In vivo mathematical modeling of tumor growth from imaging data: soon to come in the future?

Hypothetical generalized framework for a new imaging endpoint of therapeutic activity in early phase clinical trials in brain tumors

Imaging response assessment is a cornerstone of patient care and drug development in oncology. Clinicians/clinical researchers rely on tumor imaging to estimate the impact of new treatments and guide decision making for patients and candidate therapies. This is important in brain cancer, where associations between tumor size/growth and emerging neurological deficits are strong. Accurately measuring the impact of a new therapy on tumor growth early in clinical development, where patient numbers are small, would be valuable for decision making regarding late-stage development activation. Current attempts to measure the impact of a new therapy have limited influence on clinical development, as determination of progression, stability or response does not currently account for individual tumor growth kinetics prior to the initiation of experimental therapies. Therefore, we posit that imaging-based response assessment, often used as a tool for estimating clinical effect, is incomplete as it does not adequately account for growth trajectories or biological characteristics of tumors prior to the introduction of an investigational agent. Here, we propose modifications to the existing framework for evaluating imaging assessment in primary brain tumors that will provide a more reliable understanding of treatment effects. Measuring tumor growth trajectories prior to a given intervention may allow us to more confidently conclude whether there is an anti-tumor effect. This updated approach to imaging-based tumor response assessment is intended to improve our ability to select candidate therapies for later-stage development, including those that may not meet currently sought thresholds for "response" and ultimately lead to identification of effective treatments.

A NUMERICAL PROOF THAT CERTAIN CELLS FOLLOW THE TRAILS OF THE DIFFUSIONS OF SOME CHEMICALS IN THE EXTRACELLULAR MATRIX

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

Replication study: Melanoma exosomes educate bone marrow progenitor cells toward a pro-metastatic phenotype through MET

As part of the Reproducibility Project: Cancer Biology we published a Registered Report (Lesnik et al., 2016) that described how we intended to replicate selected experiments from the paper ‘Melanoma exosomes educate bone marrow progenitor cells toward a pro-metastatic phenotype through MET’ (Peinado et al., 2012). Here we report the results. We regenerated tumor cells stably expressing a short hairpin to reduce Met expression (shMet) using the same highly metastatic mouse melanoma cell line (B16-F10) as the original study, which efficiently downregulated Met in B16F10 cells similar to the original study (Supplementary Figure 5A; Peinado et al., 2012). Exosomes from control cells expressed Met, which was reduced in exosomes from shMet cells; however, we were unable to reliably detect phosphorylated Met in exosomes. We tested the effect of exosome-dependent Met signaling on primary tumor growth and metastasis. Similar to the results in the original study, we did not find a statistically significant change in primary tumor growth. Measuring lung and femur metastases, we found a small increase in metastatic burden with exosomes from control cells that was diminished when Met expression was reduced; however, while the effects were in the same direction as the original study (Figure 4E; Peinado et al., 2012), they were not statistically significant. Differences between the original study and this replication attempt, such as level of knockdown efficiency, cell line genetic drift, sample sizes, study endpoints, and variability of observed metastatic burden, are factors that might have influenced the outcomes. Finally, we report meta-analyses for each result.

Model-Supported Radiotherapy Personalization: In silico Test of Hyper- and Hypo-Fractionation Effects

The need for radiotherapy personalization is now widely recognized, however, it would require considerations not only on the probability of control and survival of the tumor, but also on the possible toxic effects, on the quality of the expected life and the economic efficiency of the treatment. In this paper, we propose a simulation tool that can be integrated into a decision support system that allows selection of the most suitable irradiation regimen. We used a macroscale mathematical model, which includes active and necrotic tumor dynamics and the role of oxygenation to simulate the effects of different hypo-/hyper-fractional regimens using retrospective data of seven virtual patients from as many cervical cancer patients used for its training in a previous study. The results confirmed the heterogeneous response across the patients as a function of treatment regimen and suggested the tumor growth rate as a main factor in the final tumor regression. In addition to the maximum regression, another criterion was suggested to select the most suitable regimen (minimum number of fractions to achieve a regression of 80%) minimizing the toxicity and maximizing the cost-effectiveness ratio. Despite the lack of direct validation, the simulation results are in agreement with the literature findings that suggest the need for hypo-fractionated regimens in case of aggressive tumor phenotypes. Finally, the paper suggests a possible exploitation of the model within a tool to support clinical decisions.

Replication Study: The CD47-signal regulatory protein alpha (SIRPa) interaction is a therapeutic target for human solid tumors

In 2015, as part of the Reproducibility Project: Cancer Biology, we published a Registered Report (Chroscinski et al., 2015) that described how we intended to replicate selected experiments from the paper "The CD47-signal regulatory protein alpha (SIRPa) interaction is a therapeutic target for human solid tumors "(Willingham et al., 2012). Here we report the results of those experiments. We found that treatment of immune competent mice bearing orthotopic breast tumors with anti-mouse CD47 antibodies resulted in short-term anemia compared to controls, consistent with the previously described function of CD47 in normal phagocytosis of aging red blood cells and results reported in the original study (Table S4; Willingham et al., 2012). The weight of tumors after 30 days administration of anti-CD47 antibodies or IgG isotype control were not found to be statistically different, whereas the original study reported inhibition of tumor growth with anti-CD47 treatment (Figure 6A,B; Willingham et al., 2012). However, our efforts to replicate this experiment were confounded because spontaneous regression of tumors occurred in several of the mice. Additionally, the excised tumors were scored for inflammatory cell infiltrates. We found IgG and anti-CD47 treated tumors resulted in minimal to moderate lymphocytic infiltrate, while the original study observed sparse lymphocytic infiltrate in IgG-treated tumors and increased inflammatory cell infiltrates in anti-CD47 treated tumors (Figure 6C; Willingham et al., 2012). Furthermore, we observed neutrophilic infiltration was slightly increased in anti-CD47 treated tumors compared to IgG control. Finally, we report a meta-analysis of the result.

Proposal of a hybrid approach for tumor progression and tumor-induced angiogenesis

One of the main challenges in cancer modelling is to improve the knowledge of tumor progression in areas related to tumor growth, tumor-induced angiogenesis and targeted therapies efficacy. For this purpose, incorporate the expertise from applied mathematicians, biologists and physicians is highly desirable. Despite the existence of a very wide range of models, involving many stages in cancer progression, few models have been proposed to take into account all relevant processes in tumor progression, in particular the effect of systemic treatments and angiogenesis. Composite biological experiments, both in vitro and in vivo, in addition with mathematical modelling can provide a better understanding of theses aspects. In this work we proposed that a rational experimental design associated with mathematical modelling could provide new insights into cancer progression. To accomplish this task, we reviewed mathematical models and cancer biology literature, describing in detail the basic principles of mathematical modelling. We also analyze how experimental data regarding tumor cells proliferation and angiogenesis in vitro may fit with mathematical modelling in order to reconstruct in vivo tumor evolution. Additionally, we explained the mathematical methodology in a comprehensible way in order to facilitate its future use by the scientific community.

Classical mathematical models for description and prediction of experimental tumor growth

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.