical trials is RECIST. The criterion involves taking information at the individual lesion level and combining it to produce a single value, response category, at each imaging visit for a patient in the following way. The tumours within a patient are first classified as either target or non-target lesions based on whether a lesion is repeatedly measurable or not. Target lesions are then recorded quantitatively by taking the longest diameter of each of them and summing them together to produce the sum of longest diameters (SLD) value at each imaging visit. Non-target lesions are not recorded quantitatively but are recorded qualitatively by assessing whether they have disappeared, still visible/partially shrunk but not grown or experienced unequivocal growth. The information on target lesions, non-target lesions and whether a new lesion has occurred is combined, such that at each visit the patient is placed into one of the following four categories: complete response (CR), partial response (PR), stable disease (SD) or progressive disease (PD). This categorisation scheme is further simplified by combining CR and PR to create the objective response rate (ORR). Once a patient enters the PD category or the patient dies, all imaging stops. This brief introduction to the RECIST criteria clearly highlights that quantitative information at the individual lesion level, through measurement of the target lesions, is available. It is this information that can be leveraged to explore quantitatively the dynamics of response and resistance of tumours at both the between patient and within patient level.The goal of this study is to explore the variability in the dynamics of the time-series of these target lesions under treatment. This will be done by placing a mathematical model of tumour growth within a statistical framework used routinely for population analysis. The model and statistical framework will allow us to explore the following three biological questions: (1) is there a degree of correlation in the dynamics of tumour size within a patient; (2) if so what is the difference in-between and within patient variability in tumour shrinkage and resistance rates; (3) is there a correlation between tumour shrinkage and resistance rates at either the individual lesion level or patient level. The framework described in this study is applied to three treatments currently used within the metastatic melanoma setting, vemurafenib (BRAF/CRAF inhibitor) , 7, dabrData from the vemurafenib , dabrafeThe choice of growth law to be used to analyse the data was based on prior knowledge of our understanding of tumour growth based on empirical observations and biological understanding.td, then the total number of growing cells will double every td hours, so their volume will be given by If cells have a cell cycle length While this suggests that tumour volume will grow in an exponential or modified-exponential fashion , it has d, which is assumed to be small relative to the radius r, and is growing at a rate a, then the volume of the layer is approximately  to tumour growth, we, therefore, need just two additional parameters, which are the thickness of the growing layer d, and the initial radius R0. The linear growth in diameter translates to cubic, rather than exponential, growth of the tumour volume.To translate from cell population growth . Also, it does not account for the saturation observed at larger volumes, therefore, only applies for tumours of intermediate size. We assume that the linear equation holds for tumour shrinkage as well as tumour growth; this seems justifiable given that, for the tumour to shrink, dead cells need to be removed, which to a first approximation can be modelled as a linear process. Most relevantly for this study, as with any other simple growth law, it does not account for the effects of resistance. As seen next, we have, therefore, modified it in the simplest way possible, by introducing a separate linear growth rate for the resistant phase.Individual lesion time-series were modelled using a piecewise linear model, and this was done in two parts. In the first part, we treated each lesion as being independent from each other, i.e. we did not account for which patient the lesions belonged to. This model was represented by the following pair of equations, j represents each lesion , subscript k represents each time-point , Ljk and ejk are the longest diameter and residual error, respectively, for lesion j at time k, BSLj, dj and gj are the initial longest diameter value, decay rate and re-growth rate, respectively, for lesion j. The switching time-point, sp, represents the switch from decay to re-growth. The value of sp was determined in the following way due to identifiability issues with allowing it to vary across lesions. We created a small set of possible sp values, day 63, 116 and 179, by taking the mid-point between on-treatment imaging visit time-points, on days 42, 84, 147 and 210. For each sp value, we fitted the pair of linear equations and chose the sp value which gave the best fit according to the log-likelihood; higher log-likelihood implies better fit. This approach gives an approximate switching time-point rather than an exact value.where subscript i, which represents each patient , The second part involved accounting for which patient the lesions belonged to. This was done by modifying the above pair of equations by introducing a new level of hierarchy Both models were placed within a mixed effects statistical framework. This approach assumes that the individual effects (random effects component) do not correlate with the independent variables. Within this analysis framework, the parameter BSL was assumed to follow a log-normal distribution, chosen to ensure positivity of lesion size values, and all other parameters assumed to be normally distributed. Furthermore, all the random variables were assumed to be independent. The within and between patient variability in decay and re-growth rates was explored through the distribution of the model parameters, using the coefficient of variation (standard deviation divided by the mean).nlme package used for the mixed effects analysis.All analyses were done in R v 3.0.2 with the The imaging characteristics of all the patients used in the analyses here can be seen in Table The time-series of the individual longest diameters for all lesions across the three studies can be seen in Fig. The piecewise linear models for the individual lesion time-series described in the Methods section were fitted to tumour data, and the final models (used throughout the rest of the study) were chosen based on the higher log-likelihood . The fits to the final piecewise linear model for each study, can be seen in Fig. Having established that the extra information on which lesion belongs to which patient is important, we next explore the between and within patient variability of tumour decay and resistance growth rates through model parameters, see Fig. Fitting the best model (as determined by the log-likelihood) to clinical data, we obtained that the switching point between tumour decay and re-growth, at 63 days, is the same for all drugs. It must be noted that this does not imply that the switch from the decaying and re-growth phase is not the same across lesions/patients, just that from a population perspective this was an optimal value. The value of 63 days is in-between the first, week 6, and second, week 12, on-treatment imaging visits; see Supplementary Tables S1, S2 and S3 for log-likelihood values at other time-points.Overall, these results show that the piecewise linear model highlights both qualitative and quantitative differences between these drugs, when comparing both between and within patient variability of tumour size dynamics.r2 < 0.1). These findings suggest that how quickly a tumour shrinks under treatment has no relationship to how quickly resistance within that lesion occurs for any of the drugs.The final question to address in this study is whether there is any correlation between the decay rate and re-growth rate of tumour lesions. For vemurafenib, no distribution was required for the re-growth rate in the final model  , dabrafeTo analyse the target lesion size time-series data, we derived an empirical model based on biological observations and mechanistic insights on tumour growth. The empirical model, which was piecewise linear, was then placed within a mixed effects framework to analyse the data. The main results of the analysis were:Knowing which lesion belongs to which patient improved our ability to describe the data over assuming all lesions are independent of each other.The within and between patient variability in decay rates is different for all three drugs.For the re-growth rate, no variability was required for vemurafenib, and the within and between patient variability was similar for trametinib and dabrafenib.Finally, no correlation was found between target lesion shrinkage and resistance growth rate.The first result suggests that although there is heterogeneity in the dynamics of tumour size over time, there is also some degree of correlation in these dynamics across lesions within a patient. This suggests that there may be a degree of homogeneity across lesions, which is likely the result of the system-level effect that the drug has on the patient . This system-level effect seems to be more pronounced in dabrafenib and trametinib (low tumour shrinkage variability) and less pronounced in vemurafenib (high tumour shrinkage variability). These conclusions are relevant in the context of recent studies  which shThe differences seen across treatments, in terms of shrinkage and resistance dynamics (points 2 and 3), could be attributed to the fact that these drugs have different pharmacological profiles. Indeed, there have been reports highlighting the subtle difference between the two BRAF inhibitors, vemurafenib and dabrafenib, both preclinically and clinically –23. OverThe final result was that there was no correlation between the rate of tumour shrinkage and the growth rate of the resistant clone. This result is quite important as it highlights that the rate at which drug-sensitive cells are killed has no bearing on how quickly a resistant clone will grow. This result could have implications for how these drugs and maybe new treatments are dosed. That is there may be no need to use doses and schedules that aim to eradicate tumour cells quickly. This could lead to treatments being less toxic to a patient and increase the options for combination therapies.This study is not without its caveats. The model used to analyse the dynamics was unable to accurately estimate the switching point from decay to re-growth due to identifiability issues related to the sparseness of the data. Thus, exploring the variability in this switching point across lesions and patients was not possible and is likely to be an issue with other clinical imaging datasets too given the study design here is typical of the field.In summary, the mathematical modelling and analysis approach undertaken here highlights how more information can be gained from routinely collected clinical data. We hope this encourages the community to consider analysis at the individual lesion level in addition to the patient level results that are routinely reported.Below is the link to the electronic supplementary material.Supplementary material 1 (DOCX 28 KB)


Cachexia is one of the most important causes of cancer-related death. Supplementation with branched-chain amino acids, particularly leucine, has been used to minimise loss of muscle tissue, although few studies have examined the effect of this type of nutritional supplementation on the metabolism of the tumour-bearing host. Therefore, the present study evaluated whether a leucine-rich diet affects metabolomic derangements in serum and tumour tissues in tumour-bearing Walker-256 rats .1H-NMR as a means to study the serum and tumour metabolomic profile, tumour proliferation and tumour protein synthesis pathway.After 21 days feeding Wistar female rats a leucine-rich diet, distributed in L-leucine and LW-leucine Walker-256 tumour-bearing groups, we examined the metabolomic profile of serum and tumour tissue samples and compared them with samples from tumour-bearing rats fed a normal protein diet . We utilised Among the 58 serum metabolites examined, we found that 12 were altered in the tumour-bearing group, reflecting an increase in activity of some metabolic pathways related to energy production, which diverted many nutrients toward tumour growth. Despite displaying increased tumour cell activity , there were no differences in tumour mass associated with changes in 23 metabolites  in the leucine-tumour group. This result suggests that the majority of nutrients were used for host maintenance.A leucine rich-diet, largely used to prevent skeletal muscle loss, did not affect Walker 256 tumour growth and led to metabolomic alterations that may partially explain the positive effects of leucine for the whole tumour-bearing host. Cancer is a worldwide health problem associated with an increasing number of deaths every year. Cachexia is one of the leading causes of death in cancer patients, accounting for nearly 30 % of such cases –3, and iCancer cachexia also leads to metabolic derangements, and an increasing number of studies are emerging that examine altered metabolite profiles associated with various diseases, especially for cancer-associated cachexia . Given t1H NMR metabolomic profile (serum and tumour tissue) to evaluate the therapeutic effect of a leucine-rich diet in rats bearing Walker 256 tumours, which offer an experimental model of cachexia [Because cancer cachexia promotes metabolic alterations that lead to poor quality of life, it is imperative to increase the number of studies on and treatments for cachexia to improve patient care. One promising area of research is related to the use of nutritional supplementation to counteract physical changes accompanying disease . For exacachexia . In thisad libitum. Semi-purified diets were constructed in accordance with American Institute of Nutrition  for a protein content of approximately 18 %. All components of the diets are presented in Table Female Wistar rats  weighing approximately 265 ± 10 g were housed in collective cages under controlled environmental conditions . The animals were monitored daily, weighed 3 times/week and received food and water  while t were injected subcutaneously into the right flank of the experimental rats on the first day of the experiment. The general guidelines of the UKCCCR  [This study employed the Walker 256 tumour, which is widely used as an experimental model of cancer cachexia syndrome. Walker 256 carcinoma cells   regardinn = 9) and W, Walker 256 tumour-bearing group (n = 9), while the other two other groups were fed a leucine-rich diet (18 % protein + 3 % leucine): L, leucine control group (n = 8) and LW, leucine Walker 256 tumour-bearing group (n = 9). All rats were monitored and weighed 3 times/week. At the end of the nutritional supplementation period, i.e., 21 days after tumour evolution, the animals were sacrificed without an overnight fast, their blood was collected, and tumours were resected and weighed. Blood samples were centrifuged at 1000 × g at 4 °C for 10 min and serum was stored at −20 °C for metabolomic analyses. The tumour tissue samples were frozen directly in liquid nitrogen and stored at −80 °C for metabolomic assays, western blotting and immunochemistry.Thirty-five animals were randomly distributed into four experimental groups according to tumour implant status and nutritional leucine supplementation: two groups were fed a control diet (18 % protein): C, control group , phosphate buffer  and 0.5 mM TMSP-d4 (3-(trimethylsilyl)-2,2',3,3'-tetradeuteropropionic acid from Sigma-Aldrich), then transferred to a 5-mm NMR tube  for immediate acquisition.Plasma samples were filtered through a Microcon YM-3 column  with a 3-kDa membrane centrifuge filter for serum recovery (at 4 °C). Serum (0.2 mL) was diluted in an aqueous solution (0.6 mL) containing 10 % (v/v) deuterium oxide  was collected and dried in a vacuum concentrator . The remaining solid phase was rehydrated in 0.6 mL of D2O-containing phosphate buffer  and 0.5 mM of TMSP-d4. Samples were added to a 5-mm NMR tube for immediate acquisition.Tumour samples were processed following Le Belle and colleagues’ protocol . Briefly1H NMR spectra of samples were acquired using a Varian Inova NMR spectrometer  equipped with a triple resonance probe and operating at a 1H resonance frequency of 500 MHz and constant temperature of 298 K (25 °C). A total of 256 free induction decays were collected with 32-k data points over a spectral width of 16 ppm. A 1.5-s relaxation delay was incorporated between scans, during which a continual water presaturation radio frequency (RF) field was applied. Spectral phase and baseline corrections, as well as the identification and quantification of metabolites present in samples, were performed using Chenomx NMR Suite 7.6 software .2O2 for endogenous peroxidase activity blockade. The sections were then permeabilised for 1 h with 0.1 % Tween® 20 and 5 % of fat-free milk in TBS. The sections were then incubated with a rabbit monoclonal anti-Ki67  antibody at 4 °C overnight and, after this period, incubated with anti-rabbit for rat tissues  for 1.5 h. The positive proliferating cells were detected with 3,3'-diaminobenzidine  solution (10 % DAB and 0.2 % H2O2 in TBS). Finally, the sections were stained with Ehrlich’s haematoxylin and mounted for microscopy. The Ki67-positive cells were counted using Image-Pro Plus software after capturing the image on a Leica microscope using 100× magnification. For negative controls, tumour sections from each group were incubated in PBS without the first antibody and then incubated with the biotinylated anti-goat secondary antibody followed by reaction with DAB, as described above. The number of positive cells and vessel number were determined by counting 5 fields (500 μm2 each) in one slide from each of at least six rats per group.Fragments of tumour tissue were fixed for 24 h in 4 % paraformaldehyde solution before being embedded in paraffin. From each tissue sample, 5-μm sections were selected for the Ki-67 immunoperoxidase reaction. For the immunohistochemistry assay, the paraffin was removed. For antigen retrieval, the sections were incubated with 10 mM sodium citrate buffer (pH 6) for 1 h at 80 °C, washed with 0.05 M Tris-buffered saline  and incubated with TBS containing 0.3 % HTumour tissue samples were homogenised in protein extraction buffer  followed by centrifugation at 10,000 × g for 15 min at 4°C and were then separated by 10 % SDS–PAGE electrophoresis under reducing conditions. After gel electrophoresis and protein transference onto a nitrocellulose membrane, the proteins were blocked at room temperature for 1 h in 5 % non-fat dry milk. The membranes were then incubated overnight at 4 °C with antibodies against mTOR . Immunoreactivity was detected by the sequential incubation of membranes with anti-mouse secondary antibody for 1 h at room temperature, which was visualised using a chemiluminescence detection system. The level of mTOR was estimated versus the constant level of the 50 kDa protein α-tubulin .P ≤ 0.05. Metabolite set enrichment analysis (MSEA) was performed to determine the metabolic pathways impacted with the changed metabolites among experimental groups. MSEA was conducted using the MetaboAnalyst 3.0 tool, and a significant difference was indicated for P ≤ 0.05 [Results are shown as the mean ± standard deviation, after analysis of all data by Graph Pad Prism 6.0 software . For comparisons among multiple groups , data were evaluated with analysis of variance (two-way ANOVA) followed by post-hoc comparison using Bonferroni’s test . For dirP ≤ 0.05 .P = 0.0561 (Table Both tumour-bearing groups (W and LW) exhibited a decrease in the rat carcass weight, a tumour weight to body weight ratio higher than 10 % and a reduction in serum albumin concentration Table . Leucine61 Table .Table 2MTumour weight and vessel number did not differ between the W and LW groups Table , even th1H NMR metabolomics analysis system, which mainly targeted water-soluble/polar metabolites, we detected 58 metabolites in serum samples for all four experimental groups. Among these metabolites, only 3 were exclusive to tumour-bearing rats: 3-Methyl-2-oxovalerate, 4-Hydroxyphenyl Lactate and 3-Methylhistidine  and found that leucine was the only metabolite that increased in the L group in comparison with the C group Table ; Fig. 2aP ≤ 0.05) due to the evolution of the Walker 256 tumour  and control (C) groups showed changes in 12 metabolites (21.8 %), demonstrating that the cancer cachexia severely affected metabolism in the whole body Table , Fig. 2bP ≤ 0.05) were impacted by Walker 256 tumour evolution under a leucine-rich diet, namely glycine, serine and threonine metabolism, ketone body metabolism and valine, leucine and isoleucine degradation  showed alterations in 23 (39.6 %) serum metabolites in comparison to the control group (L) Table . Among tion Fig. .In order to evaluate the effect of the leucine-rich diet in tumour-bearing rats, we compared the W and LW groups. In the LW group, we found increased metabolites, such as β-hydroxybutyrate Fig. , 4-hydro1H-NMR metabolomic analysis system largely targeted water-soluble metabolites (methanol phase), and 69 metabolites in total were detected in tumour tissue samples (Table P ≤ 0.05) of cholesterol and a fatty acyl chain in comparison to the W group  tissues. Moreover, the altered metabolites are those that play a role in amino acid synthesis (aminoacyl t-RNA biosynthesis) [P = 0.0561). These results suggest that leucine supplementation may be capable of stimulating protein synthesis and, consequently, may lead to a positive protein net balance even amidst a high rate of protein degradation, as shown in our previous studies [The present work utilised nthesis) , and thenthesis) , 41, whenthesis) , 34. Indnthesis) . Researcnthesis) . In agre studies , 45. The studies , 24, 45  studies .Tumour cells require a large energy supply to grow and exhibit a special mechanism for nutrient uptake, preferentially utilising glucose and glutamine as energy sources . Thus, aIn spite of their tumours, the LW group was observed to maintain a serum leucine content, which was slightly elevated compared to the W group Table . The absMost of the cancer cells exhibit a dysregulated metabolic phenotype characterised by lactate fermentation in the presence of oxygen, a phenomenon known as Warburg effect –62. The 1H NMR-derived metabolomic profiles, we found that tumour tissue from the LW group had a higher content of lipid deposits in comparison to tumour tissue from the W group. This result suggests a reduction in the ß-oxidation of fatty acids in the Walker 256 cells treated with leucine. In agreement with these results, Shen and colleagues [The tumour-bearing rats also generally showed increases in metabolic pathways that provide nutrient and energy sources for tumour cell growth. The LW group recruited various metabolic pathways (such as ketone body metabolism) that have the potential to increase tumour cell activity , however, the nutritional supplementation did not appear to benefit tumour growth Fig. . Based olleagues  have attOur results also revealed two potential candidate serum biomarkers for Walker 256 tumour growth, namely 3-methyl-2-oxovaleric acid and 4-hydroxyphenyllactate that were exclusively detected in serum from tumour-bearing groups. The metabolite 3-methyl-2-oxovaleric acid is the alpha-keto acid analogue of isoleucine, produced from isoleucine by cytosolic branched-chain aminotransferase 1, which is a clinical marker of maple syrup urine disease (MSUD) . Notably1H NMR, supplementation did lead to metabolomic alterations that could partially explain the positive effects of leucine supplementation in the rats. In particular, our data suggest that a leucine-rich diet drives metabolomic changes, such as lower levels of tryptophan and lactate (as seen in the LW group), may be associated with a decreased hypermetabolic state and therefore indirectly contribute to minimise the cachexia. Also, the high availability of β-hydroxybutyrate and acetoacetate in the LW group could potentially provide an efficient energy source for skeletal muscle, which also may indirectly contribute to the prevention of cachexia. Although some studies have demonstrated that leucine supplementation may in fact increase cell signalling and tumour cell proliferation [Ultimately, a leucine-rich diet implemented to prevent skeletal muscle loss and ameliorate cachexia in Walker 256 cancer rat hosts had no effect on the tumour growth. As determined by solution-phase feration , here we


N = 4.1 or 8.2 s−1 inducing transitional (Re = 499 or 1307) or turbulent (Re = 2.43 × 104) flow of the fluid. The experiments were performed for a Newtonian fluid (water) and a non-Newtonian fluid  exhibiting mild viscoelastic properties. Measurements were carried out using laser light scattering on tracer particles which follow the flow (2-D PIV). For both the water and the CMC solution one primary and two secondary circulation loops were observed within the fluid volume; however, the secondary loops were characterized by much lower intensity. The applied PMT-type impeller produced in the Newtonian fluid an axial primary flow, whilst in the non-Newtonian fluid the flow was more radial. The results obtained in the form of the local mean velocity components were in satisfactory agreement with the literature data from LDA. Distribution of the shear rate in the studied system was also analyzed. For the non-Newtonian fluid an area was computed where the elastic force dominates over the viscous one. The area was nearly matching the region occupied by the primary circulation loop.The paper presents results of an experimental study of the fluid velocity field in a stirred tank equipped with a Prochem Maxflo T (PMT) type impeller which was rotating at a constant frequency of  The selection of the correct type of impeller for implementation in a mixing process is very important to ensure process requirements and objectives are met. Therefore, basic knowledge about the flow field is needed in order to optimize the mixing tank design as well as assessment of its practical applications. It should be noted that the flow field generated in a mixing tank depends not only on the impeller type and shape of the tank, but also on the rheological parameters of the stirred medium. A large number of published papers presenting results of the study of the flow field in stirred tanks are focused on the flow of Newtonian fluids  type impeller. The PMT impeller was often applied in experimental studies of bioprocesses . Both the tank wall and baffles were made of Plexiglass to allow optical access from the sidewall. Thickness of the Plexiglass items was either 5 or 3 mm for the tank wall or baffles, respectively. The baffles were fixed in the cutters made in the tank bottom and the lid. The tank was filled with liquid (water or 0.2 wt% CMC) to a height H = T. A six-blade PMT-type impeller with a diameter D = 0.35 T was mounted centrally inside the tank. The impeller clearance was at a distance of C = 0.1 m from the tank bottom. The impeller was rotated at a constant frequency of N = 4.1 s−1 in the case of water, and either N = 4.1 or 8.2 s−1 in the case of CMC solution. Value of the mixing Reynolds number for water as the stirred fluid was Re = ND2ρ/μ = 2.43 × 104, thus the flow was turbulent. For the non-Newtonian fluid, though, values of the mixing Reynolds number were estimated on the basis of the Metzner–Otto method, assuming the value of the Metzner–Otto coefficient equal to ks = 11 , similar or higher than the shear stress, τ (viscous characteristics), even for low values of the shear rate. In addition, the author proposed an empirical correlation for calculating the normal stresses of the CMC solutions as a function of shear stress:D and E values were determined on the basis of the measurement results obtained for the CMC (Blanose 9H4) polymer solution with concentrations ranging from 0.1 to 0.5 wt% over a wide range of the shear rate. The coefficients are equal to E = 1.41 and D = 1.4 PaE) was equal to 43.4 mm and inner diameter of the rotor (DG 41 DIN 53544) was 36 mm. The temperature of the fluid was kept at the constant level of 20.5 ± 0.5 °C. Graphs of the measured shear stress, τ, and the apparent viscosity, µApp, as a function of shear rate, An aqueous 0.2 wt% solution of the same CMC (Blanose 9H4 from Hercules) of high viscosity was used in this study as a model non-Newtonian fluid. Degree of substitution of this grade of CMC varies from 0.8 to 0.95 with its typical value approximately 0.9. The viscosity of 1% CMC 9H4 solution is in the range from 2500 to 4500 mPa s, while the weight average molecular weight of this solution is about K is the consistency coefficient and n is flow index. However, the power law does not include any elastic properties of the liquid, such as the first difference of normal stresses in the shear flow. However, the previous experimental study , typical shown in Fig. −1, reaching a maximum value just below the impeller blades. The maximum value of the water mean velocity was equal to 0.52 vTIP, with the impeller peripheral speed defined as vTIP = πDN. This value closely matches that from the literature LDA data  caused less than twofold increase of the fluid velocity (0 to 0.87 m s−1). The maximum values of the non-Newtonian fluid mean velocity were 0.47 and 0.44 vTIP for the N = 4.1 and 8.2 s−1, respectively. Analogous values calculated from the LDA measurements  for water and 0.2 wt% CMC (N = 8.2 s−1), obtained from the two measurements techniques were plotted. Sample of such profiles, at level z = 0 mm and z = −17 mm, where z = 0 indicates the impeller center, as well as values of mean square deviation of the mean fluid velocity between LDA and PIV data  was obtained for the impeller speed N = 4.1 s−1. The increased values of the shear rate in CMC solution were also observed near the tank wall; however, they were not as high as those in the impeller area. When taking into account isolines of the −1  and non-Newtonian (0.2 wt% CMC) fluids in a stirred tank equipped with a high-speed PMT-type impeller were presented. The experimental study was performed using a 2-D PIV technique and positively compared to the literature velocity data from LDA.N = 4.1 s−1 and CMC solution and N = 8.2 s−1. The applied impeller produced a larger primary circulation loop for the Newtonian fluid than for the non-Newtonian solution.Based on the experimental study results, it was found that, both the rheological properties of the stirred medium and an increase of the impeller speed, affect the generated velocity field as well as the size and location of the circulation loops. The radial–axial mean fluid velocity reached maximum values just below the impeller blades and they were equal to N = 4.1 and N = 8.2 s−1, respectively. It was also highlighted that the size of the indicated area may be underestimated due to the applied measurement technique (2-D PIV). Nevertheless, based on the performed study it was concluded that the elastic properties can dominate over the viscous in a considerable volume of the fluid that was characterized by intensive circulation. Therefore, it is concluded that elastic forces should be taken into account during numerical qualitative and quantitative flow analyses of such mildly viscoelastic fluids.During the processing of the results and their analysis, emphasis was placed on generation of the shear rate distribution for the non-Newtonian fluid in order to indicate area where the normal stress surpasses the shear stress. It was estimated that within the analyzed plane, located at an angle of 45° between adjacent baffles, this area occupied 20 and 39% for the


This article investigates heat transfer enhancement in free convection flow of Maxwell nanofluids with carbon nanotubes (CNTs) over a vertically static plate with constant wall temperature. Two kinds of CNTs i.e. single walls carbon nanotubes (SWCNTs) and multiple walls carbon nanotubes (MWCNTs) are suspended in four different types of base liquids . Kerosene oil-based nanofluids are given a special consideration due to their higher thermal conductivities, unique properties and applications. The problem is modelled in terms of PDE’s with initial and boundary conditions. Some relevant non-dimensional variables are inserted in order to transmute the governing problem into dimensionless form. The resulting problem is solved via Laplace transform technique and exact solutions for velocity, shear stress and temperature are acquired. These solutions are significantly controlled by the variations of parameters including the relaxation time, Prandtl number, Grashof number and nanoparticles volume fraction. Velocity and temperature increases with elevation in Grashof number while Shear stress minimizes with increasing Maxwell parameter. A comparison between SWCNTs and MWCNTs in each case is made. Moreover, a graph showing the comparison amongst four different types of nanofluids for both CNTs is also plotted. Moreover, Maxwell fluid model is the elementary rate type model used for fluid rheological effects. Maxwell fluid, also known as Maxwell material, has the properties of elasticity and viscosity both. Fetecau and Fetecau2 found “a new exact solution for Maxwell fluid flow past an infinite plate”. In another study, Fetecau et al.3 provided “a note on the second problem of Stokes for Maxwell fluid over an infinite plate oscillating in its plane”. Khan et al.4 extended Fetecau et al.3 work by taking into account magnetohydrodynamic (MHD) and porosity effects. Jordan et al.5 analysed Stokes’ first problem for Maxwell fluids and obtained new exact solutions. Some important studies performed for Maxwell fluid, include the work of Zierep and Fetecau6, Sohail et al.7, Fetecau et al.8, Jamil et al.10, Vieru and Rauf11, Vieru and Zafar12.Numerous industrial fluids such as plastics, toothpaste and food stuff are non-Newtonian in nature, therefore study of non-Newtonian fluids have practical significance. To forecast the features of all non-Newtonian fluids, there exists no single model. In non-Newtonian fluids, the relation who connects shear stress and shear rate is non-linear. The constitutive correlation forms equations of non-Newtonian fluids which are higher order and intricate than Navier-Stokes equation. These fluids are hard to handle because of supplementary non-linear terms in the momentum equation. Therefore, a number of mathematical models are presented to predict the behavior of such fluids. Mainly, these models have three types: Differential, rate and integral type models. The differential and rate type are of great importance among them. In differential type fluids stress is deduced by its various higher time derivatives. First grade, second and third grade fluids falls in this category. In rate type, stress and its higher derivatives have an implicit relation. Integral type models describes materials like polymers melts with considerable memory, stress depends upon the history of relative deformation gradient. Rate type fluids have more significance in research as they predict both elastic and memory effects together. Therefore, in the present work, a subdivision of rate type fluids called Maxwell fluid is chosen. This fluid model was initially introduced by Maxwell to predict the elastic and viscous behavior of air18 are either solved numerically or analytically by using an approximate method and, exact solutions for such problems are rare. Such investigations are further narrowed down when the convection flow of Maxwell fluid with nanoparticles is considered. According to authors’ knowledge, even not a single article is published in the literature for Maxwell fluid containing nanoparticles where the exact solution is obtained. Such a fluid is known as Maxwell nanofluid or generally a nanofluid.However, all these attempts were made for Maxwell fluid for momentum transfer only and the analysis of heat transfer due to convection was not considered. But most of the existing studies are on the convective flow of Maxwell fluid19, when he dropped solid nano-sized particles in a carrier fluid and the new type of composite fluid was named as nanofluid. Of course the structure of nanofluid is not as simple as of regular fluid, because the suspended nanoparticles can be of different types, shapes and sizes, see for example Aaiza et al.20, Hussanan et al.21, Ellahi22, Sheikholeslami et al.25 and the references therein. In addition, nanofluid also depends on base fluid. So, the researchers are continuously trying via experimental, theoretical and numerical studies to choose a nanofluid with such a combination of base fluid and nanoparticles that have maximum rate of heat transfer. Amongst various types of base fluid and nanoparticles, in this work we have chosen Kerosene oil as base fluid and carbon nanotubes as nanoparticles. For the sake of comparison, three other types of nanofluids namely engine oil; ethylene glycol and water are also used.The idea of nanofluid was initially introduced by Choi26 investigated the impact of heat source/sink on a Maxwell nanofluid. Nandy27 and Afify and Elgazery28 analyzed Flow of Maxwell nanofluid. Cao et al.29 investigated fractional derivatives of Maxwell viscoelastic nanofluid over a moving plate. Nadeem et al.30 and Ramesh et al.31 surveyed Maxwell nanofluids. In all the above studies on Maxwell fluid nanoparticles of tube shapes (CNTs) were not incorporated. Compare to other nanoparticles, CNTs are of great interest for researchers because of their significant thermal conductivities and mechanical strength. They can be bent without any damage; this property makes them useful for high resolution scanning probe microscopy. Two types of CNTs i.e. SWCNTs and MWCNTs are used in this work. Their thermal conductivity is affected by length and diameter which makes them interesting to be arranged in the desirable way in different applications. CNTs are indicated to be the best heat-conducting material. They have applications in fuel cells gas diffusion layers, molecular electronics and current collectors due to their high electrical conductivities. CNTs based filtration devices have been flourished which not only obstruct the mini particles but vanish most bacteria. The wall of SWCNTs consists of one tube of graphite as shown in Fig. Ramesh and Gireeshaet al.32 studied mixed convection axisymmetric chemically reactive flow of Maxwell fluid. Zhang et al.33 and Kandasamy et al.34 examined carbon nanotubes nanofluids. Implementation of Laplace transform for the exact impact of MHD on heat transfer of CNTs nanofluids is studied by Ebaid and Sharif 35. Wang et al.36 detected the impact of CNTs length on their thermal, electrical and mechanical aspects. Competence of CNTs nanofluids as coolants was studied experimentally by Halelfadl37. Hussain et al.38 and Khan et al.39 analyzed fluid flow with CNTs. Few other attempts on CNTs nanofluids are given in refs Khan 48.The mechanism of convection has three main types which are free, forced and mixed convections. Amongst these three modes of convection, free convection is investigated in this research. In free convection the heat transfer is induced density differences in the fluid owe to temperature gradient. More exactly, free convection is induced by buoyancy force. Free convection has enormous applications in nature and engineering for example microstructure formation, solar ponds, molten metal cooling and much high power output devicesThe present work targets to inspect unsteady free convection flow of CNTs Maxwell nanofluid over a stationary vertical plate with constant temperature. Two types of CNTs (SWCNTs and MWCNTs) are suspended in four different kinds of molecular liquids  also known as regular or base fluids. Exact solutions of the problem are evaluated by Laplace transform method. Expressions for velocity, shear stress and temperature are established purely in exact form. The flow and heat transfer features of the present problem are detected for distinct values of non-dimensional parameters. The results thus detected are displayed graphically via computational software MathCAD and discussed in detail.x,y)− plane of a Cartesian coordinate system x,y and z. Initially, both the plate and fluid are static with constant wall temperature Let us consider unsteady flow of an Maxwell fluid with free convection over a vertical flat plate situated in nf, heat capacitance (ρcp)nf, are derived by using the relations given by:50ϕ represents nanoparticles volume fraction, ρf and ρCNT is the density of the base fluid and CNTs, the volumetric coefficient of thermal expansions of carbon nanotubes and base fluids are denoted by βCNT and βf respectively, (cp)CNT and (cp)f is the specific heat capacities of CNTs and carrier fluids.The density Inserting the below non-dimensional quantities:into Eqs –3), we , we 3), y, q)- plane.In order to solve the equations , 7) and and7) anExerting Laplace transform of Eqs , 10), ,  and usinThe solution of the partial differential (12) subject to conditions (13) is given as:Taking the inverse Laplace transform and using (A1), we obtain1, 1, 1, 10)1, 1, 1 and usiIntroducing Eq.  into Eq.Solve the partial differential Eq. , we haveThe last equality can be written as:Taking the inverse Laplace transform, Eq.  emit:23\Taking the inverse Laplace, Eq.  emits26\Applying the inverse Laplace transform and convolution product, Eq.  emits:28Exerting Laplace transform to Eq. , emit:29Differentiate Eq.  with resPut Eq.  into Eq.Using the inverse Laplace transform into Eqs , 32), ,  and 34)34) emitsNusselt number is 49 for various values of volume fraction ϕ of CNTs as given in Table ϕ of CNTs. Also we observed that for the same values of volume fraction ϕ, the nanofluids with SWCNTs have higher effective thermal conductivities as compared to that having MWCNTs. The logic for this is the elevated value of thermal conductivity of SWCNTs which is 6600 Wm−1/k−1 while 3000 Wm−1/k−1 for MWCNTs as given in Table ϕ. The enhancement of heat transfer rate can be seen from the table, heat transfer rate increases with increasing volume fraction of nanoparticles which was our main target because the purpose of adding nanoparticles to our working fluid is to enhance its rate of heat transfer and to make it useful for the practical purpose. SWCNTs have higher rate of heat transfer than MWCNTs at the same volume fraction. It is due to the fact that SWCNT has greater thermal conductivity than MWCNT. A comparison of Nusselt number (Nu) which measures the heat transfer rate of the present result with the previous published result of Farhad et al.47, Table ϕ = 0) are in excellent agreement with published results of Farhad et al.47. This theoretical comparison confirms the accuracy of the present work.Thermo physical properties of the carrier fluids  and CNTs nanoparticles are given in Table Gr, Maxwell parameter λ and nanoparticles volume fraction ϕ is studied in Figs y. Note that in all these figures, (a) and (b) plots shows the results for SWCNTs and MWCNTs respectively. Figure ϕ of Carbon nanotubes. Temperature is found to be an elevating function of volume fraction ϕ for both types of Carbon nanotubes. Physically, the logic is increase in thermal conductivities of nanofluids due to insertion of more CNTs. The more the volume fraction of CNTs in the nanofluids, the more will be its thermal conductivity which in turn enhances the fluids temperature. This increase in thermal conductivities is shown numerically in Table ϕ of CNTs, a gradual elevation is observed in thermal conductivity. Figure Gr for SWCNTs and MWCNTs. It is spotted that the fluid velocity (for both types of CNTs) increases by maximizing the Grashof number Gr. When Gr = 0, the fluid velocity becomes zero. Physically, it shows that there is no flow in the absence of buoyancy force, as we know that Grashoff number is the ratio of buoyancy force to the viscous force. Thus, here it is concluded from this figure that the flow is due to buoyancy force and in the absence of this force the fluid is in static position. Figure λ for both SWCNTs and MWCNTs. Figure ϕ on the flow of Maxwell nanofluid. It is spotted that velocity profile minimizes with increasing volume fraction ϕ for both type of CNTs (SWCNT and MWCNT). Physically, it is due to the fact that the fluids gets viscous by adding nanoparticles and its viscosity/density increases by increasing its amount, thus minimizes the velocity of nanofluid. Figure Gr It is detected that the shear stress at the bounding wall is zero for Gr = 0 For increasing values of Grashof number Gr shear stress decreases. Figure λ. Figure ϕ on profile of shear stress. It is found that shear stress decreases with an elevation of volume fraction ϕ of carbon nanotubes (SWCNT and MWCNTs). Comparison graphs are made for SWCNTs and MWCNTs to observe the behavior of nanofluid velocity with various base fluids i.e. Kerosene oil, Engine oil, water and ethylene glycol in Fig. et al.42. It is found that at ϕ = 0 and λ = 0.00001 the present result is in good agreement with the previous result found by Chandran et al.42, showing that at these values the present Maxwell nanofluid reduces to viscous fluid.The alteration of dimensionless temperature, velocity and shear stress for distinct values of inserted parameter such as Grashof number ϕ of CNTs was evaluated and values are obtained by using Xue model49 for thermal conductivities as given in Table ϕ. For an increase in Grashof number velocity increases while shear stress were decreased and when Gr = 0, they becomes zero which shows graphically that the fluid flow is induced by buoyancy force.In this attempt, the first exact solutions for unsteady free convection problem of Maxwell nanofluid are acquired via Laplace transform method. Exact expressions of velocity, shear stress and temperature are acquired and then mapped graphically for various embedded parameters. Carbon nanotubes (SWCNTs and MWCNT) were chosen as nanoparticles inside four different base fluids . The impact of volume fraction Supplementary file


Gastrorenal shunts may induce hyperammonemia. Portosystemic shunts should be suspected when hyperammonemia occurs in patients with chronic kidney disease. Clinical Question: What is the cause of hyperammonemia in this patient?μg/dL). Because of diabetes, chronic heart failure, and chronic kidney disease (CKD) , he developed fluid overload. However, he had no history of abdominal surgery or liver dysfunction. He was given a laxative, and a solution containing branched‐chain amino acids was administered. His level of consciousness improved after excess fluid, and solutes were removed by hemodialysis (HD). Abdominal‐enhanced computed tomography revealed a gastrorenal shunt (Fig. A 72‐year‐old male patient presented with sudden loss of consciousness and hyperammonemia, with blood ammonia levels that were much higher than the levels 2 days prior (increase from 129 to 340 In patients on maintenance hemodialysis, a gastrorenal portosystemic shunt can easily develop due to fluid overload and increased backflow with hemodialysis‐related fluid removal YN: wrote the first draft of the manuscript. IO: revised the manuscript critically, made critical revisions, and approved the final version. YG and HG: developed the structure and arguments jointly for the paper. All the authors reviewed and conceded the final version of the manuscript.None declared.


We show that the Cahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation at a length scale Lc, which we evaluate from S(k), the spectrum of the fluctuations of ϕ. We demonstrate that (a) Lc ~ LH, the Hinze scale that follows from balancing inertial and interfacial-tension forces, and (b) Lc is independent, within error bars, of the diffusivity D. We elucidate how this coupling modifies E(k) by blocking the inverse energy cascade at a wavenumber kc, which we show is ≃2π/Lc. We compare our work with earlier studies of this problem.We study two-dimensional (2D) binary-fluid turbulence by carrying out an extensive direct numerical simulation (DNS) of the forced, statistically steady turbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In the absence of any coupling, we choose parameters that lead (a) to spinodal decomposition and domain growth, which is characterized by the spatiotemporal evolution of the Cahn-Hilliard order parameter  We elucidate the turbulence-induced arrest of phase separation in a 2D, symmetric, binary-fluid mixture.Binary-fluid mixtures (such as oil and water) have played a pivotal role in the development of the understanding of (a) equilibrium critical phenomena at the consolute point, above which the two fluids mix1257810111214151617LH  ~ k−5/3  ~ ε ≡ 〈ε(t)〉t assumes a constant value. For the Cahn-Hilliard model, if it is not coupled to the Naiver-Stokes equation, E(k) and S are modified when we study forced 2D turbulence, in the inverse-cascade regime in the coupled Cahn-Hilliard-Navier-Stokes equations.Forced, 2D, statistically steady, Navier-Stokes-fluid turbulence displays a forward cascade of enstrophy, from We model a symmetric binary-fluid mixture by using the incompressible Navier-Stokes equations coupled to the Cahn-Hilliard or Model-H equations343637u ≡  is the fluid velocity at the point x and time t, x, tϕ is the Cahn-Hilliard order parameter that is positive in one phase and negative in the other, x, tp is the pressure, ξ controls the width of the interface between the two phases of the binary-fluid mixture, ν is the kinematic viscosity, the surface tension M, and fω is the external driving force. For simplicity, we study mixtures in which M is independent of ϕ and both components have the same density and viscosityL = 2π. To obtain a substantial inverse-cascade regime, we stir the fluid at an intermediate length scale by forcing in Fourier space in a spherical shell with wave-number Re ∝ 1/ν, the more turbulent is the flow; and the higher the Weber number We ∝ 1/σ, the more the fluctuations in the domains . To elucidate the physics of coarsening arrest, we conduct direct numerical simulations (DNSs) of Here ϕ, at late times when coarsening arrest has occurred, for four different values of We at Re = 124; we find that the larger the value of We the smaller is the linear size that can be associated with domains; this size is determined by the competition between turbulence-shear and interfacial-tension forces. This qualitative effect has also been observed in earlier studies of 2D and 3D turbulence of symmetric binary-fluid mixtures1920213940414243In We calculate the coarsening-arrest length scaleLc is determined by the Hinze scale LH, which we obtain, as in Hinze’s pioneering study of droplet break-upwe now show that Lc ~ LH  from our DNS, we obtain the red points in σLc versus εinj/σ4; the black line is the Hinze result (4) for LH, with a constant of proportionality that we find is LH gives an excellent approximation to the arrest scale Lcover several orders of magnitude on both vertical and horizontal axes. Note that the Hinze estimate also predicts that, for fixed values of εinj and σ, the coarsening-arrest scale is independent of D; the plot of Lc versus D, in the inset of Lc are consistent (within error bars) with this prediction.We obtain for 2D, binary-fluid turbulence the intuitively appealing result S(k), at small k . This suppression increases as We increases ; and S(k) develops a broad and gentle maximum whose peak moves out to large values of k as We grows. These changes in S(k) are associated with We-dependent modifications in the probability distribution function (PDF) P(ϕ) of the order parameter ϕ, which is symmetrical about ϕ = 0 and has two peaks at ϕ = ϕ±, where ϕ+ = −ϕ− > 0; we display P(ϕ)/Pm(ϕ) in ϕ+; as We increases, ϕ+ decreases; here Pm(ϕ) is the maximum value of P(ϕ). In particular, our DNS suggests that We.In P(ϕ) can be understood qualitatively by making the approximation that the effect of the fluid on the equation for ϕ can be encapsulated into an eddy diffusivity De4245tϕ = (De − D)∇2ϕ + D∇2ϕ3 + MΛ∇4ϕ, which gives the maximum and minimum values of ϕ as Dk2[(1 − De/D) − MΛk2]; i.e., all wave numbers larger than π/kd) decay in the presence of coupling with the velocity field; we expect, therefore, that, in the presence of fluid turbulence, the peak of P(ϕ) broadens and shifts as it does in our DNS. For a quantitative description of this broadening and the shift of the peak, we must, of course, carry out a full DNS of the Cahn-Hilliard-Navier-Stokes equation as we have done here.The modification in ϕ and its statistical properties such as those embodied in S(k) and P(ϕ). We show next how the turbulence of the fluid is modified by ϕ, which is an active scalar insofar as it affects the velocity field. In the statistically steady state of our driven, dissipative system, the energy injection must be balanced by both viscous dissipation and dissipation that arises because of the interface, i.e., we must have εinj = εν + εμ.We have investigated, so far, the effect of fluid turbulence on the phase-field εν decreases and εμ increases as we increase We, while keeping εinj constant, because Lc diminishes (εμ increase. This decrease of Lc is mirrored strikingly in plots of the fluid-kinetic-energy spectrum E(k)   , which dS(k) see . The valWe. Here P(k) is the transverse projector with components Pij(k) ≡ δij − kikj/k2. We define kc as the wave-number at which ΠE(k) comes within 4% of εinj. We find that the wave-numer corresponding to the arrest scale 2π/Lc  is comparable to kc.To provide clear evidence that the blocking of the energy flux is closely related to the arrest scale, we show in ν∇2u and the Ekman drag uα, it is not possible to see a large range of constant energy flux47HR1 and HR2. Consistent with the earlier discussion, we find that the coarsening length Lc decreases on increasing We. Furthermore, the formation of arrest-scale domains leads to a blockage of the energy cascade; because we use hypoviscosity, we now see clear evidence of a constant energy flux over a decade for the single-phase Navier-Stokes run. For the binary-fluid case, the energy flux remains constant for a shorter range and then decreases to zero around a wave-number In the presence of the standard viscous term ϕ is advected passively by the fluid velocity. Such a passive-advection model is clearly inadequate because it cannot lead to the phase-field-induced modifications in the statistical properties of the turbulent fluid /Pm(ϕ); we can see this by comparing the passive-advection result, shown in the middle panel of ϕ in the vicinity of the peak, with its counterpart in Lc on D: in the passive-advection case we find Lc ~ D0.27 [D-independent behavior of Lc shown in the inset of It has been suggested2245luid see . The pasLc, which follows from S(k). We demonstrate that Lc ~ LH, the Hinze scale that we find by balancing inertial and interfacial-tension forces, and that Lc is independent, within error bars, of the diffusivity D. We also elucidate how the coupling between the Cahn-Hilliard and Navier-Stokes equations modifies the properties of fluid turbulence in 2D. In particular, we show that there is a blocking of the inverse energy cascade at a wavenumber kc, which we show is In conclusion, our extensive study of two-dimensional (2D) binary-fluid turbulence shows how the Cahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation at a length scale ϕ obtain results that are qualitatively similar to those we obtain for S(k) and the spatiotemporal evolution of ϕ, they cannot capture the phase-field-induced modification of the statistical properties of fluid turbulence and the correct dependence of Lc on D. We find our results to be in qualitative agreement with the earlier studies on the advection of binary-fluid mixtures with synthetic chaotic flows45Earlier DNSs of turbulence-induced coarsening arrest in binary-fluid phase separation have concentrated on regimes in which there is a forward cascade of energy in 3D see ref.  and a foSome groups have also studied the statistical properties of turbulent, symmetric, binary-fluid mixtures above the consolute point, where the two fluids mix even in the absence of turbulence4049Lc and the blocking of the inverse cascade of energy.We hope our study will lead to new experimental studies of turbulence in binary-fluid mixtures, especially in 2D515253μ, we use N/2-dealiasing. For time integration we use the exponential Adams-Bashforth method ETD2We conduct direct numerical simulations (DNSs) of u and x, tϕ from our DNS, we calculate the energy and order-parameter (or phase-field) spectra, which are, respectively, t denotes the average over time in the statistically steady state of our system. The total kinetic energy is x denotes the average over space, 〈fωω〉 is the enstrophy-injection rate, which is related to the energy-injection rate via E = 0.5∑kE(k) is the fluid kinetic energy, εν = ν∑kk2E(k) is the fluid-energy dissipation rate, and ϕ.Given The Cahn-Hilliard-Navier-Stokes equations with modified viscosity terms areνi∇−4ω to dissipate energy at large scales and a hyperviscosity term −νu∇16ω to dissipate enstrophy at small scales. As discussed in the main text, we use a constant-energy-injection forcing with kinj = 130. The other parameters for our simulations are given in Here we use a hypo-viscosity term −How to cite this article: Perlekar, P. et al. Two-dimensional Turbulence in Symmetric Binary-Fluid Mixtures: Coarsening Arrest by the Inverse Cascade. Sci. Rep.7, 44589; doi: 10.1038/srep44589 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Giant-cell tumour is a locally aggressive tumour of long bones of epiphyseal region commonly occurring in adults aged 20–40 years.Most common location is distal femur, proximal tibia, and distal radius. Different treatment options being used are curettage with bone graft or bone cement, resection with arthrodesis, reconstruction, radiation, and chemotherapy. We are reporting a case of giant-cell tumour of right proximal radius in a 50-year-old female with posterior interosseous nerve palsy. It is very rare, and only four cases have been reported in the literature. It was treated by wide margin resection with fibular grafting, titanium elastic nail system along with cancellous bone graft reconstruction. Giant-cell tumour is a locally aggressive tumour of long bones in epiphyseal region . It occuA 50-year-old female presented to our department with a swelling over the anterolateral aspect of right elbow along with wrist drop in February 2014. Roentgenogram was taken which showed expansile lesion in the metaphyseal region of proximal radius with the rim of cartilage and ballooning of proximal radius Fig. . Wide maProximal interosseous membrane left untouched as distal diaphyseal interosseous membrane was intact and radioulnar joint was stable enough in supination and pronation. She did not have wound problems post-operatively but had weakness in finger and wrist extension for which cock-up splint and physiotherapy was advised. She has been under regular clinical and radiological follow-up. After 2 months of follow-up, she regained her finger and wrist movements. Bone scan conducted 9 months after surgery did not show any recurrence. There are no clinical or radiological symptoms (as shown in Fig. Giant-cell tumour is mostly found in the third and fourth decade of life though it has been rarely seen in younger age group also. It is locally aggressive tumour involving epiphyseal region of mature bones. Most of the tumours are found around knee joint in distal femur, proximal tibia, and distal radius. Various treatment options are used depending on the stage and location of tumour. Four cases have been reported so far in the literature which shows unusual age and presentation in proximal radius. Akmaz et al., Mir, Singh, and Song –9 have rIn our patient, the giant-cell tumour was extracompartmental invading surrounding muscle fibres and stretching posterior interosseous nerve, which had to be removed. Cases reported by above-mentioned authors were also extracompartmental tumours. Mir did marginal resection, and Singh performed above-elbow amputation , 8. SongDell et al.  and Brow Gokaraju et al.  found goAccording to Izaak et al. , the maiIn our patient on last follow-up, she had nearly complete range of flexion/extension movements at elbow, supination/pronation, wrist, and fingers after extensive physiotherapy. Spared radial head showed no signs of avascular necrosis with good radiological union. Repair of annular ligament and biceps tendon reattachment on proximal fibula along with intact interosseous membrane of the distal diaphysis contributed to the desired stability of proximal radioulnar joint which is vital for supination and pronation movements and plays a role in valgus stability. There were no signs of recurrence. She was satisfied with her treatment. Early detection, wide margin resection of extracompartmental tumour along with fibular, and iliac bone grafting with TENS are good options for giant-cell tumour of proximal radius with no recurrence, minimal complications, and disability.