Modeling Spontaneous Metastasis following Surgery: An In Vivo-In Silico Approach

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.

Machine-learning and mechanistic modeling of metastatic breast cancer after neoadjuvant treatment

Clinical trials involving systemic neoadjuvant treatments in breast cancer aim to shrink tumors before surgery while simultaneously allowing for controlled evaluation of biomarkers, toxicity, and suppression of distant (occult) metastatic disease. Yet neoadjuvant clinical trials are rarely preceded by preclinical testing involving neoadjuvant treatment, surgery, and post-surgery monitoring of the disease. Here we used a mouse model of spontaneous metastasis occurring after surgical removal of orthotopically implanted primary tumors to develop a predictive mathematical model of neoadjuvant treatment response to sunitinib, a receptor tyrosine kinase inhibitor (RTKI). Treatment outcomes were used to validate a novel mathematical kinetics-pharmacodynamics model predictive of perioperative disease progression. Longitudinal measurements of presurgical primary tumor size and postsurgical metastatic burden were compiled using 128 mice receiving variable neoadjuvant treatment doses and schedules (released publicly at https://zenodo.org/records/10607753). A non-linear mixed-effects modeling approach quantified inter-animal variabilities in metastatic dynamics and survival, and machine-learning algorithms were applied to investigate the significance of several biomarkers at resection as predictors of individual kinetics. Biomarkers included circulating tumor- and immune-based cells (circulating tumor cells and myeloid-derived suppressor cells) as well as immunohistochemical tumor proteins (CD31 and Ki67). Our computational simulations show that neoadjuvant RTKI treatment inhibits primary tumor growth but has little efficacy in preventing (micro)-metastatic disease progression after surgery and treatment cessation. Machine learning algorithms that included support vector machines, random forests, and artificial neural networks, confirmed a lack of definitive biomarkers, which shows the value of preclinical modeling studies to identify potential failures that should be avoided clinically.

Computational markers for personalized prediction of outcomes in non-small cell lung cancer patients with brain metastases

Intracranial progression after curative treatment of early-stage non-small cell lung cancer (NSCLC) occurs from 10 to 50% and is difficult to manage, given the heterogeneity of clinical presentations and the variability of treatments available. The objective of this study was to develop a mechanistic model of intracranial progression to predict survival following a first brain metastasis (BM) event occurring at a time [Formula: see text]. Data included early-stage NSCLC patients treated with a curative intent who had a BM as the first and single relapse site (N = 31). We propose a mechanistic mathematical model able to derive computational markers from primary tumor and BM data at [Formula: see text] and estimate the amount and sizes of (visible and invisible) BMs, as well as their future behavior. These two key computational markers are [Formula: see text], the proliferation rate of a single tumor cell; and [Formula: see text], the per day, per cell, probability to metastasize. The predictive value of these individual computational biomarkers was evaluated. The model was able to correctly describe the number and size of metastases at [Formula: see text] for 20 patients. Parameters [Formula: see text] and [Formula: see text] were significantly associated with overall survival (OS) (HR 1.65 (1.07-2.53) p = 0.0029 and HR 1.95 (1.31-2.91) p = 0.0109, respectively). Adding the computational markers to the clinical ones significantly improved the predictive value of OS (c-index increased from 0.585 (95% CI 0.569-0.602) to 0.713 (95% CI 0.700-0.726), p < 0.0001). We demonstrated that our model was applicable to brain oligoprogressive patients in NSCLC and that the resulting computational markers had predictive potential. This may help lung cancer physicians to guide and personalize the management of NSCLC patients with intracranial oligoprogression.

Radiation necrosis after radiation therapy treatment of brain metastases: A computational approach

Metastasis is the process through which cancer cells break away from a primary tumor, travel through the blood or lymph system, and form new tumors in distant tissues. One of the preferred sites for metastatic dissemination is the brain, affecting more than 20% of all cancer patients. This figure is increasing steadily due to improvements in treatments of primary tumors. Stereotactic radiosurgery (SRS) is one of the main treatment options for patients with a small or moderate number of brain metastases (BMs). A frequent adverse event of SRS is radiation necrosis (RN), an inflammatory condition caused by late normal tissue cell death. A major diagnostic problem is that RNs are difficult to distinguish from BM recurrences, due to their similarities on standard magnetic resonance images (MRIs). However, this distinction is key to choosing the best therapeutic approach since RNs resolve often without further interventions, while relapsing BMs may require open brain surgery. Recent research has shown that RNs have a faster growth dynamics than recurrent BMs, providing a way to differentiate the two entities, but no mechanistic explanation has been provided for those observations. In this study, computational frameworks were developed based on mathematical models of increasing complexity, providing mechanistic explanations for the differential growth dynamics of BMs relapse versus RN events and explaining the observed clinical phenomenology. Simulated tumor relapses were found to have growth exponents substantially smaller than the group in which there was inflammation due to damage induced by SRS to normal brain tissue adjacent to the BMs, thus leading to RN. ROC curves with the synthetic data had an optimal threshold that maximized the sensitivity and specificity values for a growth exponent β* = 1.05, very close to that observed in patient datasets.

Mathematical modeling of radiotherapy: impact of model selection on estimating minimum radiation dose for tumor control

Introduction

Radiation therapy (RT) is one of the most common anticancer therapies. Yet, current radiation oncology practice does not adapt RT dose for individual patients, despite wide interpatient variability in radiosensitivity and accompanying treatment response. We have previously shown that mechanistic mathematical modeling of tumor volume dynamics can simulate volumetric response to RT for individual patients and estimation personalized RT dose for optimal tumor volume reduction. However, understanding the implications of the choice of the underlying RT response model is critical when calculating personalized RT dose.

Methods

In this study, we evaluate the mathematical implications and biological effects of 2 models of RT response on dose personalization: (1) cytotoxicity to cancer cells that lead to direct tumor volume reduction (DVR) and (2) radiation responses to the tumor microenvironment that lead to tumor carrying capacity reduction (CCR) and subsequent tumor shrinkage. Tumor growth was simulated as logistic growth with pre-treatment dynamics being described in the proliferation saturation index (PSI). The effect of RT was simulated according to each respective model for a standard schedule of fractionated RT with 2 Gy weekday fractions. Parameter sweeps were evaluated for the intrinsic tumor growth rate and the radiosensitivity parameter for both models to observe the qualitative impact of each model parameter. We then calculated the minimum RT dose required for locoregional tumor control (LRC) across all combinations of the full range of radiosensitvity and proliferation saturation values.

Results

Both models estimate that patients with higher radiosensitivity will require a lower RT dose to achieve LRC. However, the two models make opposite estimates on the impact of PSI on the minimum RT dose for LRC: the DVR model estimates that tumors with higher PSI values will require a higher RT dose to achieve LRC, while the CCR model estimates that higher PSI values will require a lower RT dose to achieve LRC.

Discussion

Ultimately, these results show the importance of understanding which model best describes tumor growth and treatment response in a particular setting, before using any such model to make estimates for personalized treatment recommendations.

Harnessing immunotherapy to enhance the systemic anti-tumor effects of thermosensitive liposomes

Chemotherapy plays an important role in debulking tumors in advance of surgery and/or radiotherapy, tackling residual disease, and treating metastatic disease. In recent years many promising advanced drug delivery strategies have emerged that offer more targeted delivery approaches to chemotherapy treatment. For example, thermosensitive liposome-mediated drug delivery in combination with localized mild hyperthermia can increase local drug concentrations resulting in a reduction in systemic toxicity and an improvement in local disease control. However, the majority of solid tumor-associated deaths are due to metastatic spread. A therapeutic approach focused on a localized target area harbors the risk of overlooking and undertreating potential metastatic spread. Previous studies reported systemic, albeit limited, anti-tumor effects following treatment with thermosensitive liposomal chemotherapy and localized mild hyperthermia. This work explores the systemic treatment capabilities of a thermosensitive liposome formulation of the vinca alkaloid vinorelbine in combination with mild hyperthermia in an immunocompetent murine model of rhabdomyosarcoma. This treatment approach was found to be highly effective at heated, primary tumor sites. However, it demonstrated limited anti-tumor effects in secondary, distant tumors. As a result, the addition of immune checkpoint inhibition therapy was pursued to further enhance the systemic anti-tumor effect of this treatment approach. Once combined with immune checkpoint inhibition therapy, a significant improvement in systemic treatment capability was achieved. We believe this is one of the first studies to demonstrate that a triple combination of thermosensitive liposomes, localized mild hyperthermia, and immune checkpoint inhibition therapy can enhance the systemic treatment capabilities of thermosensitive liposomes.

Mechanistic modeling of metastatic relapse in early breast cancer to investigate the biological impact of prognostic biomarkers

BACKGROUND AND OBJECTIVE

Estimating the risk of metastatic relapse is a major challenge to decide adjuvant treatment options in early-stage breast cancer (eBC). To date, distant metastasis-free survival (DMFS) analysis mainly relies on classical, agnostic, statistical models (e.g., Cox regression). Instead, we propose here to derive mechanistic models of DMFS.

METHODS

The present series consisted of eBC patients who did not receive adjuvant systemic therapy from three datasets, composed respectively of 692 (Bergonié Institute), 591 (Paoli-Calmettes Institute, IPC), and 163 (Public Hospital Marseille, AP-HM) patients with routine clinical annotations. The last dataset also contained expression of three non-routine biomarkers. Our mechanistic model of DMFS relies on two mathematical parameters that represent growth (α) and dissemination (μ). We identified their population distributions using mixed-effects modeling. Critically, we propose a novel variable selection procedure allowing to: (i) identify the association of biological parameters with either α, μ or both, and (ii) generate an optimal candidate model for DMFS prediction.

RESULTS

We found that Ki67 and Thymidine Kinase-1 were associated with α, and nodal status and Plasminogen Activator Inhibitor-1 with μ. The predictive performances of the model were excellent in calibration but moderate in discrimination, with c-indices of 0.72 (95% CI [0.48, 0.95], AP-HM), 0.63 ([0.44, 0.83], Bergonié) and 0.60 (95% CI [0.54, 0.80], IPC).

CONCLUSIONS

Overall, we demonstrate that our novel method combining mechanistic and advanced statistical modeling is able to unravel the biological roles of clinicopathological parameters from DMFS data.

Practical identifiability analysis of a mechanistic model for the time to distant metastatic relapse and its application to renal cell carcinoma

Distant metastasis-free survival (DMFS) curves are widely used in oncology. They are classically analyzed using the Kaplan-Meier estimator or agnostic statistical models from survival analysis. Here we report on a method to extract more information from DMFS curves using a mathematical model of primary tumor growth and metastatic dissemination. The model depends on two parameters, α and μ, respectively quantifying tumor growth and dissemination. We assumed these to be lognormally distributed in a patient population. We propose a method for identification of the parameters of these distributions based on least-squares minimization between the data and the simulated survival curve. We studied the practical identifiability of these parameters and found that including the percentage of patients with metastasis at diagnosis was critical to ensure robust estimation. We also studied the impact and identifiability of covariates and their coefficients in α and μ, either categorical or continuous, including various functional forms for the latter (threshold, linear or a combination of both). We found that both the functional form and the coefficients could be determined from DMFS curves. We then applied our model to a clinical dataset of metastatic relapse from kidney cancer with individual data of 105 patients. We show that the model was able to describe the data and illustrate our method to disentangle the impact of three covariates on DMFS: a categorical one (Führman grade) and two continuous ones (gene expressions of the macrophage mannose receptor 1 (MMR) and the G Protein-Coupled Receptor Class C Group 5 Member A (GPRC5a) gene). We found that all had an influence in metastasis dissemination (μ), but not on growth (α).

Understanding biological mechanisms leading to metastasis development is a major challenge in order to prevent distant relapse of cancer. Classical methods to study associations of biomarkers with subsequent metastatic relapse rely on the analysis of metastasis free survival curves by means of statistical models such as proportional hazards Cox regression. These models act as black boxes and don’t provide detailed information about the specific mechanism involved. In our study, we propose to use a method based on mechanistic modeling of the metastatic development, that is, a mathematical model that simulates the biological process. The main challenge for these models is to implement the right level of complexity, because if too many parameters are included, these cannot be precisely identified from the data. We reduced the metastatic process to two main aspects: growth and dissemination. We then proposed a theoretical study of the identifiability of the two associated parameters from metastasis-free survival curves. Eventually, we applied our method to a clinical dataset in kidney cancer and illustrated how we could gain biological insights about the role of some diagnosis markers.

Current challenges in metastasis research and future innovation for clinical translation

While immense strides have been made in understanding tumor biology and in developing effective treatments that have substantially improved the prognosis of cancer patients, metastasis remains the major cause of cancer-related death. Improvements in the detection and treatment of primary tumors are contributing to a growing, detailed understanding of the dynamics of metastatic progression. Yet challenges remain in detecting metastatic dissemination prior to the establishment of overt metastases and in predicting which patients are at the highest risk of developing metastatic disease. Further improvements in understanding the mechanisms governing metastasis have great potential to inform the adaptation of existing therapies and the development of novel approaches to more effectively control metastatic disease. This article presents a forward-looking perspective on the challenges that remain in the treatment of metastasis, and the exciting emerging approaches that promise to transform the treatment of metastasis in cancer patients.

Immunization with short peptide particles reveals a functional CD8+ T-cell neoepitope in a murine renal carcinoma model

BACKGROUND

Induction of CD8⁺ T cells that recognize immunogenic, mutated protein fragments in the context of major histocompatibility class I (MHC-I) is a pressing challenge for cancer vaccine development.

METHODS

Using the commonly used murine renal adenocarcinoma RENCA cancer model, MHC-I restricted neoepitopes are predicted following next-generation sequencing. Candidate neoepitopes are screened in mice using a potent cancer vaccine adjuvant system that converts short peptides into immunogenic nanoparticles. An identified functional neoepitope vaccine is then tested in various therapeutic experimental tumor settings.

RESULTS

Conversion of 20 short MHC-I restricted neoepitope candidates into immunogenic nanoparticles results in antitumor responses with multivalent vaccination. Only a single neoepitope candidate, Nesprin-2 L4492R (Nes2LR), induced functional responses but still did so when included within 20-plex or 60-plex particles. Immunization with the short Nes2LR neoepitope with the immunogenic particle-inducing vaccine adjuvant prevented tumor growth at doses multiple orders of magnitude less than with other vaccine adjuvants, which were ineffective. Nes2LR vaccination inhibited or eradicated disease in subcutaneous, experimental lung metastasis and orthotopic tumor models, synergizing with immune checkpoint blockade.

CONCLUSION

These findings establish the feasibility of using short, MHC-I-restricted neoepitopes for straightforward immunization with multivalent or validated neoepitopes to induce cytotoxic CD8⁺ T cells. Furthermore, the Nes2LR neoepitope could be useful for preclinical studies involving renal cell carcinoma immunotherapy.

Experimental and computational modeling for signature and biomarker discovery of renal cell carcinoma progression

BACKGROUND

Renal Cell Carcinoma (RCC) is difficult to treat with 5-year survival rate of 10% in metastatic patients. Main reasons of therapy failure are lack of validated biomarkers and scarce knowledge of the biological processes occurring during RCC progression. Thus, the investigation of mechanisms regulating RCC progression is fundamental to improve RCC therapy.

METHODS

In order to identify molecular markers and gene processes involved in the steps of RCC progression, we generated several cell lines of higher aggressiveness by serially passaging mouse renal cancer RENCA cells in mice and, concomitantly, performed functional genomics analysis of the cells. Multiple cell lines depicting the major steps of tumor progression (including primary tumor growth, survival in the blood circulation and metastatic spread) were generated and analyzed by large-scale transcriptome, genome and methylome analyses. Furthermore, we performed clinical correlations of our datasets. Finally we conducted a computational analysis for predicting the time to relapse based on our molecular data.

RESULTS

Through in vivo passaging, RENCA cells showed increased aggressiveness by reducing mice survival, enhancing primary tumor growth and lung metastases formation. In addition, transcriptome and methylome analyses showed distinct clustering of the cell lines without genomic variation. Distinct signatures of tumor aggressiveness were revealed and validated in different patient cohorts. In particular, we identified SAA2 and CFB as soluble prognostic and predictive biomarkers of the therapeutic response. Machine learning and mathematical modeling confirmed the importance of CFB and SAA2 together, which had the highest impact on distant metastasis-free survival. From these data sets, a computational model predicting tumor progression and relapse was developed and validated. These results are of great translational significance.

CONCLUSION

A combination of experimental and mathematical modeling was able to generate meaningful data for the prediction of the clinical evolution of RCC.

The Intersection of Regional Anesthesia and Cancer Progression: A Theoretical Framework

The surgical stress and inflammatory response and volatile anesthetic agents have been shown to promote tumor metastasis in animal and in-vitro studies. Regional neuraxial anesthesia protects against these effects by decreasing the surgical stress and inflammatory response and associated changes in immune function in animals. However, evidence of a similar effect in humans remains equivocal due to the high variability and retrospective nature of clinical studies and difficulty in directly comparing regional versus general anesthesia in humans. We propose a theoretical framework to address the question of regional anesthesia as protective against metastasis.

This theoretical construct views the immune system, circulating tumor cells, micrometastases, and inflammatory mediators as distinct populations in a highly connected system. In ecological theory, highly connected populations demonstrate more resilience to local perturbations but are prone to system-wide shifts compared with their poorly connected counterparts. Neuraxial anesthesia transforms the otherwise system-wide perturbations of the surgical stress and inflammatory response and volatile anesthesia into a comparatively local perturbation to which the system is more resilient. We propose this framework for experimental and mathematical models to help determine the impact of anesthetic choice on recurrence and metastasis and create therapeutic strategies to improve cancer outcomes after surgery.

Development and Validation of a Prediction Model of Overall Survival in High-Risk Neuroblastoma Using Mechanistic Modeling of Metastasis

Prognosis of high-risk neuroblastoma (HRNB) remains poor despite multimodal therapies. Better prediction of survival could help to refine patient stratification and better tailor treatments. We established a mechanistic model of metastasis in HRNB relying on two processes: growth and dissemination relying on two patient-specific parameters: the dissemination rate μ and the minimal visible lesion size S_vis. This model was calibrated using diagnosis values of primary tumor size, lactate dehydrogenase circulating levels, and the meta-iodobenzylguanidine International Society for Paediatric Oncology European (SIOPEN) score from nuclear imaging, using data from 49 metastatic patients. It was able to describe the data of total tumor mass (lactate dehydrogenase, R² > 0.99) and number of visible metastases (SIOPEN, R² = 0.96). A prediction model of overall survival (OS) was then developed using Cox regression. Clinical variables alone were not able to generate a model with sufficient OS prognosis ability (P = .507). The parameter μ was found to be independent of the clinical variables and positively associated with OS (P = .0739 in multivariable analysis). Critically, addition of this computational biomarker significantly improved prediction of OS with a concordance index increasing from 0.675 (95% CI, 0.663 to 0.688) to 0.733 (95% CI, 0.722 to 0.744, P < .0001), resulting in significant OS prognosis ability (P = .0422).

Metastasis Initiation Precedes Detection of Primary Cancer-Analysis of Metastasis Growth in vivo in a Colorectal Cancer Test Case

Most cases of deaths from colorectal cancer (CRC) result from metastases, which are often still undetectable at disease detection time. Even so, in many cases, shedding is assumed to have taken place before that time. The dynamics of metastasis formation and growth are not well-established. This work aims to explore CRC lung metastasis growth rate and dynamics. We analyzed a test case of a metastatic CRC patient with four lung metastases, with data of four serial computed tomography (CT) scans measuring metastasis sizes while untreated. We fitted three mathematical growth models—exponential, logistic, and Gompertzian—to the CT measurements. For each metastasis, a best-fitted model was determined, tumor doubling time (TDT) was assessed, and metastasis inception time was extrapolated. Three of the metastases showed exponential growth, while the fourth showed logistic restraint of the growth. TDT was around 93 days. Predicted metastasis inception time was at least 4–5 years before the primary tumor diagnosis date, though they did not reach detectable sizes until at least 1 year after primary tumor resection. Our results support the exponential growth approximation for most of the metastases, at least for the clinically observed time period. Our analysis shows that metastases can be initiated before the primary tumor is detectable and implies that surgeries accelerate metastasis growth.

An Overview of In Vitro, In Vivo, and Computational Techniques for Cancer-Associated Angiogenesis Studies

Angiogenesis is a crucial area in scientific research because it involves many important physiological and pathological processes. Indeed, angiogenesis is critical for normal physiological processes, including wound healing and embryonic development, as well as being a component of many disorders, such as rheumatoid arthritis, obesity, and diabetic retinopathies. Investigations of angiogenic mechanisms require assays that can activate the critical steps of angiogenesis as well as provide a tool for assessing the efficacy of therapeutic agents. Thus, angiogenesis assays are key tools for studying the mechanisms of angiogenesis and identifying the potential therapeutic strategies to modulate neovascularization. However, the regulation of angiogenesis is highly complex and not fully understood. Difficulties in assessing the regulators of angiogenic response have necessitated the development of an alternative approach. In this paper, we review the standard models for the study of tumor angiogenesis on the macroscopic scale that include in vitro, in vivo, and computational models. We also highlight the differences in several modeling approaches and describe key advances in understanding the computational models that contributed to the knowledge base of the field.

Machine Learning and Mechanistic Modeling for Prediction of Metastatic Relapse in Early-Stage Breast Cancer

PURPOSE

For patients with early-stage breast cancer, predicting the risk of metastatic relapse is of crucial importance. Existing predictive models rely on agnostic survival analysis statistical tools (eg, Cox regression). Here we define and evaluate the predictive ability of a mechanistic model for time to distant metastatic relapse.

METHODS

The data we used for our model consisted of 642 patients with 21 clinicopathologic variables. A mechanistic model was developed on the basis of two intrinsic mechanisms of metastatic progression: growth (parameter α) and dissemination (parameter μ). Population statistical distributions of the parameters were inferred using mixed-effects modeling. A random survival forest analysis was used to select a minimal set of five covariates with the best predictive power. These were further considered to individually predict the model parameters by using a backward selection approach. Predictive performances were compared with classic Cox regression and machine learning algorithms.

RESULTS

The mechanistic model was able to accurately fit the data. Covariate analysis revealed statistically significant association of Ki67 expression with α (P = .001) and EGFR expression with μ (P = .009). The model achieved a c-index of 0.65 (95% CI, 0.60 to 0.71) in cross-validation and had predictive performance similar to that of random survival forest (95% CI, 0.66 to 0.69) and Cox regression (95% CI, 0.62 to 0.67) as well as machine learning classification algorithms.

CONCLUSION

By providing informative estimates of the invisible metastatic burden at the time of diagnosis and forward simulations of metastatic growth, the proposed model could be used as a personalized prediction tool for routine management of patients with breast cancer.

A mathematical model of the metastatic bottleneck predicts patient outcome and response to cancer treatment

Metastases are the main reason for cancer-related deaths. Initiation of metastases, where newly seeded tumor cells expand into colonies, presents a tremendous bottleneck to metastasis formation. Despite its importance, a quantitative description of metastasis initiation and its clinical implications is lacking. Here, we set theoretical grounds for the metastatic bottleneck with a simple stochastic model. The model assumes that the proliferation-to-death rate ratio for the initiating metastatic cells increases when they are surrounded by more of their kind. For a total of 159,191 patients across 13 cancer types, we found that a single cell has an extremely low median probability of successful seeding of the order of 10-8. With increasing colony size, a sharp transition from very unlikely to very likely successful metastasis initiation occurs. The median metastatic bottleneck, defined as the critical colony size that marks this transition, was between 10 and 21 cells. We derived the probability of metastasis occurrence and patient outcome based on primary tumor size at diagnosis and tumor type. The model predicts that the efficacy of patient treatment depends on the primary tumor size but even more so on the severity of the metastatic bottleneck, which is estimated to largely vary between patients. We find that medical interventions aiming at tightening the bottleneck, such as immunotherapy, can be much more efficient than therapies that decrease overall tumor burden, such as chemotherapy.

Artificial Intelligence and Mechanistic Modeling for Clinical Decision Making in Oncology

The amount of "big" data generated in clinical oncology, whether from molecular, imaging, pharmacological, or biological origin, brings novel challenges. To mine efficiently this source of information, mathematical models able to produce predictive algorithms and simulations are required, with applications for diagnosis, prognosis, drug development, or prediction of the response to therapy. Such mathematical and computational constructs can be subdivided into two broad classes: biologically agnostic, statistical models using artificial intelligence techniques, and physiologically based, mechanistic models. In this review, recent advances in the applications of such methods in clinical oncology are outlined. These include machine learning applied to big data (omics, imaging, or electronic health records), pharmacometrics and quantitative systems pharmacology, as well as tumor kinetics and metastasis modeling. Focus is set on studies with high potential of clinical translation, and particular attention is given to cancer immunotherapy. Perspectives are given in terms of combinations of the two approaches: "mechanistic learning."

The initial engraftment of tumor cells is critical for the future growth pattern: a mathematical study based on simulations and animal experiments

Background

Xenograft mouse tumor models are used to study mechanisms of tumor growth and metastasis formation and to investigate the efficacy of different therapeutic interventions. After injection the engrafted cells form a local tumor nodule. Following an initial lag period of several days, the size of the tumor is measured periodically throughout the experiment using calipers. This method of determining tumor size is error prone because the measurement is two-dimensional (calipers do not measure tumor depth). Primary tumor growth can be described mathematically by suitable growth functions, the choice of which is not always obvious. Growth parameters provide information on tumor growth and are determined by applying nonlinear curve fitting.

Methods

We used self-generated synthetic data including random measurement errors to research the accuracy of parameter estimation based on caliper measured tumor data. Fit metrics were investigated to identify the most appropriate growth function for a given synthetic dataset. We studied the effects of measuring tumor size at different frequencies on the accuracy and precision of the estimated parameters. For curve fitting with fixed initial tumor volume, we varied this fixed initial volume during the fitting process to investigate the effect on the resulting estimated parameters. We determined the number of surviving engrafted tumor cells after injection using ex vivo bioluminescence imaging, to demonstrate the effect on experiments of incorrect assumptions about the initial tumor volume.

Results

To select a suitable growth function, measurement data from at least 15 animals should be considered. Tumor volume should be measured at least every three days to estimate accurate growth parameters. Daily measurement of the tumor volume is the most accurate way to improve long-term predictability of tumor growth. The initial tumor volume needs to have a fixed value in order to achieve meaningful results. An incorrect value for the initial tumor volume leads to large deviations in the resulting growth parameters.

Conclusions

The actual number of cancer cells engrafting directly after subcutaneous injection is critical for future tumor growth and distinctly influences the parameters for tumor growth determined by curve fitting.

A Novel 4-Gene Score to Predict Survival, Distant Metastasis and Response to Neoadjuvant Therapy in Breast Cancer

We generated a 4-gene score with genes upregulated in LM2-4, a metastatic variant of MDA-MB-231 (DOK 4, HCCS, PGF, and SHCBP1) that was strongly associated with disease-free survival (DFS) in TCGA cohort (hazard ratio [HR]>1.2, p < 0.02). The 4-gene score correlated with overall survival of TCGA (HR = 1.44, p < 0.001), which was validated with DFS and disease-specific survival of METABRIC cohort. The 4-gene score was able to predict worse survival or clinically aggressive tumors, such as high Nottingham pathological grade and advanced cancer staging. High score was associated with worse survival in the hormonal receptor (HR)-positive/Her2-negative subtype. High score enriched cell proliferation-related gene sets in GSEA. The score was high in primary tumors that originated, in and metastasized to, brain and lung, and it predicted worse progression-free survival for metastatic tumors. Good tumor response to neoadjuvant chemotherapy or hormonal therapy was accompanied by score reduction. High scores were also predictive of response to neoadjuvant chemotherapy for HR-positive/Her2-negative subtype. High score tumors had increased expression of T cell exhaustion marker genes, suggesting that the score may also be a biomarker for immunotherapy response. Our novel 4-gene score with both prognostic and predictive values may, therefore, be clinically useful particularly in HR-positive breast cancer.

Individualized growth prediction of mice skin tumors with maximum likelihood estimators

BACKGROUND & OBJECTIVE

In this work, we focus on estimating the parameters of the Gompertz model in order to predict tumor growth. The estimation is based on measurements from mice skin tumors of de novo carcinogenesis. The main objective is to compare the Maximum Likelihood estimator with the best performance from our previous work with the Non-linear Least Squares estimator which is commonly used in the literature to estimate the growth parameters of the Gompertz model.

METHODS

To describe tumor growth, we propose a stochastic model which is based on the Gompertz growth function. The principle of Maximum Likelihood is used to estimate both the growth rate and the carrying capacity of the Gompertz function, along with the characteristics of the additive Gaussian process and measurement noise. Moreover, we examine whether a Maximum A Posteriori estimator is able to utilize any available prior knowledge in order to improve the predictions.

RESULTS

Experimental data from a total of 24 tumors in 8 mice (3 tumors each) were used to study the performance of the proposed methods with respect to prediction accuracy. Our results show that the Maximum Likelihood estimator is able to provide, in most cases, more accurate predictions. Moreover, the Maximum A Posteriori estimator has the potential to correct potentially non-realistic estimates for the carrying capacity at early growth stages.

CONCLUSION

In most cases, the Maximum Likelihood estimator is able to provide more reliable predictions for the tumor's growth on individual test subjects. The Maximum A Posteriori estimator, it has the potential to improve the prediction when the available experimental data do not provide adequate information by utilizing prior knowledge about the unknown parameters.

Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors

Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported population-level correlation between the Gompertz parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a reduced Gompertz function consisting of a single individual parameter (and one population parameter). Leveraging the population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.

A Transient Pseudosenescent Secretome Promotes Tumor Growth after Antiangiogenic Therapy Withdrawal

VEGF receptor tyrosine kinase inhibitors (VEGFR TKIs) approved to treat multiple cancer types can promote metastatic disease in certain limited preclinical settings. Here, we show that stopping VEGFR TKI treatment after resistance can lead to rebound tumor growth that is driven by cellular changes resembling senescence-associated secretory phenotypes (SASPs) known to promote cancer progression. A SASP-mimicking antiangiogenic therapy-induced secretome (ATIS) was found to persist during short withdrawal periods, and blockade of known SASP regulators, including mTOR and IL-6, could blunt rebound effects. Critically, senescence hallmarks ultimately reversed after long drug withdrawal periods, suggesting that the transition to a permanent growth-arrested senescent state was incomplete and the hijacking of SASP machinery ultimately transient. These findings may account for the highly diverse and reversible cytokine changes observed in VEGF inhibitor-treated patients, and suggest senescence-targeted therapies ("senotherapeutics")-particularly those that block SASP regulation-may improve outcomes in patients after VEGFR TKI failure.

Assessing the interactions between radiotherapy and antitumour immunity

Immunotherapy, specifically the introduction of immune checkpoint inhibitors, has transformed the treatment of cancer, enabling long-term tumour control even in individuals with advanced-stage disease. Unfortunately, only a small subset of patients show a response to currently available immunotherapies. Despite a growing consensus that combining immune checkpoint inhibitors with radiotherapy can increase response rates, this approach might be limited by the development of persistent radiation-induced immunosuppression. The ultimate goal of combining immunotherapy with radiotherapy is to induce a shift from an ineffective, pre-existing immune response to a long-lasting, therapy-induced immune response at all sites of disease. To achieve this goal and enable the adaptation and monitoring of individualized treatment approaches, assessment of the dynamic changes in the immune system at the patient level is essential. In this Review, we summarize the available clinical data, including forthcoming methods to assess the immune response to radiotherapy at the patient level, ranging from serum biomarkers to imaging techniques that enable investigation of immune cell dynamics in patients. Furthermore, we discuss modelling approaches that have been developed to predict the interaction of immunotherapy with radiotherapy, and highlight how they could be combined with biomarkers of antitumour immunity to optimize radiotherapy regimens and maximize their synergy with immunotherapy.

Towards quantitative imaging biomarkers of tumor dissemination: A multi-scale parametric modeling of multiple myeloma

The advent of medical imaging and automatic image analysis is bringing the full quantitative assessment of lesions and tumor burden at every clinical examination within reach. This opens avenues for the development and testing of functional disease models, as well as their use in the clinical practice for personalized medicine. In this paper, we introduce a Bayesian statistical framework, based on mixed-effects models, to quantitatively test and learn functional disease models at different scales, on population longitudinal data. We also derive an effective mathematical model for the crossover between initially detected lesions and tumor dissemination, based on the Iwata-Kawasaki-Shigesada model. We finally propose to leverage this descriptive disease progression model into model-aware biomarkers for personalized risk-assessment, taking all available examinations and relevant covariates into account. As a use case, we study Multiple Myeloma, a disseminated plasma cell cancer, in which proper diagnostics is essential, to differentiate frequent precursor state without end-organ damage from the rapidly developing disease requiring therapy. After learning the best biological models for local lesion growth and global tumor burden evolution on clinical data, and computing corresponding population priors, we use individual model parameters as biomarkers, and can study them systematically for correlation with external covariates, such as sex or location of the lesion. On our cohort of 63 patients with smoldering Multiple Myeloma, we show that they perform substantially better than other radiological criteria, to predict progression into symptomatic Multiple Myeloma. Our study paves the way for modeling disease progression patterns for Multiple Myeloma, but also for other metastatic and disseminated tumor growth processes, and for analyzing large longitudinal image data sets acquired in oncological imaging. It shows the unprecedented potential of model-based biomarkers for better and more personalized treatment decisions and deserves being validated on larger cohorts to establish its role in clinical decision making.

Quantitative mathematical modeling of clinical brain metastasis dynamics in non-small cell lung cancer

Brain metastases (BMs) are associated with poor prognosis in non-small cell lung cancer (NSCLC), but are only visible when large enough. Therapeutic decisions such as whole brain radiation therapy would benefit from patient-specific predictions of radiologically undetectable BMs. Here, we propose a mathematical modeling approach and use it to analyze clinical data of BM from NSCLC. Primary tumor growth was best described by a gompertzian model for the pre-diagnosis history, followed by a tumor growth inhibition model during treatment. Growth parameters were estimated only from the size at diagnosis and histology, but predicted plausible individual estimates of the tumor age (2.1-5.3 years). Multiple metastatic models were further assessed from fitting either literature data of BM probability (n = 183 patients) or longitudinal measurements of visible BMs in two patients. Among the tested models, the one featuring dormancy was best able to describe the data. It predicted latency phases of 4.4-5.7 months and onset of BMs 14-19 months before diagnosis. This quantitative model paves the way for a computational tool of potential help during therapeutic management.

Enhanced efficacy of sitravatinib in metastatic models of antiangiogenic therapy resistance

Tyrosine kinase inhibitors (TKIs) that primarily target angiogenesis are approved to treat several cancers in the metastatic setting; however, resistance is common. Sequential treatment or 'switching' from one TKI to another following failure can be effective, but predicting which drugs will have cross-over sensitivity remains a challenge. Here we examined sitravatinib (MGCD516), a spectrum-selective TKI able to block MET, TAM (TYRO3, AXL, MerTK) and multiple receptor families (including PDGFRs, VEGFRs, and Ephs). Transcriptomic analysis of several mouse and human cell lines revealed diverse molecular changes after resistance to two TKIs (sunitinib and axitinib) with multiple sitravatinib targets found to be upregulated. Sitravatinib treatment in vitro resulted in enhanced anti-proliferative effects in resistant cells and was improved compared to TKIs with similar target profiles. In vivo, primary tumor growth inhibition after sitravatinib treatment in mice was enhanced in resistant tumors and metastasis suppression improved when tumors were surgically removed. Together, these results suggest that the diverse and often inconsistent compensatory signaling mechanisms found to contribute to TKI resistance may paradoxically improve the tumor-inhibiting effects of broad-spectrum TKIs such as sitravatinib that are able to block multiple signaling pathways. Sitravatinib in the second-line setting following antiangiogenic TKI treatment may have enhanced inhibitory effects in local and disseminated disease, and improve outcomes in patients with refractory disease.

Local and Metastatic Relapse Features in Patients After a Primary Soft Tissue Sarcoma: Advocating for a Better-Tailored Follow-Up

Background: No consensus exists on how to follow patients after complete remission of a primary Soft Tissue Sarcoma (STS). Studying relapse features could help tailor guidelines for follow-up.

Patients and Methods: Patients in complete remission after initial management of a localized STS at Institut Bergonié who presented a first local and/or metastatic relapse between January 1995 and July 2015 were eligible. Characteristics of relapse diagnosis were retrospectively collected.

Results: 359 patients met inclusion criteria. 197 and 187 patients presented a local relapse and a metastatic relapse, respectively. In group 1 (limbs/trunk wall) and 2 (trunk/gynecological/other location), local relapse was diagnosed on clinical symptoms in 89 and 44% of cases, first detected by the patient himself in 68.5 and 34% of cases, and outside a planned visit in 67 and 36% of cases, respectively. In patients with metastatic relapse, diagnosis was made during a planned visit in 63% of cases, and by imaging in 62% of cases. Median survival after relapse was not different whether the first local relapse was diagnosed clinically or by imaging (44 [95%CI: 28–69.8] vs. 57 months [95%CI: 33.9–84.5], p = 0.35) but was longer if diagnosis of metastatic relapse was made on planned chest-CT scan rather than chest X-ray (58 [95%CI: 35.5–103.9] vs. 25 months [95%CI: 16.5–32.6], p < 0.05).

Conclusion: Patient's education for regular clinical examination can be recommended for follow-up of local relapses after a primary STS of the limbs or superficial trunk. Modeling studies aiming at better understanding and predicting tumor biology to improve tailoring STS patients' follow-up are warranted.

A Mathematical Framework for Modelling the Metastatic Spread of Cancer

Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network, they can spread to distant secondary sites in the body. This process, known as metastatic spread, is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer. To shed light on the metastatic process, we present a mathematical modelling framework that captures for the first time the interconnected processes of invasion and metastatic spread of individual cancer cells in a spatially explicit manner-a multigrid, hybrid, individual-based approach. This framework accounts for the spatiotemporal evolution of mesenchymal- and epithelial-like cancer cells, membrane-type-1 matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase-2 (MMP-2), and for their interactions with the extracellular matrix. Using computational simulations, we demonstrate that our model captures all the key steps of the invasion-metastasis cascade, i.e. invasion by both heterogeneous cancer cell clusters and by single mesenchymal-like cancer cells; intravasation of these clusters and single cells both via active mechanisms mediated by matrix-degrading enzymes (MDEs) and via passive shedding; circulation of cancer cell clusters and single cancer cells in the vasculature with the associated risk of cell death and disaggregation of clusters; extravasation of clusters and single cells; and metastatic growth at distant secondary sites in the body. By faithfully reproducing experimental results, our simulations support the evidence-based hypothesis that the membrane-bound MT1-MMP is the main driver of invasive spread rather than diffusible MDEs such as MMP-2.

Inferring rates of metastatic dissemination using stochastic network models

The formation of metastases is driven by the ability of cancer cells to disseminate from the site of the primary tumour to target organs. The process of dissemination is constrained by anatomical features such as the flow of blood and lymph in the circulatory system. We exploit this fact in a stochastic network model of metastasis formation, in which only anatomically feasible routes of dissemination are considered. By fitting this model to two different clinical datasets (tongue & ovarian cancer) we show that incidence data can be modelled using a small number of biologically meaningful parameters. The fitted models reveal site specific relative rates of dissemination and also allow for patient-specific predictions of metastatic involvement based on primary tumour location and stage. Applied to other data sets this type of model could yield insight about seed-soil effects, and could also be used in a clinical setting to provide personalised predictions about the extent of metastatic spread.

Modeling Growth of Tumors and Their Spreading Behavior Using Mathematical Functions

Computer simulations of the spread of malignant tumor cells in an entire organism provide important insights into the mechanisms of metastatic progression. Key elements for the usefulness of these models are the adequate selection of appropriate mathematical models describing the tumor growth and its parametrization as well as a proper choice of the fractal dimension of the blood vessels in the primary tumor. In addition, survival in the bloodstream and evasion into the connective spaces of the target organ of the future metastasis have to be modeled. Determination of these from experimental models is complicated by systematic and unsystematic experimental errors which are difficult to assess. In this chapter, we demonstrate how to select the best-suited mathematical function to describe tumor growth for experimental xenograft mouse tumor models and how to parametrize them. Common pitfalls and problems are described as well as methods to avoid them.

Tumor growth modeling: Parameter estimation with Maximum Likelihood methods

BACKGROUND & OBJECTIVE

In this work, we focus on estimating the parameters of the widely used Gompertz tumor growth model, based on measurements of the tumor's volume. Being able to accurately describe the dynamics of tumor growth on an individual basis is very important both for growth prediction and designing personalized, optimal therapy schemes (e.g. when using model predictive control).

METHODS

Our analysis aims to compute both the growth rate and the carrying capacity of the Gompertz function, along with the characteristics of the additive Gaussian process and measurement noise of the system. Three methods based on Maximum Likelihood estimation are proposed. The first utilizes an assumption regarding the measurement noise that simplifies the problem, the second combines the Extended Kalman Filter and Maximum Likelihood estimation, and the third is a nonstandard exact form of Maximum Likelihood estimation, where numerical integration is used to approximate the likelihood of the measurements, along with a novel way to reduce the required computations.

RESULTS

Synthetic data were used in order to perform extensive simulations aiming to compare the methods' effectiveness, with respect to the accuracy of the estimation. The proposed methods are able to estimate the growth dynamics, even when the noise characteristics are not estimated accurately. Another very important finding is that the methods perform best in the case that corresponds to the problem needed to be solved when dealing with experimental data.

CONCLUSION

Using nonstandard, problem specific techniques can improve the estimation accuracy and best exploit the available data.

Modeling therapeutic response to radioiodine in metastatic thyroid cancer: a proof-of-concept study for individualized medicine

Purpose

Radioiodine therapy (RAI) has traditionally been used as treatment for metastatic thyroid cancer, based on its ability to concentrate iodine. Propositions to maximize tumor response with minimizing toxicity, must recognize the infinite possibilities of empirical tests. Therefore, an approach of this study was to build a mathematical model describing tumor growth with the kinetics of thyroglobulin (Tg) concentrations over time, following RAI for metastatic thyroid cancer.

Experimental Design

Data from 50 patients with metastatic papillary thyroid carcinoma treated within eight French institutions, followed over 3 years after initial RAI treatments, were included in the model. A semi-mechanistic mathematical model that describes the tumor growth under RAI treatment was designed.

Results

Our model was able to separate patients who responded to RAI from those who did not, concordant with the physicians' determination of therapeutic response. The estimated tumor doubling-time (Td was found to be the most informative parameter for the distinction between responders and non-responders. The model was also able to reclassify particular patients in early treatment stages.

Conclusions

The results of the model present classification criteria that could indicate whether patients will respond or not to RAI treatment, and provide the opportunity to perform personalized management plans.

Biotinylated Bioluminescent Probe for Long Lasting Targeted in Vivo Imaging of Xenografted Brain Tumors in Mice

Bioluminescence is a useful tool for imaging of cancer in in vivo animal models that endogenously express luciferase, an enzyme that requires a substrate for visual readout. Current bioluminescence imaging, using commonly available luciferin substrates, only lasts a short time (15-20 min). To avoid repeated administration of luciferase substrate during cancer detection and surgery, a long lasting bioluminescence imaging substrate or system is needed. A novel water-soluble biotinylated luciferase probe, B-YL (1), was synthesized. A receptor-targeted complex of B-YL with streptavidin (SA) together with a biotinylated epidermal growth factor short peptide (B-EGF) (SA/B-YL/B-EGF = 1:3:1, molar ratio) was then prepared to demonstrate selective targeting. The complex was incubated with brain cancer cell lines overexpressing the EGF receptor (EGFR) and transfected with the luciferase gene. Results show that the complex specifically detects cancer cells by bioluminescence. The complex was further used to image xenograft brain tumors transfected with a luciferase gene in mice. The complex detects the tumor immediately, and bioluminescence lasts for 5 days. Thus, the complex generates a long lasting bioluminescence for cancer detection in mice. The complex with selective targeting may be used in noninvasive cancer diagnosis and accurate surgery in cancer treatment in clinics in the future.

Dose- and time-dependence of the host-mediated response to paclitaxel therapy: a mathematical modeling approach

It has recently been suggested that pro-tumorigenic host-mediated processes induced in response to chemotherapy counteract the anti-tumor activity of therapy, and thereby decrease net therapeutic outcome. Here we use experimental data to formulate a mathematical model describing the host response to different doses of paclitaxel (PTX) chemotherapy as well as the duration of the response. Three previously described host-mediated effects are used as readouts for the host response to therapy. These include the levels of circulating endothelial progenitor cells in peripheral blood and the effect of plasma derived from PTX-treated mice on migratory and invasive properties of tumor cells in vitro. A first set of mathematical models, based on basic principles of pharmacokinetics/pharmacodynamics, did not appropriately describe the dose-dependence and duration of the host response regarding the effects on invasion. We therefore provide an alternative mathematical model with a dose-dependent threshold, instead of a concentration-dependent one, that describes better the data. This model is integrated into a global model defining all three host-mediated effects. It not only precisely describes the data, but also correctly predicts host-mediated effects at different doses as well as the duration of the host response. This mathematical model may serve as a tool to predict the host response to chemotherapy in cancer patients, and therefore may be used to design chemotherapy regimens with improved therapeutic outcome by minimizing host mediated effects.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

Revisiting Bevacizumab + Cytotoxics Scheduling Using Mathematical Modeling: Proof of Concept Study in Experimental Non-Small Cell Lung Carcinoma

Concomitant administration of bevacizumab and pemetrexed‐cisplatin is a common treatment for advanced nonsquamous non‐small cell lung cancer (NSCLC). Vascular normalization following bevacizumab administration may transiently enhance drug delivery, suggesting improved efficacy with sequential administration. To investigate optimal scheduling, we conducted a study in NSCLC‐bearing mice. First, experiments demonstrated improved efficacy when using sequential vs. concomitant scheduling of bevacizumab and chemotherapy. Combining this data with a mathematical model of tumor growth under therapy accounting for the normalization effect, we predicted an optimal delay of 2.8 days between bevacizumab and chemotherapy. This prediction was confirmed experimentally, with reduced tumor growth of 38% as compared to concomitant scheduling, and prolonged survival (74 vs. 70 days). Alternate sequencing of 8 days failed in achieving a similar increase in efficacy, thus emphasizing the utility of modeling support to identify optimal scheduling. The model could also be a useful tool in the clinic to personally tailor regimen sequences.

Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth

Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. Here, we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bearing two simultaneously implanted tumors, growth of only one of the tumors was significantly suppressed (61% size reduction at day 15, P < 0.05). The competition model had to be rejected, whereas the angiogenesis inhibition and proliferation inhibition models were able to describe the data. Additional models including a theory based on distant cytotoxic log-kill effects were unable to fit the data. The proliferation inhibition model was identifiable and minimal (four parameters), and its descriptive power was validated against the data, including consistency in predictions of single tumor growth when no secondary tumor was present. This theory may also shed new light on single cancer growth insofar as it offers a biologically translatable picture of how local and global action may combine to control local tumor growth and, in particular, the role of tumor-tumor inhibition. This model offers a depiction of concomitant resistance that provides an improved theoretical basis for tumor growth control and may also find utility in therapeutic planning to avoid postsurgery metastatic acceleration. Cancer Res; 77(18); 5183-93. ©2017 AACR.

Metastatic triple-negative breast cancer is dependent on SphKs/S1P signaling for growth and survival

About 40,000 American women die from metastatic breast cancer each year despite advancements in treatment. Approximately, 15% of breast cancers are triple-negative for estrogen receptor, progesterone receptor, and HER2. Triple-negative cancer is characterized by more aggressive, harder to treat with conventional approaches and having a greater possibility of recurrence. Sphingosine-1-phosphate (S1P) is a bioactive sphingolipid signaling mediator has emerged as a key regulatory molecule in breast cancer progression. Therefore, we investigated whether cytosolic sphingosine kinase type 1 (SphK1) and nuclear sphingosine kinase type 2 (SphK2), the enzymes that make S1P are critical for growth and PI3K/AKT, ERK-MAP kinase mediated survival signaling of lung metastatic variant LM2-4 breast cancer cells, generated from the parental triple-negative MDA-MB-231 human breast cancer cell line. Similar with previous report, SphKs/S1P signaling is critical for the growth and survival of estrogen receptor positive MCF-7 human breast cancer cells, was used as our study control. MDA-MB-231 did not show a significant effect of SphKs/S1P signaling on AKT, ERK, and p38 pathways. In contrast, LM2-4 cells that gained lung metastatic phenotype from primary MDA-MB-231 cells show a significant effect of SphKs/S1P signaling requirement on cell growth, survival, and cell motility. PF-543, a selective potent inhibitor of SphK1, attenuated epidermal growth factor (EGF)-mediated cell growth and survival signaling through inhibition of AKT, ERK, and p38 MAP kinase pathways mainly in LM2-4 cells but not in parental MDA-MB-231 human breast cancer cells. Moreover, K-145, a selective inhibitor of SphK2, markedly attenuated EGF-mediated cell growth and survival of LM2-4 cells. We believe this study highlights the importance of SphKs/S1P signaling in metastatic triple-negative breast cancers and targeted therapies.

In Vivo Bioluminescence Tomography for Monitoring Breast Tumor Growth and Metastatic Spreading: Comparative Study and Mathematical Modeling

This study aimed at evaluating the reliability and precision of Diffuse Luminescent Imaging Tomography (DLIT) for monitoring primary tumor and metastatic spreading in breast cancer mice, and to develop a biomathematical model to describe the collected data. Using orthotopic mammary fat pad model of breast cancer (MDAMB231-Luc) in mice, we monitored tumor and metastatic spreading by three-dimensional (3D) bioluminescence and cross-validated it with standard bioluminescence imaging, caliper measurement and necropsy examination. DLIT imaging proved to be reproducible and reliable throughout time. It was possible to discriminate secondary lesions from the main breast cancer, without removing the primary tumor. Preferential metastatic sites were lungs, peritoneum and lymph nodes. Necropsy examinations confirmed DLIT measurements. Marked differences in growth profiles were observed, with an overestimation of the exponential phase when using a caliper as compared with bioluminescence. Our mathematical model taking into account the balance between living and necrotic cells proved to be able to reproduce the experimental data obtained with a caliper or DLIT imaging, because it could discriminate proliferative living cells from a more composite mass consisting of tumor cells, necrotic cell, or inflammatory tissues. DLIT imaging combined with mathematical modeling could be a powerful and informative tool in experimental oncology.

Balancing efficacy of and host immune responses to cancer therapy: the yin and yang effects

Local and systemic treatments for cancer include surgery, radiation, chemotherapy, hormonal therapy, molecularly targeted therapies, antiangiogenic therapy, and immunotherapy. Many of these therapies can be curative in patients with early stage disease, but much less frequently is this the case when they are used to treat advanced-stage metastatic disease. In the latter setting, innate and/or acquired resistance are among the reasons for reduced responsiveness or nonresponsiveness to therapy, or for tumour relapse after an initial response. Most studies of resistance or reduced responsiveness focus on 'driver' genetic (or epigenetic) changes in the tumour-cell population. Several studies have highlighted the contribution of therapy-induced physiological changes in host tissues and cells that can reduce or even nullify the desired antitumour effects of therapy. These unwanted host effects can promote tumour-cell proliferation (repopulation) and even malignant aggressiveness. These effects occur as a result of systemic release of numerous cytokines, and mobilization of various host accessory cells, which can invade the treated tumour microenvironment. In short, the desired tumour-targeting effects of therapy (the 'yin') can be offset by a reactive host response (the 'yang'); proactively preventing or actively suppressing the latter represents a possible new approach to improving the efficacy of both local and systemic cancer therapies.

Plasminogen Activator System and Breast Cancer: Potential Role in Therapy Decision Making and Precision Medicine

Shifting from the historical TNM paradigm to the determination of molecular and genetic subtypes of tumors has been a major improvement to better picture cancerous diseases. The sharper the picture is, the better will be the possibility to develop subsequent strategies, thus achieving higher efficacy and prolonged survival eventually. Recent studies suggest that urokinase-type plasminogen activator (uPA), uPA Receptor (uPAR), and plasmino-gen activator inhibitor-1 (PAI-1) may play a critical role in cancer invasion and metastasis. Consistent with their role in cancer dissemination, high levels of uPA, PAI-1, and uPAR in multiple cancer types correlate with dismal prognosis. In this respect, upfront determination of uPA and PAI-1 as invasion markers has further opened up the possibilities for individualized therapy of breast cancer. Indeed, uPA and PAI-1 could help to classify patients on their risk for metastatic spreading and subsequent relapse, thus helping clinicians in their decision-making process to propose, or not propose, adjuvant therapy. This review covers the implications for cancer diagnosis, prognosis, and therapy of uPA and PAI-1, and therefore how they could be major actors in the development of a precision medicine in breast cancer.

Computational Modelling of Metastasis Development in Renal Cell Carcinoma

The biology of the metastatic colonization process remains a poorly understood phenomenon. To improve our knowledge of its dynamics, we conducted a modelling study based on multi-modal data from an orthotopic murine experimental system of metastatic renal cell carcinoma. The standard theory of metastatic colonization usually assumes that secondary tumours, once established at a distant site, grow independently from each other and from the primary tumour. Using a mathematical model that translates this assumption into equations, we challenged this theory against our data that included: 1) dynamics of primary tumour cells in the kidney and metastatic cells in the lungs, retrieved by green fluorescent protein tracking, and 2) magnetic resonance images (MRI) informing on the number and size of macroscopic lesions. Critically, when calibrated on the growth of the primary tumour and total metastatic burden, the predicted theoretical size distributions were not in agreement with the MRI observations. Moreover, tumour expansion only based on proliferation was not able to explain the volume increase of the metastatic lesions. These findings strongly suggested rejection of the standard theory, demonstrating that the time development of the size distribution of metastases could not be explained by independent growth of metastatic foci. This led us to investigate the effect of spatial interactions between merging metastatic tumours on the dynamics of the global metastatic burden. We derived a mathematical model of spatial tumour growth, confronted it with experimental data of single metastatic tumour growth, and used it to provide insights on the dynamics of multiple tumours growing in close vicinity. Together, our results have implications for theories of the metastatic process and suggest that global dynamics of metastasis development is dependent on spatial interactions between metastatic lesions.

We used mathematical modelling to formalize the standard theory of metastatic initiation, under which secondary tumours, after establishment in a distant organ, grow independently from each other and from the primary tumour. When calibrated on the experimental data of primary tumour and total metastatic burden in the lungs in an animal model of renal cell carcinoma, the initial model predicted a size distribution of metastatic foci that did not fit with observations obtained experimentally using magnetic resonance imaging (which provided size and number of macro-metastases). The model predicted an increase in the number of lesions, but of smaller size when compared to the data. This led us to revise the standard theory and to propose two hypotheses in order to explain the observations: 1) small metastatic foci merge into larger ones and/or 2) circulating tumour cells may join already established tumours. We then derived a spatial model of tumour growth in order to explore the quantitative implications of tumours merging on global tumour growth and estimated the numbers of required metastatic foci to obtain the observed metastatic volumes.