We have developed a compartment model of VEGF distribution in tumor-bearing mouse. The model incorporates tumor-specific properties, including the rate of tumor growth and VEGF secretion. We have used in vivo experimental data for the levels of free and bound VEGF Trap in mice bearing human tumor xenografts in order to predict the endogenous rate of VEGF secretion by myocytes and ECs and compared them to the predicted secretion rates in normal mice. We also predicted the rate at which cells from different human tumor xenografts secrete VEGF. To our knowledge, VEGF secretion rates can only be obtained from in vitro experiments and cannot be directly measured in vivo; however, VEGF concentrations that depend on the secretion rates can be measured experimentally, although such interstitial measurements are presently not available. Therefore, this work provides new insight into VEGF levels in a pre-clinical in vivo model of cancer. In addition, using the optimized model for tumor-bearing mice, we have estimated the concentration of VEGF in the mouse following administration of VEGF Trap, as well as the distribution of VEGF in mice and circulating levels of VEGF Trap and the VEGF/VEGF Trap complex. These results show that the concentration of free VEGF in the tumor depends on the tumor-specific properties such as the rate of tumor growth and the amount of VEGF secreted by tumor cells. Lastly, we used the predicted level of VEGF Trap and hVEGF/VEGF Trap complex to compare various dosages. The model predicted that all hVEGF originating from the tumor is neutralized at higher doses of the drug. This demonstrates an important application of the model: to incorporate tumor-specific properties and investigate the efficacy of different drug doses.
We used the two-compartment model to estimate VEGF secretion rates, clearance of free and bound VEGF Trap, and the binding affinity of VEGF Trap for normal mice. The value of binding affinity of VEGF Trap estimated by the model is comparable to the experimentally measured value (11
). Additionally, the estimated EC secretion is comparable to the experimentally determined value of 0.028
). However, the predicted rate at which muscle cells secrete VEGF is very low, and varying this parameter over one order of magnitude does not significantly change the fit. In contrast, EC secretion can be specified and changing this parameter drastically influences the fit to experimental data (results not shown). These results may indicate that the rate of VEGF secretion from muscle and ECs cannot be simultaneously estimated using the available experimental data. That is, measurements of free and bound VEGF Trap in plasma do not allow us to distinguish how muscle and ECs contribute to VEGF levels. Additional experimental measurements such as interstitial levels of VEGF in skeletal muscle are needed in order to predict VEGF secretion by muscle fibers with confidence. Currently, interstitial VEGF concentrations are only available in human tissue (28
); however, similar studies in mice are of great interest.
We found that fitted parameters from normal mice were not sufficient to match the levels of unbound and complexed VEGF Trap in the model of tumor-bearing mice. We first attempted to use the fitted parameters from the two-compartment model in the model of tumor-bearing mice and use in vivo
experimental data to fit the rate of VEGF secretion from tumor cells. However, the model overestimated the amount of VEGF Trap complexed with mVEGF (results not shown). We are able to more closely fit the experimental data for the tumor-bearing mice by optimizing the three-compartment model independent of the optimized model for normal mice. This indicates that endogenous VEGF secretion may be different in normal and tumor-bearing mice (Tables vs ). Experimental studies are needed to validate these results; however, evidence shows that VEGF secretion is reduced following administration of VEGF Trap (34
) or other anti-angiogenic therapies (35
The three-compartment model predicted that the in vivo
tumor VEGF secretion rates needed to fit experimental data are lower than data obtained from in vitro
measurements. In vitro
experimental measurements of the VEGF secretion rate vary widely: 0.03–2.65
). We predicted that human tumors secrete VEGF at rates range ranging from 0.007 to 0.023
molecules/cell/s. Interestingly, there is little variability in the predicted tumor secretion rate, as indicated by the small standard deviation (~10−5
molecules/cell/s). Having experimental measurements of the plasma concentration of VEGF Trap bound to hVEGF (i.e., VEGF originating from the tumor) enables us to predict the rate at which the tumor secretes VEGF in vivo
. In this way, xenograft models are preferable to syngeneic tumor models, in which VEGF derived from tumor and other tissues are indistinguishable. Similarly, plasma measurements in human patients would not be sufficient to specify tumor VEGF. Thus, xenograft models provide unique insight into the effects of anti-angiogenic therapies and are relevant to human studies.
Tumor VEGF secretion is predicted to depend on the tumor microenvironment. HT1080 tumors are predicted to secrete ~2-fold more VEGF than A673 tumors. Additionally, average- and fast-growing tumors are predicted to secrete different amounts of VEGF, where VEGF secretion in fast-growing tumors is slightly lower than that of tumors that grow at an average rate. To our knowledge, experimental data for VEGF secretion rates is limited to in vitro measurements. Therefore, the ability to use the model to determine the VEGF secretion from in vivo data and track and quantify normal and tumor VEGF are important features of the model.
Using the optimized model, it is possible to estimate VEGF concentrations in the mouse before and after VEGF Trap administration. In the model, we allowed the tumor to grow for 2
weeks before the VEGF Trap injection. Just before the injection, the estimated plasma VEGF levels are within the range of experimental measurements in mouse of 0.3–1.4
). The model indicates that plasma VEGF depends on properties of the tumor, such as volume, a result that is validated by experimental evidence (44
). Using the model, free VEGF in muscle interstitium is predicted to range from 0.2 to 1.5
pM. To our knowledge, interstitial VEGF in normal tissues has only been quantified in human samples. Interstitial muscle VEGF in humans ranges from 0.3 to 3
). It is not clear how this concentration range varies across species. However, since the range of plasma VEGF measurements is similar between mice and humans, where human plasma VEGF is measured to be 0.4–3
), it is possible that interstitial VEGF is also comparable in mice and humans. Thus, our model results and predictions provide a framework to compare VEGF distribution in different species and can be experimentally validated. Additionally, we are able to predict the concentration of specific VEGF isoforms (i.e., the percentage of free VEGF in the form of VEGF164
, as compared to the shorter isoforms VEGF120
). These results may be useful in identifying predictive biomarkers for anti-VEGF treatment, where the level of VEGF121
is being evaluated as a biomarker (47
). We also applied the model to estimate the relative contribution of sVEGFR1-bound and α2M-bound VEGF to total circulating VEGF. The soluble factors compete with anti-VEGF agents; therefore, it is of interest to investigate the effect of sVEGFR1 on the response to anti-VEGF treatment. In this way, the model complements studies evaluating sVEGFR1 as a potential biomarker to predict resistance to anti-VEGF treatment (49
We can also compare the estimated levels of plasma VEGF generated by the model following administration of VEGF Trap with experimental studies. In vivo
studies of mice with breast tumor xenografts indicate the plasma VEGF is reduced following VEGF Trap treatment, particularly at the higher doses (34
). Additionally, Hoff and coworkers report that VEGF Trap is able to bind all free VEGF 11
days after treatment in an experimental model of rat glioma (50
). These studies support the computational model predictions. However, we are not aware of animal studies that provide the time course of VEGF and VEGF/VEGF Trap concentration, which is an important contribution of the model and can complement pre-clinical studies that investigate the efficacy of VEGF Trap.
We show that interstitial tumor VEGF levels depend on specific properties of the tumor. To our knowledge, there are no experimental measurements for interstitial tumor VEGF concentrations. However, a sampling of available experimental measurements of total VEGF in tumor tissue (free and bound VEGF, both intracellular and extracellular) reveals a wide range of values, depending on tumor type and size. File 1 in Supplementary Material shows a compilation of measurements of tumor VEGF for various tumor types. Experimental studies to measure free VEGF in tumor tissue in mouse models would provide much needed quantitative data to test and validate the model predictions presented here.
We consider the model presented here to be a minimal model that accurately reproduces experimental data, both qualitatively and quantitatively. The model includes several assumptions, which may be addressed as quantitative data become available. For example, we assume the normal tissue is skeletal muscle, although other tissues and organs secrete and contain VEGF (51
), but are not as well-characterized as muscle. We include two major VEGF isoforms (VEGF120
); however, other isoforms such as VEGF188
) and VEGFxxxb
) also influence angiogenesis and may impact anti-VEGF therapies. Recent studies also show that other VEGF ligands and receptors contribute to angiogenesis (55
), and the model can be expanded in the future to include these molecular species. Additionally, although platelets contain large amounts of VEGF and contribute to angiogenesis (58
), we have not included them in the model as the rate and conditions under which they secrete or unload VEGF are unknown. We assume that as the tumor grows, the relative proportions of interstitial space, vascular volume, and tumor cells remain constant. However, experimental studies indicate that these proportions should change as the tumor grows (59
). Finally, we have not included the effects of anti-VEGF treatment on tumor volume or vascular permeability. Pre-clinical studies show tumor growth inhibition and even regression of the tumor following anti-angiogenic therapy that targets VEGF. We have performed preliminary studies where the tumor volume is constant after 1
week of anti-VEGF treatment since experimental studies indicate that tumor growth is halted during 2
weeks of twice-weekly VEGF Trap injections (34
). We found that the predicted tumor secretion rate is slightly larger when accounting for tumor growth stagnation. This is because the tumor is smaller and consists of fewer cells. Therefore, the amount of VEGF that must be secreted on a per cell basis in order to obtain a certain level of VEGF or VEGF/VEGF Trap complex is higher. Tumor permeability may decrease with anti-angiogenic therapy, as the tumor normalizes neovasculature and it begins to resemble normal vessels; however, we have not included that effect in the current model. In a human model of VEGF transport and kinetics, we considered “low” and “high” vascular permeability between the tumor and blood (22
). Interestingly, the model predicts that tumor VEGF can increase above the pre-treatment level depending on properties of the tumor microenvironment, even when tumor permeability is high. Future computational studies may investigate the effect of anti-VEGF treatment on tumor volume and vascular permeability in greater detail.
The compartment model presented here provides a framework to investigate the action of VEGF-targeting agents for particular types of tumors. The physiologically based and experimentally validated model, based on currently available animal data, predicted the dynamic concentrations of molecular species and other biological parameters that are difficult to quantify experimentally. Thus, the model complements pre-clinical experiments, can aid in the development of agents that target VEGF and inhibit angiogenesis, and may be useful in evaluating biomarkers of anti-angiogenic therapies. The model can be extended to human patients; this is particularly important since in 2012 aflibercept has been approved to treat metastatic colorectal cancer in humans (60