We analysed tumour growth in untreated mice (control) and mice treated with an anti-angiogenic agent and determined the Kaplan–Meier survival estimates based on simulated tumour volume data. We found that the ratio between two kinetic parameters, k0 and k1, which characterize the tumour's exponential and linear growth rates, as well as k1 alone, can be used as prognostic biomarkers of the population survival outcome. Our work demonstrates a robust, quantitative approach for identifying tumour growth kinetic parameters as prognostic biomarkers and serves as a template that can be used to identify other biomarkers for anti-angiogenic treatment.Angiogenesis is a crucial step in tumour progression, as this process allows tumours to recruit new blood vessels and obtain oxygen and nutrients to sustain growth. Therefore, inhibiting angiogenesis remains a viable strategy for cancer therapy. However, anti-angiogenic therapy has not proved to be effective in reducing tumour growth across a wide range of tumours, and no reliable predictive biomarkers have been found to determine the efficacy of anti-angiogenic treatment. Using our previously established computational model of tumour-bearing mice, we sought to determine whether tumour growth kinetic parameters could be used to predict the outcome of anti-angiogenic treatment. A model trained with datasets from six  This process facilitates tumour growth by allowing tumour cells to obtain oxygen and nutrients through the newly formed blood vessels. As excessive vascularization is often seen in many types of cancer, inhibiting angiogenesis is thought to decrease tumour growth. Therefore, anti-angiogenic treatment is pursued as an attractive therapeutic strategy in oncology ,2.Bevacizumab is a humanized monoclonal antibody against vascular endothelial growth factor A (VEGF), a key angiogenic promoter in tumours . This drKtrans) [More broadly, there is a need for biomarkers to predict the response to treatment and identify the tumours for which anti-angiogenic treatment will be effective. A number of mechanistic biomarkers have been investigated for their ability to predict response to anti-angiogenic treatment and to determine an optimal treatment strategy. Promising biomarker candidates include the concentration ranges of circulating angiogenic molecules (such as plasma levels of VEGF) ,14, tissKtrans) ,19,20. HKtrans) ,15.in vivo experimental data, we estimated the kinetic parameters that characterize tumour growth. We then used the trained model to predict the effect of anti-VEGF treatment on tumour volume, using only the estimated parameter values. The model predictions of tumour growth in response to anti-VEGF treatment closely matched experimental data. In this study, we concluded that there is a strong correlation between particular intrinsic kinetic parameters and the response to anti-VEGF treatment in terms of the end relative tumour volume (RTV).As an alternative, tumour growth kinetics may be used as biomarkers. There is a body of work that investigates how tumour growth kinetics can serve as prognostic biomarkers of the response to anti-angiogenic treatment –25. Recein silico randomized mouse study and estimated the survival of tumour-bearing mice in response to anti-VEGF treatment. Here, we introduced variability in the mouse population by allowing the tumour growth kinetic parameter values to vary within defined ranges. A total of 2400 mice with different tumour growth profiles were simulated in this study. By generating this large, heterogeneous in silico population of tumour-bearing mice, we can eliminate the likely bias caused by animals dropping out of experimental xenograft studies due to high tumour burden. In general, the average tumour size, particularly in the control group, can be underestimated in an experimental study, thereby underestimating the treatment effect, because large tumours are excluded from the analysis [Taking advantage of our established model framework and its strong predictive power, we now use this model to further investigate the utility of tumour growth kinetics to serve as a biomarker for anti-angiogenic treatment outcome. We performed an analysis . By contanalysis . Furtheranalysis –31. Suchanalysis ,32,33.in silico population tumour growth data. We examined tumour growth kinetic parameters as prognostic biomarkers to distinguish the tumour response to anti-angiogenic treatment among the stratified groups.In our previous work, we did not explore how tumour growth parameters affect the response to treatment for individual tumours, nor did we examine time-based tumour growth inhibition. Therefore, in this study, we simulate the tumour volume over time in a heterogeneous population of mice and use more reliable and appropriate read-outs. Specifically, we performed time-to-event analysis  by deter2.2.1.in silico randomized mouse study using our whole-body mouse model , and Ang0  were estimated. A global sensitivity analysis indicated that ψ did not significantly influence tumour volume; thus, it was held constant. Here, we simulated the tumour growth of the six in silico populations of mice , with and without anti-VEGF treatment, in mice with different tumour growth kinetic parameters. For each population, the values of parameters k0 and k1 are randomly varied simultaneously with a uniform distribution within the ranges of their estimated values from our previous model fitting. Previously, a sensitivity analysis showed that the Ang0 parameter was an influential parameter to the model output when the model was fitted; however, further analysis using partial least-squares regression (PLSR) indicated that Ang0 was not a strong predictor of response to treatment [Ang0 is set as the median of the range of its estimated values. We generated 400 in silico mice for each of the six cases.We performed an se model . The modreatment . Therefoa,c,d,f), the treated tumour volumes are less than the untreated tumours. Meanwhile, for Zibara and Volk2011a , there is no apparent difference in the tumour volumes for the treated and control groups. Thus, the model simulations reveal distinct differences in the effect of anti-VEGF treatment.Our simulations show that among the six cases, the anti-VEGF treatment has differential effects in reducing tumour growth, when compared with the control group . For allfigure 2b,e). Comparing the endpoint RTV among all six cases, the effect of anti-VEGF treatment in limiting tumour growth is the strongest for Volk2011b (RTV = 0.459 ± 0.054), followed by Roland (0.454 ± 0.096), Volk2008 (0.615 ± 0.066) and Tan (0.638 ± 0.049). This treatment effect is the least significant in Zibara (0.979 ± 0.009) and Volk2011a (0.987 ± 0.013).We further studied the effect of anti-VEGF treatment on tumour growth using RTV, the ratio between the mean tumour volumes of the treated and control groups. We calculated the RTV at each time point for all simulated tumours . We also determined the RTV at the end of treatment . The RTV values in all cases are smaller than one, indicating that the anti-VEGF treatment limits tumour growth, similar to what has been observed experimentally –39. For figure 22.2.k0/k1 ratios were also significantly different. This implies that k0/k1 is a large contributor in predicting the endpoint RTV [k0, k1, and k0/k1 shows some relationship between the endpoint RTV and the tumour growth parameters . Therefore, we investigated whether these tumour growth parameters could stratify the simulated mouse populations, and distinguish their tumour growth and survival estimates. To address this question, we used our simulated tumour growth data for each case, noting the number of in silico mice at each time point. We record the time at which a mouse is ‘sacrificed’, which happens when the tumour volume reaches 2 cm3, as typically done in experimental studies [We investigated the relationship between the parameters that characterize tumour growth kinetics and the effect of the anti-VEGF treatment. Previously, our PLSR analysis indicated that for nearly all pairwise comparisons, if the RTV values for two datasets were significantly different, their oint RTV . Additio studies . This apk0, k1 or k0/k1 can be used to discriminate between tumours for which anti-VEGF treatment is effective or not. We found that, in each case, a range of k0/k1 ratios, as well as k1, can be used to distinguish the population response to the anti-VEGF treatment . We term these ‘ratiothresh’ and ‘k,thresh1’ the values of the growth kinetic parameters that separate the simulated mouse population into groups with significantly different survival estimates. By contrast, we did not find any values of k0 alone that could be used to separate the simulated mouse population into groups whose survival estimates are statistically different for the Roland, Zibara and Volk2011b cases. For Tan and Volk2008, we only found one such k0 value in each case (a).We used the simulated population survival data to determine if reatment b,c. We tach case a.Figurek0/k1 ratios and k1 were different for each of the six sets of tumour growth data, we found that there is an overlap among the potential ratiothresh or k,thresh1 values found in each of the six cases. The common range of ratiothresh is 9.757 to 17.982, and that of k,thresh1 is 1.391 × 10−6 to 1.931 × 10−6. This means that separating the treatment group by any k,thresh1or ratiothresh value within its respective range will produce two groups of treated mice that have statistically different survival estimates. Specifically, the treated group with k0/k1 ratios larger than ratiothresh has a better survival estimate than the treated group with smaller ratios. The treated group with k1 smaller than k,thresh1 has a better survival estimate than the treated group with larger k1.Interestingly, although the ranges of generated thresh value (13.689) to illustrate this distinction. We compare the survival estimates for a total of six groups: (i) all mice in the control group; (ii) all mice in the treatment group; (iii) control group with k0/k1 < ratiothresh; (iv) control group with k0/k1 > ratiothresh; (v) treatment group with k0/k1 < ratiothresh; and (vi) treatment group with k0/k1 > ratiothresh. We generated the Kaplan–Meier survival curves for these groups for each of the six cases investigated , the stratified groups yield significantly different survival estimates. That is, the control and treated groups with k0/k1 ratios larger than ratiothresh have better survival estimates than those with smaller k0/k1 ratios.We used the median ratiostigated . We alsostigated , the Manmparison . When cok,thresh1 value (1.661 × 10−6) to show the distinction between the survival estimates . The control and treated groups with k1 smaller than k,thresh1 have better survival estimates than those with larger k1 values. We also estimated the median survival of the six groups separated using the median k,thresh1 .We performed a similar analysis using the median 1,thresh , the Manmparison . From th2.3.−1 biweekly treatment upon tumour engraftment  [k0/k1 ratios larger than the median ratiothresh, or with k1 smaller than the median k,thresh1, the HR between the treated and control groups is smaller than one, and the survival curves are significantly different (p < 0.0001) . This protocol starts the 10 mg kg004 cm3) . The pre−1 biweekly treatment when the tumour volume reaches 0.5 cm3, a start time extracted from the published preclinical study [p > 0.05). Again, the treated group with k0/k1 ratios larger than the median ratiothresh, or with k1 smaller than the median k,thresh1, has a significantly better survival estimate than the opposite group (p < 0.0001)  tables . This ph3, and the drug dosage is doubled to 20 mg kg−1. This treatment protocol significantly limits the tumour growth , and the survival curves are significantly better for the treated group compared to the control (p < 0.0001). Overall, the treated and control groups have an HR of 0.2016 (95% CI: 0.1343–0.3027)  .2.4.thresh and k,thresh1 values that we found, we used a recently published independent set of data that measures tumour growth in mice with MDA-MB-231 xenografts, with or without bevacizumab treatment [k0, k1 and Ang0 that allow the model to best fit to the control data. We then validated the fitted model by simulating anti-VEGF treatment and comparing to the experimental measurements. The predicted tumour growth with treatment matches closely to the experimental data (a).To validate the use of the range of ratioreatment . First, tal data a.Figurein silico mouse population with and without treatment (referred to as ‘Mollard’). To do so, we randomly varied k0 and k1 from the ranges of the 12 sets of estimated parameter values from model fitting to the Mollard dataset, with Ang0 held constant at the median of its estimated values. The simulated tumour volumes for the control and treated groups are shown in figure 5b.Using the same approach as described above, we generated 400 sets of tumour volumes for an thresh and k,thresh1 values identified using the six datasets described above are able to separate the population survival data for this validation case (Mollard). For all ratiothesh values within the range, the survival estimate of the treated mice with k0/k1 ratios larger than the threshold is better than those with smaller k0/k1 ratios. Examples using the median ratiothresh and the median k,thresh1 are shown in figure 5c,d. We calculated the HR values, as well as the p-value from the Mantel–Cox log rank test among the treated and control groups, separated using the median of the common ratiothresh range  in each case.We explored the dynamics of the tumour growth for the groups separated by the threshold values to better understand why the anti-VEGF treatment has differential effects in the simulated mouse populations. As researchers have pointed out, log transformation of tumour growth data provides information on tumour growth rates (given by the slope of the curve) and is more suitable for detecting a transient biological or therapeutic effect ,42,43. Tk0/k1 ratios  is initially larger, and then becomes smaller relative to the opposite group. This switch occurs because in the group with larger k0/k1 ratios, the difference between the treated and control tumour volumes is smaller at early times, and then becomes larger . Meanwhile, the actual tumour volumes for this group are both relatively low. As a result, this group survives longer , giving rise to the larger mean RTV (figure 6a). However, the group with larger k0/k1 ratios still survives longer because the actual tumour volumes are relatively low (c).For Roland, Tan and Volk2008, the mean RTV of the group with larger s longer . For thevely low c.Figurea). However, the tumour volumes plotted on the log scale show that their growth rates are mostly different during days 14–40. The growth rates become similar during the later stage (after 40 days), as evidenced by the parallel curves on the log scale (b). Therefore, the increasingly large gap between the tumour volumes is a result of early differences in the tumour growth rates. A similar phenomenon is observed for Volk2011b, where the tumour growth rate of the treated group is suppressed transiently at early times but not in the later stage . In Zibara, Tan and Volk2008, the growth rates become different between day 30 and day 45, and only gradually become similar towards the end of the simulated time. Overall, analysis of the growth curves plotted on the log scale reveals that the anti-VEGF treatment has differential effects in limiting tumour growth, and the effects occur at different stages for the simulated cases. The treatment effect is predicted to be stronger for the group with k0/k1 ratios larger than the median ratiothresh.The tumour volume data plotted on the log scale also reveal that the tumour growth rates of the control and treated groups diverge at different time points. For Roland, the gap between the control and treated groups continually increases when plotted on a linear scale a. Howeveog scale b. Theref3.In this study, we focus on identifying tumour growth kinetic parameters as potential biomarkers for the outcome of anti-VEGF treatment. We developed a computational approach that incorporates model training, simulation of tumour growth within a heterogeneous population, and estimation and analysis of population response.b,e), which is different from the effect seen experimentally. This difference occurs for two reasons. First, our simulated treatment protocol A is universal across the six cases, and is different from what was used in each of the original six experimental studies. Second, in our simulations, k0 and k1 are varied simultaneously and independently of each other, possibly resulting in more variability than what occurs experimentally.We simulated anti-VEGF treatment and compared the effect of treatment across tumour-bearing mice generated from our previous fitting to six independent preclinical studies. For most simulated tumours, the anti-VEGF agent significantly reduces tumour volume compared to the control. However, our simulations for Zibara and Volk2011a show that these populations do not respond to the treatment b,e, whick0/k1 ratio or k1 alone can be used to stratify the population response with or without anti-VEGF treatment. This finding agrees with our previous finding through PLSR analysis that the ratio is a key predictor of the tumour response to anti-VEGF treatment [k0/k1 ratios or smaller k1 is better compared to those with smaller ratios or higher k1. Interestingly, the result for the ratio is the opposite of the conclusion we drew previously (that a larger ratio correlates with a poorer response to treatment). However, in that work, we focused only on whether the final RTV value was low. This highlights the fact that only evaluating the endpoint RTV of the treated and control group and neglecting the actual tumour volume data over time can lead to misinterpretation of the treatment effect. Indeed, researchers have recognized that while most preclinical studies focus on the endpoints of tumour growth, monitoring tumour growth kinetically may be more insightful [Our study demonstrates that the reatment . Buildinsightful ,43.k0/k1 ratios  or k1 value . This indicates that even when the treatment is not effective in reducing tumour volume, there is still a difference in tumour growth dynamics between the two populations stratified based on the tumour's growth kinetic parameters. Thus, we believe that the k0/k1 ratio or k1 may be prognostic biomarkers to stratify populations for their survival estimate without anti-angiogenic treatment. Interestingly, the parameters provide mechanistic insight into tumour growth. In particular, they highlight that slower linear growth  results in less aggressive overall tumour growth  and, therefore, a better survival outcome.We found that, in two cases (Volk2011a simulated with protocols A and V11a), no significant difference is observed in the survival estimates between the treated and control groups. However, even for these cases, two populations with significantly different survival estimates can be identified based on their 1 ratios b,e or k1k1 to serve as a prognostic biomarker. Although k1 was not revealed as a strong predictor of the final RTV previously in the PLSR analysis, it is inversely correlated with the k0/k1 ratio, and therefore, in our study, it also can be used to stratify the population survival outcome. Here, performing the survival analysis addresses one limitation from our previous PLSR analysis, where we were able to identify which parameters were related to treatment efficacy, but could not identify the specific relationship between the kinetic parameter values and effectiveness of the treatment.Another interesting aspect is the utility of k0/k1 ratios often yield slower tumour growth in a population, and therefore, lead to a better survival estimate of the population. This conclusion could not be made if we were to only analyse the RTV data. In addition, the tumour volumes plotted on the log scale reveal that the effect of anti-VEGF treatment in tumour growth can be relatively transient or gradual.Compared to the mean RTV data, the tumour volume data provide more useful insight into the tumour growth characteristics of the stratified population. In particular, the tumour volume plotted on the log scale more clearly illustrates the source of the differences in the population survival estimates. Specifically, we found that larger Our study uses a predictive computational model of tumour growth. This is a pharmacokinetics–pharmacodynamics model with mechanistic detail that goes beyond what is found in other models. However, in the future, this model can be expanded to address limitations that are not currently accounted for. For example, we do not account for changes in tumour vascularity relative to tumour volume. We assume the vascular volume relative to total tumour volume remains constant, given the lack of robust quantitative data needed to develop a mathematical function describing how tumour vascularization changes over time. In addition, vascular normalization is an important process that has been shown to affect tumour growth and can be regulated by anti-VEGF agents ; howeverin silico mouse populations, predict anti-VEGF treatment outcome and stratify the populations. This approach provides useful information that could facilitate efficient experimental design, such as predicting the effect of different treatment protocols (varying the dosage and the timing of the injections). Additionally, our modelling approach can be adapted for analysis of the patient treatment outcome in clinical studies. With data from a small patient population, we can develop a patient-specific model and generate a larger in silico population. Analysis of the simulated tumour growth and survival data can be used to identify biomarkers that predict responders versus non-responders to anti-VEGF treatment, stratify the predicted population survival and test the response to various treatment schedules.Our study demonstrates a time- and cost-effective way to generate large 4.in silico mouse population and related the kinetic parameters that characterize tumour growth to the response to anti-VEGF treatment. We found that the ratio between two tumour growth kinetic parameters, k0 and k1, as well as k1 alone, can be prognostic biomarkers and that the simulated treatment protocol may have a better outcome for mice whose tumours have smaller linear growth rates. In fact, we found ranges of threshold values for the k0/k1 ratio and k1 that distinguish tumours' response to the anti-VEGF treatment. This study demonstrates an approach for identifying tumour growth kinetic parameters as potential biomarkers, and this model framework can be adapted to predict the efficacy of other anti-angiogenic strategies.We examined tumour growth kinetic parameters as potential biomarkers of anti-angiogenic treatment outcome. Using a computational model that simulates VEGF-dependent tumour growth in tumour-bearing mice, we generated an 5.5.1.121 and VEGF165) secreted by tumour cells, as well as mouse isoforms (VEGF120 and VEGF164) secreted by endothelial cells and muscle fibres. The model includes cell surface VEGF receptors, VEGFR1 and VEGFR2 and soluble VEGFR1 (sVEGFR1). We include neuropillin co-receptors (NRP1 and NRP2) that bind VEGF directly and also form tertiary complexes with the VEGFRs. The protease inhibitor α-2-macroglobulin binds VEGF in blood plasma. We consider the luminal and abluminal endothelial surfaces at the interface between the blood and each tissue compartment. The VEGF isoforms and sVEGFR1 are transported between compartments via transendothelial macromolecular permeability and lymphatic flow. Additionally, species are removed via clearance.We use our previously calibrated and validated model of VEGF binding and distribution in a tumour-bearing mouse . ElectroVEGF binding to its receptors on endothelial cells promotes intracellular signalling that mediates angiogenesis. Thus, we explicitly account for VEGF-mediated tumour growth by incorporating the concentration of ligated receptors localized on tumour endothelial cells into the tumour volume equation . We simu5.2.lsqnonlin function in Matlab. Kaplan–Meier survival estimation was performed using the kmplot function in Matlab, and GraphPad Prism was used for statistical survival analyses.Model equations were implemented in Matlab using the SimBiology toolbox. The model is provided as the SimBiology project file, SBML, Matlab m-file and full list of equations . Parameter fitting was performed using the 5.3.k0, k1 and Ang0). The parameter ψ was held constant, as it was not shown to significantly influence tumour growth, compared to the other parameters. The model-predicted tumour growth curves match closely to the experimental data (fitting error range: 0.0405–0.1833).We previously fitted the model to six independent control datasets to estimate the growth kinetic parameters . The Ang0 value is set to be the median of the best fits in each case. These sets were used to calculate tumour growth with or without anti-VEGF treatment, simulating a population of mice for each dataset. To keep tumour growth profiles realistic, tumours that do not reach 0.1 cm3 within 10 days upon tumour engraftment  were excluded from the analyses.Here, we generated 400 sets of values for 3, as the switch where angiogenesis is more strongly promoted occurs when the tumour reaches 1–2 mm in diameter. The treatment dosage is 10 mg kg−1. The model was simulated for 12 weeks after treatment started. We also simulated alternative treatment protocols: Z denotes biweekly treatment at a dosage of 10 mg kg−1 starting when the tumour volume is 0.004 cm3; V11a denotes biweekly treatment (twice a week) at a dosage of 10 mg kg−1, starting when the tumour volume is 0.5 cm3; and V11a-D denotes biweekly treatment at a dosage of 20 mg kg−1, starting when the tumour volume is 0.5 cm3. Information for all treatment protocols is given in electronic supplementary material, table S3.We simulated anti-VEGF treatment for each dataset. Treatment protocol A is simulated universally across the six cases. In this protocol, weekly treatment starts when the tumour volume reached 0.1 cm5.4.Based on the model-generated tumour growth data, the RTV is calculated at any simulated time point as follows:5.5.in silico mouse is recorded as ‘sacrificed’ when its tumour reaches 2 cm3 within the simulated time. Alternatively, a mouse is recorded as ‘censored’ at a particular time point, t, if its tumour volume simulation remains below 2 cm3 but ends before time t. All other mice are retained in the study and recorded as ‘alive’. Survival curves were estimated by the Kaplan–Meier method using the kmplot function in Matlab [We applied time-to-event analysis to determine the survival of each mouse population . An in sn Matlab , and comThe HR compares the rate of death in two groups, with the assumption that the population HR is consistent over time. It is calculated using the Mantel–Haneszel approach, which is more accurate than the log rank approach . As an e5.6.k0/k1 ratio, we ordered the simulated mouse tumour volume data for each of the six populations according to the k0/k1 ratio. Then, we systematically tested each k0/k1 ratio  value to see if there is a significant difference between the survival estimates for the mice with the k0/k1 ratio above and below ‘ratiothresh’ in the log rank test (p < 0.05). We performed a similar analysis for k0 and k1 individually to determine any k,thresh0 and k,thresh1 values.To determine threshold values for the 5.7.in silico mouse population based on the fitted parameters.Upon identifying a potential predictive biomarker for the efficacy of anti-VEGF treatment, we validated our findings using an independent set of data that was not used to determine the range of the threshold values. To do so, we fitted the control tumour growth for the independent dataset and generated an 5.7.1.in vivo experimental study of MDA-MB-231 xenograft tumour growth in mice by Mollard et al. were used for parameter estimation and validation [For threshold validation, data from the published lidation . Experimlidation  and are 5.7.2.k0, k1 and Ang0 were estimated. In their study, Mollard and co-workers only reported the tumour volumes relative to day 8. However, the absolute tumour volumes are needed to determine how the tumour interstitial volume varies as a function of the total tumour volume. Therefore, we compared the RTV at each time point in the work by Mollard and co-workers to that of all the available control datasets . We then chose to use the interstitial volume equation from the Zibara data, given that the RTV closely matches that of the data in Mollard. Finally, we fitted our tumour growth model to the Mollard control dataset.We trained the model to fit the control tumour growth dataset from  using thlsqnonlin function in Matlab to minimize the sum of squared residuals (SSR):VIexp, is the ith experimental data point of tumour volume, V,Isim is the ith simulated volume at the corresponding time point and n is the total number of experimental data points. The minimization is subject to Θ, the set of upper and lower bounds on each of the free parameters.Fitting was performed using the −8 to 10−2 for k0 and k1 and 10−16 to 10−14 for Ang0. After fitting to the control data, we validated the estimated parameters with data not used in the fitting for model validation. Specifically, we applied the fitted model to simulate anti-angiogenic treatment (bevacizumab) and compared to the experimental measurements for the treatment case. We simulated the dosing regimen used by Mollard et al.: three cycles of weekly intravenous injections lasting for 1 min starting from day 5. We used the combined SSR for the RTV between model prediction and the experimental data (both control and treatment) to identify the optimal parameters. Twelve parameter sets with the smallest errors were taken to be the ‘best’ sets  and the ranges of the estimated parameter values were used for subsequent model simulations .The bounds for each parameter spanned at least two orders of magnitude: 10We extracted the absolute tumour volume at day 8 from previously reported data from Mollard and co-workers  to deter


Recognition of <3 metastases in <2 organs, particularly in cancers with a known predisposition to oligometastatic disease (OMD) , offers the opportunity to focally treat the lesions identified and confers a survival advantage. The reliability with which OMD is identified depends on the sensitivity of the imaging technique used for detection and may be predicted from phenotypic and genetic factors of the primary tumour, which determine metastatic risk. Whole‐body or organ‐specific imaging to identify oligometastases requires optimization to achieve maximal sensitivity. Metastatic lesions at multiple locations may require a variety of imaging modalities for best visualisation because the optimal image contrast is determined by tumour biology. Newer imaging techniques used for this purpose require validation. Additionally, rationalisation of imaging strategies is needed, particularly with regard to timing of imaging and follow‐up studies. This article reviews the current evidence for the use of imaging for recognising OMD and proposes a risk‐based roadmap for identifying patients with true OMD, or at risk of metastatic disease likely to be OM. The development of metastases is driven by a variety of tumour and host characteristicsThe conditions that favour development of OM as opposed to a PM have been modelled by Withers and Lee.This article reviews the role of imaging in defining OMD. It acknowledges the limitations of current imaging modalities, which may be poorly sensitive, and the challenges of implementing newer, more sensitive imaging modalities that largely remain nonstandardised and invalidated, issues that have been recently addressed comprehensively.It has long been known that histological type and grade of a tumour is indicative of metastatic risk.n vitro assays of adhesion and invasion using metastatic cell lines transfected with these microRNA's resulted in a significant decrease in adhesion to Matrigel as compared to nontargeted control transfected cells. Further, ectopic expression of selected 14q32‐encoded miRs or stable repression of targeted genes by shRNAs led to reversal of a PM phenotype to an OM phenotype.Comparison of the genetic features of patients with OM who subsequently turn out to be PM vs. those who were truly OM has revealed interesting differences. Distinct microRNA expression patterns were found in a small study of 34 patients, all of whom had received radiotherapy with curative intent to their oligometastases, these patterns were not just evident in the oligometastasis, but also in the primary tumour itself.In addition to T‐staging, the phenotype of a tumour on imaging is a well‐established predictor of disease progression/outcome. In rectal cancer, pre‐operative high resolution T2‐W MRI can distinguish prognostic groups based on assessment of depth of extramural spread, relationship of the tumour edge to the mesorectal fascia and extramural venous invasion.max)) has been shown to be able to predict occult nodal metastases from the metabolic activity of the primary tumour.max was independent of tumour size and importantly type of tumour, for predicting the presence of occult lymph node metastasis.max of the primary tumour was shown to predict occult metastases in NSCLCn = 163), an SUVmax of 7 was deemed to be the best threshold for indicating metastatic risk; a value <7 was shown to be an independent prognostic factor for metastasis‐free survival.max from 18FDG‐PET have been shown to be statistically significant independent risk factors for high histological grade and hence of metastatic risk.Evidence also links functional imaging‐based tumour properties to metastatic disease, prognosis and survival. In non‐small cell lung cancer (NSCLC), quantitative measures of PET tracer uptake – ; freedom from distant metastasis was superior if treatment‐induced tumour necrosis was 90% or greater  indicating likely control of micrometastases in these patients.n = 599 in each arm)Finally, the initial response of the primary tumour to a given chemotherapy is also a powerful prognostic indicatorThe commonest sites of metastases (OM or PM) are liver, lung, skeletal and nodal. While the first two require imaging with dedicated organ coverage, imaging requirements for the latter two necessitate whole‐body techniques. Important considerations are the selection of the imaging technique that delivers maximal sensitivity and specificity for disease detection, appropriate organ coverage and the optimal timing and intensity of imaging follow‐up.18FDG‐PET is directly related to metabolic activity and turnover of tumour cells and is particularly effective in recognising OM or monometastatic disease.18FDG PET‐CT for metastasis detection in lung cancer, it is not routinely recommended for follow‐upCT scans detect metastases within soft‐tissues and bone based on a change in tissue morphology and density. MRI can also detect functional features such as tumour vascularity, cellularity, stiffness and metabolism. Bone scintigraphyIf metastatic risk is more likely at a particular site, high‐resolution imaging should focus on the region‐of ‐interest . Conversely, full body coverage with MRI or PET needs to be retained where skeletal or multiple organ involvement is more likely (e.g. for prostate cancer). In addition to spatial resolution, tumour to background contrast is vital for optimal sensitivity of disease detection. A meta‐analysis of nine diagnostic accuracy studies  and four change‐in‐management studies (488 patients with 281 lesions) emphasises the vital importance of tumour to background contrast in lesion detection. The per‐lesion sensitivity and specificity for contrast‐enhanced‐MRI ranged from 86.9–100.0% and 80.2–98.0%, respectively, compared to 51.8–84.6% and 77.2–98.0% for contrast‐enhanced‐CT because of the superior image contrast of the former.18F‐FDHT) a radio‐labelled dihydrotestosterone analogue, directly targets the androgen receptor (AR) on tumour cells. However, testosterone levels above castration level means that competitive binding can hamper accurate FDHT evaluation. Similarly, 68Ga‐labelled prostate‐specific membrane antigen (PSMA) used to image prostate cancer may be falsely negative in the liver where a high background activity can potentially obscure lesions, or when liver metastases tend to lose PSMA‐expression in advanced metastatic disease. Sensitivity, specificity and accuracy against a surgical gold standard for lymph node detection in a multicentre study for 68Ga‐PSMA PET in the primary setting were 53%, 86% and 76% but improved with higher surgical sampling, increasing to 67%, 88% and 81% in a subgroup with of patients with ≥15 lymph nodes removed.18F‐DHT and 18F‐ES (Estradiol) showed that semi‐quantitative androgen or oestrogen receptor expression on immunohistochemistry and 18F‐DHT or 18F‐ES uptake respectively on PET was correlated. Moreover, using optimal cut‐offs (SUVmax of 1.94 for 18FDHT‐PET and 1.54 for 18FES‐PET) sensitivities of 91% and 100% and specificities of 100% and 100% respectively were achieved.Sensitivity and specificity of PET imaging for detecting OM may be optimised further by disease‐specific radiotracers directed against tumour specific antigens. A pitfall of these techniques lies in the differential expression of the antigens in tumour versus normal tissue and in changing tumour biology. For example, K = 0.87 ) in several studiesK = 0.60 )Whole‐body MRI has the advantage of combining morphological data (T1 and T2‐W imaging) with functional information (diffusion‐weighted and dynamic contrast‐enhanced imaging) thus simultaneously exploiting multiple contrast mechanisms to image and detect the presence of disease. As diffusion‐weighted and contrast‐enhanced MRI data are fundamentally quantitative, thresholding can be set so that the images display the required sensitivity and specificity. Anatomic images are most useful at the early stages, i.e. at presentation or first biochemical recurrence. At later stages of disease, morphologic images can be more difficult to interpret, especially with the appearance of new lesions or reactivation of previously responding metastases on a background of treated lesions. Here the role of diffusion‐weighted sequences becomes crucial.3 for dedicated organ imaging but is around 50mm3 for whole body techniques. Generally, lesions <5 mm are considered undetectable by RECIST  criteria, as specificity is low for small volume lesions. A 5 mm lesion effectively has a volume of 65mm3 and therefore approximately 150–350 million cells . Differences in cellular density and extracellular matrix composition of metastases at different anatomical locations may affect image contrast and profoundly influence detection sensitivity. Poor image contrast may mean that even a high spatial resolution technique such as CT (30 microns) does not deliver the desired detection sensitivity.Despite the exponential availability of imaging and the declining costs of genetic analyses needed to characterise tumours, several challenges in effective recognition of OM remain. Imaging detection sensitivity depends on the modalities, spatial and contrast resolution. Spatial resolution depends on hardware and software capabilities of the imaging equipment . With MRI, spatial resolution is a trade‐off against coverage, so can be as high as 0.5mm68Ga‐PSMA PET can be false negative in up to 5% of patients with prostate cancer, due to absent or low expression of PSMA on prostate cancer cells. It also has been reported that in advanced metastatic castration‐resistant prostate cancer, metastases (mainly in the liver) can lose PSMA‐expression.Radiotracer techniques that are target‐specific are highly sensitive (e.g. targeting somatostatin receptors has been widely used for imaging neuroendocrine tumours)18F‐Choline PET also has been trialled in several studies for metastatic node detection: in 130 prostate cancer patients at high‐risk for extra‐capsular disease who underwent radical prostatectomy, with 912 lymph nodes sampled 18F‐Choline PET/CT showed a better performance than CT for detecting nodal involvement, particularly for metastases greater or equal than 5 mm in size .Accurate detection of metastatic lymph nodes remains the holy grail of oncological imaging. Identification of abnormally enlarged lymph nodes is the domain of CT where the sensitivity of detection of enlarged nodes depends upon the size threshold utilised. In RECIST 1.1, nodes with short axis ≥ 10 mm but <15 mm are considered pathological, although nontarget lesions. CT is unable to detect architectural changes within normal‐sized (<10 mm) lymph nodes, which results in a low sensitivity (40%) as the majority of metastases are microscopic. The average specificity however is around 80% against a surgical gold standard because reactive or inflammatory change within lymph nodes results in false positives. Despite the high spatial resolution of CT, the poor contrast resolution means that it performs less well than MRI.Validation of OMD on imaging remains hugely problematic. It is not feasible to biopsy multiple sites, particularly in bone and brain. Confirmation of accuracy of new imaging agents is highly dependent on what is known from preclinical studies, or on longitudinal follow‐up observational data. The imaging community have produced an imaging biomarker roadmap that addresses these issues, which is being widely implemented.30 cell burden and are unlikely to be manifest in the first year. Over a decade ago Singh et al. followed 369 patients with Stage T1‐T3aN0‐NXM0 prostate cancer for 10‐years who were treated with external beam radiation with curative intent to a mean dose of 65Gy. There was a better overall survival in patients with <5 metastases than those with more numerous lesions.p = 0.02). Dominant patterns of metastasis to suggest a multi‐step hierarchical order of metastasis did not occur. Therefore, a follow‐up protocol for detection of OM in prostate cancer would ideally be intense and increased around the 4 year mark and employ the most sensitive techniques that covered the spine and pelvis, either with a targeted radioisotope or whole‐body scanning, increasingly done with MRI (Fig. The timing of longitudinal or follow‐up imaging studies is an important consideration. Conventionally, after the effective treatment of the primary tumour, patients are often imaged 3‐monthly for the first year, 6‐monthly for the next 2 years and then annually or as the clinical situation demands. Although the rationale for this is geared to detecting recurrence at the primary site it does not in fact fulfil the need for detecting OM where the likelihood of detecting disease in the first year is low with increasing likelihood thereafter. True OM amenable to curative treatment will remain undetectable until they reach a 2Recognition of the metastatic potential of a tumour is crucial in determining patients’ management pathway. Metastatic propensity is traditionally based on histologic types although increasingly genetic profiling is being used to stratify patients to various management options with surgery, radiotherapy and chemotherapy/Immunotherapy as appropriate. The addition of an imaging phenotype into this paradigm can have a major impact on treatment decisions. Thereafter, a tumour target‐specific protocol that is organ‐specific or requires a whole‐body approach can be decided on, depending on the tumour type and likely mode of spread. A regime of more frequent follow‐up between 2 and 4 years after completion of treatment rather than early post‐treatment is most likely to favour earlier recognition of OMD. Achieving an appropriate cost‐effective surveillance program for imaging patients at risk of OMD opens the door to new therapeutic strategies for these patients with the potential for cure.


Diffuse plexiform neurofibroma (DPN) in patients with neurofibromatosis type 1 (NF1) causes motility dysfunction in severe cases. Transcatheter arterial embolisation (TAE) is an effective haemorrhage control method in vascular tumour surgery.We performed debulking surgery for DPN in the buttock and posterior thigh of two NF1 patients. Preoperative TAE with gelatine particles to tumour feeder vessels was conducted in both cases. Operative bleeding volumes were 500 and 4970 mL, respectively. In the latter case, the resection area extended to the upper poles of the buttocks, and the tumour invaded deeply into the surrounding tissues. Massive haemorrhage occurred, and internal iliac arterial balloon was inflated temporarily to further suppress the bleeding. Delayed wound healing due to TAE occurred; debridement and wound closure were required. Motor function improvement was confirmed in both patients.Bleeding volumes varied because of highly developed collateral pathways and tumour invasiveness. As the upper pole of the buttock was perfused by the superior gluteal artery and its numerous collateral vessels, complete haemostasis was difficult despite adequate TAE. Because delineating the tumour border from the normal tissue was impossible due to the high tumour invasiveness, cutting into the hypervascular tumour was inevitable. As gelatine particles were absorbed but remained within the vessels, prolonged wound ischaemia and delayed healing occurred.Although TAE with gelatine particles and balloon occlusion were reliable haemorrhage control methods in debulking surgery for lower limb DPN, optimal haemorrhage control technique, compatible with haemostasis and wound healing, was desired. CriticaWhen large feeding vessels are evident, preoperative transcatheter arterial embolisation (TAE), aiming the reduction of the blood loss during the surgical procedure, is effective. This was firstly reported in 1983 . In thisThis case report has been reported in line with the SCARE criteria .2Case 1: A 20-year-old man with NF1 visited our clinic hoping to reduce the enlargement of his left lower limb. Examination confirmed a soft and drooping tumour encircling the thigh A. DPN waUnder general anaesthesia, debulking surgery was performed. The skin of the lateral thigh turned purple, probably because of ischaemia following TAE. Enclosing the discolouration area, a 3-kg tumour was resected above the fascia level. The tumour’s pedunculation and flexibility enabled us to temporarily ligate at the tumour’s base B. The toCase 2: A 40-year-old man, diagnosed with NF1 in his childhood, was referred to our department with complaints of walking difficulty. His right lower limb had begun to enlarge since his 30 s. Eventually, he had become unable to walk by himself because of his huge and heavy leg A. We estWe planned serial excision with the resection area being from the buttock to the posterior thigh. Before the procedure, interventional radiologists performed TAE with Serescue™ to the feeding vessels originated from the superior and inferior gluteal arteries and the deep femoral artery of the affected side. An occlusion balloon was placed within the right internal iliac artery (IIA) to prevent uncontrollable critical haemorrhage.Under general anaesthesia, we resected the tumour in the posterior thigh towards the head A. In theTo prevent further bleeding from the wound edge, additional TAE was performed to the superior and inferior gluteal arteries immediately after surgery. The wound edge became gradually necrotic and dehiscent B. FinallThe second debulking surgery in the lower leg was conducted 4 months after the first debulking surgery. At this time, we could apply a tourniquet to the thigh area. The total blood loss during the second surgery was 420 mL, and TAE was not conducted. Wound healing was not delayed. The patient left the hospital walking by himself C.3DPN presents as a highly vascular tumour, and the number of feeder vessels increases with the proliferation of the tumour. Histological study has confirmed that the vascular walls become vulnerable because of thinning of the tunica media and fragmentation of the tunica elastic . Hence, We assumed that the difference in the amount of bleeding between the two cases was caused by two reasons: location and invasiveness of the tumour. In case 2, the tumour resection area extended to the superior buttock. There is an abundant blood supply from the superior gluteal artery, a branch of IIA, in the superior buttock area . The colSecond, the invasiveness of the tumour was markedly different in the two cases. The tumour invaded into the muscle and its surrounding soft tissues to a higher degree in case 2 than in case 1. As delineating the tumour margin in deeply infiltrative DPN is almost impossible, unintentional intralesional resection is not rare . TherefoThe efficacy of TAE for haemorrhage control in surgical resection of lower limb DPN has been reported in several studies ,14. AmonAlthough gelatine particles are reliable haemostatic materials, focal ischaemia and necrosis of normal tissues are expected side effects of embolisation . GelatinWe struggled to achieve both adequate haemostasis and wound healing. As mentioned above, IIA receives blood supply from the contralateral side. Therefore, effective haemostasis can be expected in the buttock area by the intervention of bilateral IIAs. However, TAE with gelatine particles to bilateral IIAs leads to extensive necrosis of skin and muscle tissue in the buttock . This ca4We adopted TAE with gelatine particles and unilateral balloon occlusion as haemorrhage control for the debulking surgery of lower limb DPN. Development of the ideal method for reducing blood loss to ensure the balance of haemostasis and wound healing is necessary.The authors have no conflicts of interest to declare.None.This study was exempt from ethical approval in Kobe University Hospital.Written informed consent was obtained from the patients for publication of this article including all figures. A copy of the written consent is available for review by the Editor-in-Chief of this journal on request.Daiki Kitano, Takeo Osaki, Mika Nakasone and Tadashi Nomura performed the operations. Daiki Kitano and Takeo Osaki drafted the manuscript. Tadashi Nomura, Kazunobu Hashikawa and Hiroto Terashi supervised the operations and this case report.Research Registry.UIN: researchregistry4516.Takeo Osaki.Not commissioned, externally peer-reviewed.


The 2D lattice Boltzmann model includes an initial lymphatic vessel and a collecting lymphangion embedded in a porous tissue. The lymphangion segment has mechanically-active vessel walls and is flanked by deformable valves. Vessel wall motion is passively affected by fluid pressure, while active contractions are driven by intracellular Ca2+ fluxes. The model reproduces NO and Ca2+ dynamics, valve motion and fluid drainage from tissue. We find that valve structural properties have dramatic effects on performance, and that valves with a stiffer base and flexible tips produce more stable cycling. In agreement with experimental observations, the valves are a major source of NO. Once initiated, the contractions are spontaneous and self-sustained, and the system exhibits interesting non-linear dynamics. For example, increased fluid pressure in the tissue or decreased lymph pressure at the outlet of the system produces high shear stress and high levels of NO, which inhibits contractions. On the other hand, a high outlet pressure opposes the flow, increasing the luminal pressure and the radius of the vessel, which results in strong contractions in response to mechanical stretch of the wall. We also find that the location of contraction initiation is affected by the extent of backflow through the valves.The lymphatic system contains intraluminal leaflet valves that function to bias lymph flow back towards the heart. These valves are present in the collecting lymphatic vessels, which generally have lymphatic muscle cells and can spontaneously pump fluid. Recent studies have shown that the valves are open at rest, can allow some backflow, and are a source of nitric oxide (NO). To investigate how these valves function as a mechanical valve and source of vasoactive species to optimize throughput, we developed a mathematical model that explicitly includes Ca The collecting lymphatic vessels are responsible for pumping fluid from the tissue and delivering it to lymph nodes in order to prevent edema and maintain immune function. Although potentially beneficial for a wide variety of patients, there are currently no pharmacological modulators of lymphatic function5. The prerequisite for creating such drugs is a fundamental understanding of the mechanisms that influence lymph clearance.Lymphatic function is critical for fluid homeostasis, and local failure leads to edema with significant morbidity and local immune dysfunction6, which function as one -way valves to allow fluid to enter the vessels and prevent backflow into the tissue8. Initial lymphatics pass the fluid to collecting lymphatics, which contain distinct compartments defined by luminal one-way valves, known as lymphangions, that contract spontaneously to drive flow12. Thus, a collecting lymphatic vessel behaves as a group of distributed pumps aligned in series and regulated by local physiological conditions13. Depending on the fluid pressure conditions in the tissue and lymphatic system, collecting lymphatic vessels can adjust their behavior to maintain fluid homeostasis. Lymphatic vessels minimize contractions if existing fluid pressure gradients can drive flow, but actively pump to drive fluid otherwise15.The lymphatic system consists of lymphatic capillaries - termed initial lymphatics - that absorb interstitial fluid from the tissue and have unique overlapping endothelial cells16. In summary, our model shows that 19. However, in our previous work, the intraluminal valves were modeled by mathematically inserting a semi-permeable wall in the vessel when the flow reversed direction. Although this approach was able to reproduce the correct behaviors seen in vivo, it simplified valve performance and neglected valve leaflet structure and mechanics.Our previous work has elucidated how these behaviors are coordinated throughout the lymphatic system by mechano-sensitive feedback20. Experimental studies and mathematical models show that this property can increase flow efficiency by reducing flow resistance when the vessel is not actively contracting, even though it results in significant backflow as the downstream lymphangion contracts24. The valve leaflets are also important as sources of biomolecules. Experiments have shown that the leaflets are a significant source of nitric oxide, presumably produced by dynamic shear stress on the leaflet structures themselves25.The intraluminal valves that bias the flow in the direction away from the peripheral tissues are extremely important for lymphatic function, but little is known about their mechanical properties or how they influence lymph clearance or contraction efficiency. Previous studies have determined that lymphatic valves are biased to the open position, especially when the vessel is partially distended by a trans-wall pressure gradientHere, we extend our previous model of collecting lymphatic vessels by introducing realistic intraluminal valves. Furthermore, we embed the pumping vessel within a poro-elastic tissue that has fixed pressure boundaries in order to simulate fluid transport and edema at the tissue level.27 to calculate the fluid flow, shear stresses and pressures in the tissue and lymphatic vessel. The endothelium on the inner wall of the vessel can generate nitric oxide (NO)30 in response to increased shear stress, and contractions of the collecting lymphatic are determined by the concentration of 16. The details of the model are given in the Methods section.Figure 27 to simulate fluid flow through the tissue and lymphatic vessel. The curved boundary condition31 is used to keep track of the location of the vessel wall and the valves with respect to the lattice grid. The single relaxation time approximation to the Boltzmann equation can be discretized in both space and time ast and location x. ei is the discrete velocity. We use the lattice Boltzmann method (LBM)27u are the fluid density and velocity defined byFor the D2Q9 model, one form of the equilibrium distribution is32S can be calculated by integrating the stress tensor and momentum flux over S32:n is the unit normal vector on S oriented towards the fluid. V is the velocity of S. In order to calculate the hydrodynamic force exerted on S, the distribution function fi on S in Eq. , we use the stress -integration method. The stress tensor in the lattice Boltzmann method can be calculated asμm. Fluid from the tissue can enter the porous vessel with fixed geometry at left, which represents the initial lymphatic capillaries38. The solid regions in this segment are impermeable, while the open regions are semipermeable, simulating the primary valves in the lymphatic capillaries. Lymphatic capillary valves allow fluid entry but resist leakage back into the tissue, so we institute a partial bounce back boundary condition in the “open” regions of this segment39. We use a constant bounce back ratio μm long to reduce the effect of the right side boundary and provide structural support.The schematic diagram of a lymphatic vessel with single lymphangion defined by two valves and embedded in tissue is shown in Fig. 42, NO appears to play a major role in lymphatic muscle cells. NO is rapidly produced by endothelium in response to changes in shear stress and is quickly degraded43. For simplicity, our analysis focuses on the effects of NO on vessel contractions, but could be generalized to other flow-mediated relaxation factors. The endothelium on the inner wall of the vessel can generate nitric oxide (NO)30, which is allowed to convect and diffuse in both the fluid and tissue spaces15:Although many vasoactive substances can alter vessel contractilityλ is the chemical reaction rate constant. t is the lattice time scale. As λ increases, the chemical reaction rate increases. 45. vl indicates fluid velocity along the tangential direction of the membrane surface and xn is the normal direction vector. Within the lymphangion, the valve structures can also generate NO. In fact, as shown in Fig. Fl we calculate in Eq. . When the membranes of the valve approach the center line of the vessel, we change the rest position of the valve to a straight line and the bending force is changed to:61:V is the velocity of the center of mass of each segment, δt is the Newtonian time step, here chosen to be a is the acceleration of each segment. When the segments move, new fluid nodes are revealed; we extrapolate the status of each new fluid node based on the known quantities of those fluid nodes located on the same side of the moving boundary.For motion of the valves and vessel wall, we assume the structures have the same viscosity. The vessel and the valves move according Newton’s laws of motion. At each Newtonian dynamics time step, the center of mass of each segment is updated by a so-called half-step ‘leap-frog’ scheme62. As shown in Fig. When two membranes approach each other, they can displace all the fluid, and the hydrodynamic force cannot be calculated using LBM. In this case, we use lubrication theory to calculate the hydrodynamic force63, the Stokes equation can be represented byp is the pressure, According to lubrication theoryyIntegrating Eq.  of y23\dFrom Eq. 24\documeThe flux is:The fluid volume between two planes in Fig. δt, the variation of h0 is:During virtual variation of The flux caused by the relative movement in the normal direction is:Q and ux is also linear, the general flux can be written as:The flux ause Eq.  is linea64:Because Let n connected segments, each having length l, if each segment moves with the same velocity, the lubrication force exerted on an individual segment should be:For two planes constructed with If some segments move up  to 0.7L−1 . Larger values of B mean that the valve is more open at rest. Increasing B causes the cycle-averaged flux to increase before 0.5. This implies that, before 0.5, valves biased to stay open may allow some leakage, hurting efficiency, but this is more than offset by the decrease in overall flow resistance presented by the open valves. Above 0.6, the leakage significantly decreases the efficiency, resulting in decreased flux. This is consistent with previous models and experimental observations, which show that lymphatic valves are biased toward the open position24. In the remaining simulations, we set A = 5, B = 0.6L−1.We first investigated how valve mechanical properties affect lymph clearance and pumping behavior under equal pressure at inlet and outlet. To do this, we set the bounce back condition of the porous part of the initial lymphatic region  can determine lymph flow rates and the apparent direction of contraction propagation. Although the one-way valves ensure positive flow for any sequence of contractions, experimental observations conclude that the contractions can propagate either forward or retrograde with respect to the flow direction19. The reasons for this were previously unknown. We previously reported that if NO dominates, the contraction propagates retrograde, but if 15. Our current results with explicit mechanical valves extend this result, showing that the onset of contraction depends on the NO distribution during diastole. Many factors can shift the NO distribution along the lymphangion during diastole, including valve leakage, the double-sided nature of the valve leaflets and the pressure at the outlet. As these vary, the NO distribution can change, and the contractions initiate wherever NO is lowest. More importantly, these considerations can change the efficiency of fluid or cell transport through the lymphatic system.Our simulations reveal a number of interesting implications of the interplay between lymphatic valve structure and mechanobiological feedback control of contractions. Because of the inhibitory effect of NO on contractions, and the fact that its release is dependent on shear stresses, its spatiotemporal dynamics along the vessel wall –especially around valves and during backflow – can affect the propagation of contractions in interesting ways. In actual lymphatic vessels, the diameter is smallest at the valvein vivo. In addition, we set the NO concentration at the boundaries to zero. However, in vivo we would expect there to be dynamic changes in the NO levels in nearby tissue contributed by other nearby lymphatic elements, including upstream and downstream. Future model development will include multiple lymphangions in series, an improvement that will address all these current limitations.A limitation of the model is that we have only a single lymphangion. Nevertheless, it is possible to observe at which end of the vessel the contractions initiate and to determine overall direction of propagation. Another limitation is that the lymphangion has to be anchored to fixed walls at the left and right to establish the boundary conditions. This limits motion of the valve structures somewhat compared to what is seen Supplementary video 1Supplementary video 2Supplementary video 3


Syringe pumps are a necessary piece of laboratory equipment that are used for fluid delivery in behavioral neuroscience laboratories. Many experiments provide rodents and primates with fluid rewards such as juice, water, or liquid sucrose. Current commercialized syringe pumps are not customizable and do not have the ability to deliver multiple volumes of fluid based on different inputs to the pump. Additionally, many syringe pumps are expensive and cannot be used in experiments with paired neurophysiological recordings due to electrical noise. We developed an open source syringe pump controller using commonly available parts. The controller adjusts the acceleration and speed of the motor to deliver three different volumes of fluid reward within one common time epoch. This syringe pump controller is cost effective and has been successfully implemented in rodent behavioral experiments with paired neurophysiological recordings in the rat frontal cortex while rats lick for different volumes of liquid sucrose rewards. Our syringe pump controller will enable new experiments to address the potential confound of temporal information in studies of reward signaling by fluid magnitude. The neural basis of reward processing is a major topic in neuroscience. Many studies examine reward coding by varying the amount of fluid given to experimental animals as they perform a behavioral task. Most devices used in these studies are not capable of delivering different volumes over a common period of time. As such, reward coding is confounded by temporal information. To resolve this issue, we developed a syringe pump controller that is capable of delivering different fluid volumes, in the range used in behavioral studies, over common periods of time. Here, we report the designs of all components of the pump and the protocols needed to create and use it.In behavioral neuroscience research there is often a need to deliver fluid rewards to animals. This is typically done using passive gravity-based systems, syringe pumps, or solenoid valves. Syringe pump systems can be quite costly when purchased from a commercial vendor (>$500) and are often limited in their functionality. Commercial laboratory equipment is also not currently available to deliver multiple fluid volumes on a microliter scale. Instead, different fluid volumes are produced by using syringes of different sizes from different pumps or by leaving a syringe pump running or solenoid valve open for different periods of time. As such, published neuroscience studies of reward magnitude coding have confounded fluid volume with reward delivery time  through To address this issue, we developed an open source syringe pump control circuit using commonly available parts and a Teensy microcontroller with open source firmware. We modified an open source 3D printed syringe pump holder  to houseHere, we provide instructions for building the syringe pump controller and share the printed circuit board design, parts list, and microcontroller firmware for developing the syringe pump controller, all of which can be made for <$300. We validated the syringe pump controller by implementing it in a sucrose licking task where rats licked for different volumes of fluids, and show that neural activity in the medial frontal cortex can simultaneously be recorded while using the syringe pump controller to deliver rewards of different sizes.https://github.com/LaubachLab.To hold the syringe, we used a published 3D printed syringe pump design , and inchttps://github.com/LaubachLab.A bill of materials for constructing the syringe pump controller can be found as a spreadsheet in 10.1523/ENEURO.0240-19.2019.ed1Extended Data 1Extended Data 1, ZIP file.Teensy Code Firmware (.ino); PCB design files  and libraries in Eagle (.lbr); Syringe calibration spreadsheet for water and 16% sucrose (.xlsx); Build instructions (.pdf); Bill of materials (.xlsx); Closeup images of the device (.png). Download https://github.com/LaubachLab. PCBs were designed using AutoCAD Eagle software (Autodesk). Boards are also available directly from various PCB manufacturing houses, including for purchase on the project page of OSH Park https://oshpark.com/shared_projects/VtseE2Ia.The schematic for the PCB  and manuhttps://github.com/LaubachLab. An example of the control board is shown in A detailed protocol for constructing the syringe pump controller can be found in The syringe pump controller delivers dissimilar volumes of fluid in equal time intervals. To achieve this, we used formulae derived from the kinematics of the stepper motor driving the linear motion of the syringe plunger.x (number of steps) as the position variable, v (steps per second) as the velocity variable, and a (steps per second squared) as the acceleration variable. The amount of fluid delivered per step must be determined via a calibration procedure for a particular syringe design as detailed below.The angle of the output shaft of the motor is controlled by digital pulses issued by a microcontroller. A typical stepper motor is designed with 200 steps/revolution (or 1.8°/step). The linear motion of the syringe plunger is directly proportional to the angle of the output shaft of the motor. Consequently, the amount of fluid delivered is a function of this angle and the size of the syringe. As such, the kinematic equations are derived using xmax, the minimum amount of time required to accelerate to a maximum velocity and then immediately decelerate to zero velocity is given by:When delivering a specified volume of fluid, the stepper motor driving the linear motion of the syringe plunger undergoes three stages of motion—initial acceleration, constant velocity, and final deceleration. Given a fixed acceleration and the maximum desired number of steps, tmin, we may now calculate the velocity nv for the desired number of steps, nx, less than xmax, as follows:Given the same acceleration and fixed Therefore, given a fixed acceleration and variable distances (less than some maximum distance traveled), velocity profiles can be generated that ensure desired fluid volume delivery over an equal time interval.Perform the steps in the Calibration methods section to obtain fluid volumes based on the user’s individual setup. .Power up the device using a 12–24 volt DC power supply.Check that the values that appear on the organic light-emitting diode (OLED) screen are correct for the desired volume dispensed, according to syringe pump calibration.Load up the syringe with fluid. The motor can be advanced in either direction by pressing the switch buttons on the board so that the pusher block is flush with the plunger in the syringe.Any input to the pins on the board  from behavioral software or from pressing switch buttons will dispense fluid.t).The volume of fluid delivered by the syringe pump depends on the size of the syringe, the pitch of the pump leadscrew, and the total rotation of the motor. Stepper motor rotation is defined by the number of “steps” issued to the motor controller. If the jumper switches are set as shown in The three motor rotation values are activated by a falling voltage transition on pins 18, 19, and 20, which then rotates the motor shaft p1, p2, and p3 steps, respectively. Additionally, these step sequences can be activated simply by connecting pins 18, 19, and 20 to the GND (ground) pin on the circuit board. For example, if p2 = 100 and pin 19 is connected to the GND pin, the motor will rotate 100 steps, which for the default setup is 180°. Given that a different size or different diameter syringe will dispense different fluid, it is necessary to calibrate the syringe controller with the desired type of syringe .After connecting the controller to a power supply, there are four variables that appear on the OLED screen: p1, p2, p3, and t. p1, p2, and p3 equal different “steps” or rotations that the motor will advance by each time it receives a falling edge input to pins 18, 19, or 20 on the circuit board. By default, these are set in the Teensy code to p1 = 50, p2 = 100, and p3 = 200. These values can be changed either within the code or by using the rotary encoder. Pressing down on the rotary encoder will change between the values and rotating the knob will alter the selected value. The settings will revert to the default numbers every time the pump is unplugged. The actual volume of fluid dispensed will depend on the type of syringe used and the viscosity of the fluid, which can be determined through performing pump calibration measurements as shown in t on the TeensyView OLED screen) is determined by the fixed acceleration of the motor and the third variable, p3. The value of the variable p3 will designate the timing of the reward (t), and then the acceleration for variables p1 and p2 is automatically adjusted so that p1 and p2 will deliver their respective volumes along the same time scale as p3. These variables can all be changed either within firmware or on the rotary encoder, as seen in 2 and p3 = 200 steps, and the motor will rotate once in 316 ms.The timing of the reward  yielded timing up to 15% lower than the theoretically calculated values. Accurate timing information is available via the serial port or pin 23 on the controller board.The device can take several inputs from behavioral software. As stated above, the inputs read a falling voltage transition. The circuit board and firmware are programmed to take three inputs that each wait for a falling edge transition to be activated . Conversely, pin 23 is programmed as an output to go HIGH (3.3 V on a Teensy 3.2 microcontroller) when the motor is moving and LOW (0 V) when the motor stops. An LED may be connected to this pin to indicate motor movement or it may be used to pass accurate timing information to other instruments.Several additional general purpose input/output analog inputs and the onboard digital-to-analog converter of the microcontroller are available for controlling additional hardware or accepting inputs from switches or sensors. The firmware is easily modified and programmed using the Arduino Software IDE.There are additional advantages that come with using a NEMA-17 integrated stepper motor+driver with this control circuit. Previous syringe pump designs have made it difficult to drive the pump in reverse or pull back the plunger of the pump to use for suction instead of fluid delivery. The integrated motor has functionality to run forward or backyard through pressing one of three push-button switches on the board. Holding down one of the three push-button switches  will move the pump in a clockwise direction or a counterclockwise direction, or will cycle the pump through a short dance of the programmed values, respectively. The integrated stepper motor driver is optimal to use with the controller instead of a standard NEMA 17 motor since the integrated motor driver will provide accurate motor rotation and will therefore provide reliable fluid volumes.The syringe pump control circuit was tested first to validate adequate changes in fluid volumes at each step. We created a spreadsheet of the exact volumes delivered with 30 and 60 ml syringes, first with water and then additionally with 16% sucrose, which is commonly used in our behavioral experiments. We then validated the use of the pump in a behavioral experiment paired with electrophysiological recordings in a group of rats. We show that differences in fluid volume can be tracked both behaviorally and neurophysiologically while ensuring that no major electrical noise coming from the device would affect neurophysiological recordings.10, Plexon), which is a passive breakout board used to troubleshoot data acquisition systems. We recorded “noise” from the breakout board for 2 min while syringe pumps were activated. This was performed with our syringe pump controller and with a commercial syringe pump . Additionally, we tested the commercial syringe pump again with incorporating a resistor-capacitor (RC) “snubber,” which is a device that suppresses voltage transients. A Quencharc Arc Suppressor  was placed inside the commercial syringe pump with the leads of the snubber attached to the two ground leads on the motor inside the syringe pump.In an effort to compare the functionality of our syringe pump controller setup against a current commercial syringe pump, we performed electrophysiological recordings while activating a syringe pump 100 times for 300 ms across a 2 min test session. A headstage cable was plugged into a headstage testing board  syringe was attached to the pump and primed with fluid before data collection. Liquid was dispensed in 500 step intervals for the 30 ml syringe and 400 step intervals for the 60 ml syringe. The mass of each dispensing interval and their averages were recorded and are available in the spreadsheet in All animal procedures were performed in accordance with the regulations of the American University animal care committee. Five male Long–Evans rats were used to validate the functionality of the syringe pump controller paired with electrophysiological recordings. Rats were implanted with a 2 × 8 multielectrode array in the medial frontal cortex . Local field potential (LFP) activity was recorded using a Plexon Multichannel Acquisition Processor (Plexon).Rats were trained in a shifting values licking task. Briefly, rats must lick at a spout to receive a liquid sucrose reward. Typically, rats receive alternating concentrations of liquid sucrose rewards every 30 s at a single drinking spout in the behavior box. Here, instead of alternating the concentration of liquid sucrose rewards, the reward volume was changed. Rats received a 16% (wt/vol) concentration of sucrose, while the volume of the reward would shift from a large  to a small  reward. The timing of the reward was set at 0.5 s for both volumes. A single lick at the spout would trigger the syringe pump controller to deliver one of two fluid volumes. Subsequent licks during the fluid delivery time do not “retrigger” the fluid delivery, but instead the first lick after fluid delivery would trigger the next pump activation.Plexiglas operant chambers (Med Associates) contained a glass drinking spout that was centered on one side of the operant chamber wall at a height of 5 cm from the chamber floor. Tygon tubing connected to the back of the drinking spout would administer the fluid from a 60 ml syringe (BD) hooked up to the syringe in the syringe pump holder. A “light-pipe” lickometer (Med Associates) detected licks via an LED photobeam, and a lick would trigger the syringe pump to deliver one of the three possible fluid volumes via a falling edge transition input to the pump controller. Behavioral protocols were run though Med-PC version IV (Med Associates), and behavioral data were sent via Med Associates superport card TTL (transistor-transistor logic) pulses from the Med-PC software to the syringe pump and subsequently to the Plexon recording system via a solid-state relay.Data were analyzed in NeuroExplorer , MATLAB, and Python (lick data). The Python scipy statistics package was used to perform Wilcoxon rank sum tests for the interlick intervals of each rat.https://github.com/LaubachLab. The code is also available in The code described in the article is freely available on-line on GitHub −5) for a 60 ml syringe, and 1.24 μl (SD = 1.35 × 10−5) for a 30 ml syringe.The syringe pump controller delivers different volumes all set to a common time scale. This is accomplished through algorithm development based on simple physics. Validation of fluid volume delivered for both distilled water and sucrose solutions of 30 and 60 ml syringes can be found in a spreadsheet in Additionally, the pump can functionally be used when paired with electrophysiological recordings of LFP activity in awake, behaving rats. Rats were tested in a shifting values licking task with 30 s shifts of access to a large  volume reward and a small  volume reward of 16% sucrose. The large reward was configured to be exactly three times the size of the small reward.p < 0.0001 for all rats).Raw LFP traces in the medial frontal cortex of rats did not show any major fluctuations in electrical noise when the syringe pump was activated C, and a We have developed an open source syringe pump control circuit that delivers fluid rewards of different sizes across one common time epoch from one single syringe. There are many benefits to using this syringe pump including low cost (under $250 including the syringe pump controller and 3D printed pump holder), ease of assembly, ease of customization, delivery of multiple fluid volumes delivered on a microliter scale, the ability to dissociate the confound of time and reward size, and the ability to use the pump with electrophysiological recordings. As an alternative, we would like to point out that a solenoid-based design exists , which iThe control circuit can be attached to any stepper motor or external syringe pump holder. For accuracy, we used a calibrated stand-alone NEMA 17 integrated stepper motor + driver (Applied Motion Products), but other bipolar stepper motors can also be used with this setup. The device is all open source, and PCB designs can easily be reprinted to replicate the controller. The control board could be implemented into behavioral paradigms quite simply, as it only needs a voltage input to trigger fluid delivery. We validated the syringe pump controller by using it in a shifting values licking task with two different reward volumes. In its default form, the syringe pump controller can deliver up to three volumes and could potentially be set up for more inputs if the code is adjusted by the user.https://github.com/wgpatrick/opensyringepump/) may be sought out if submicroliter precision is desired.Through using a 30 ml syringe, we were able to dispense 1.24 μl of fluid per one single motor step. Smaller volumes of fluid may be able to be obtained through using a smaller (10 ml) syringe, though it is difficult to tell whether the animal would actually be receiving the entire bolus of fluid with a reward under 1 μl. Additional caveats that would potentially degrade the accuracy of the volume dispensed would be the setup of the syringe to a spout , and it is possible that a glass syringe (instead of a plastic syringe) would yield the most accurate fluid delivery. It is important to keep in mind that a different diameter syringe  would also yield different volumes, and therefore it is necessary to perform a syringe pump calibration for the setup of each individual laboratory. It is important to note that this syringe pump controller is intended for its functionality in the delivery of multiple fluid volumes. Other syringe pump controllers (We compared the functionality of our open source syringe pump controller with a commercial syringe pump and found that the commercial syringe pump produced significant electrical transients, or “shot noise,” just after the pump would turn off. Our open source syringe pump did not have any hint of electrical transients and makes it optimal to combine with electrophysiological recordings. We would like to note that adding an RC snubber/arc suppressor to the commercial syringe pump did effectively suppress electrical transients, as this may be a useful tip to laboratories that are already using a commercial syringe pump in their experiments or are looking to design their own syringe pump controller.The control circuit is novel to the neuroscience field since it can be used to reassess classic neuroscience studies that have confounded timing and reward delivery, for example by leaving a solenoid valve open longer to deliver a larger reward. A major benefit of using this control circuit is the implementation of the equation within the code to adjust the velocity and acceleration of the motor to provide equal timing of different volume rewards. This reduces the confound between time and reward size, which has been a potential issue of previous studies on reward magnitude. With this device, it will be possible to assess whether “reward signals” in electrophysiological data are due to the timing or size of the reward. Additionally, the device will allow for at least three different volumes to be dispensed, making it possible for future studies to investigate reward size and comparison of multiple rewards. The device minimizes the need for multiple syringe pumps or devices by having just one single syringe deliver different volumes of reward. The syringe pump controller opens the door to new studies that aim to manipulate reward size using one single device.