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

Practical parameter identifiability and handling of censored data with Bayesian inference in mathematical tumour models

Mechanistic mathematical models (MMs) are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use 5 MMs with an increasing number of parameters to explore how certain (often overlooked) decisions in estimating parameters from data of experimental tumour growth affect the outcome of the analysis. In particular, we propose a framework for including tumour volume measurements that fall outside the upper and lower limits of detection, which are normally discarded. We demonstrate how excluding censored data results in an overestimation of the initial tumour volume and the MM-predicted tumour volumes prior to the first measurements, and an underestimation of the carrying capacity and the MM-predicted tumour volumes beyond the latest measurable time points. We show in which way the choice of prior for the MM parameters can impact the posterior distributions, and illustrate that reporting the most likely parameters and their 95% credible interval can lead to confusing or misleading interpretations. We hope this work will encourage others to carefully consider choices made in parameter estimation and to adopt the approaches we put forward herein.

A Mathematical Model of Stroma-Supported Allometric Tumor Growth

Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell's location and potential to proliferate can influence its sensitivity to cancer treatments. In this paper, we use ordinary differential equations to develop spatially structured models for solid tumors wherein the growth of tumor components is coordinated. The model tumors feature two components, a proliferating peripheral growth region, which potentially includes a mix of cancerous and noncancerous stroma cells, and a solid tumor core. Mathematical and numerical analysis are used to investigate how coordinated expansion of the tumor growth region and core can influence overall growth dynamics in a variety of tumor types. Model assumptions, which are motivated by empirical and in silico solid tumor research, are evaluated through comparison to tumor volume data and existing models of tumor growth.

A multiscale model of the role of microenvironmental factors in cell segregation and heterogeneity in breast cancer development

We analyzed a quantitative multiscale model that describes the epigenetic dynamics during the growth and evolution of an avascular tumor. A gene regulatory network (GRN) formed by a set of ten genes that are believed to play an important role in breast cancer development was kinetically coupled to the microenvironmental agents: glucose, estrogens, and oxygen. The dynamics of spontaneous mutations was described by a Yule-Furry master equation whose solution represents the probability that a given cell in the tissue undergoes a certain number of mutations at a given time. We assumed that the mutation rate is modified by a spatial gradient of nutrients. The tumor mass was simulated by means of cellular automata supplemented with a set of reaction diffusion equations that described the transport of microenvironmental agents. By analyzing the epigenetic state space described by the GRN dynamics, we found three attractors that were identified with cellular epigenetic states: normal, precancer and cancer. For two-dimensional (2D) and three-dimensional (3D) tumors we calculated the spatial distribution of the following quantities: (i) number of mutations, (ii) mutation of each gene and, (iii) phenotypes. Using estrogen as the principal microenvironmental agent that regulates cell proliferation process, we obtained tumor shapes for different values of estrogen consumption and supply rates. It was found that he majority of mutations occurred in cells that were located close to the 2D tumor perimeter or close to the 3D tumor surface. Also, it was found that the occurrence of different phenotypes in the tumor are controlled by estrogen concentration levels since they can change the individual cell threshold and gene expression levels. All results were consistently observed for 2D and 3D tumors.

Asymmetric Growth of Tumor Spheroids in a Symmetric Environment

In this work, we studied the stability of radially symmetric growth in tumor spheroids using a reaction-diffusion model. In this model, nutrient concentration and internal pressure are local variables that implicitly relate the proliferation of cells to the growth of the tumor. The analytical solution of the governing model was presented in an orthonormal spherical harmonic basis. It was shown that the radially symmetric steady-state solution to the growth of tumor spheroids, under symmetric growth conditions, was unstable with respect to small asymmetric perturbations. Such perturbations excited the asymmetric modes of growth, which could grow in time and change the spherical configuration of the tumor. The number of such modes and their rates of growth depended on parameters such as surface tension, external energy and the rate of nutrient consumption. This analysis indicated that the spherical configuration of tumor spheroids, even under experimentally controlled symmetric growth conditions, were naturally unstable. This was confirmed by a comparison between the shapes of in vitro human glioblastoma (hGB) spheroids and the configuration of the first few asymmetric modes predicted by the model.

Integrated computational and in vivo models reveal Key Insights into macrophage behavior during bone healing

Myeloid-derived monocyte and macrophages are key cells in the bone that contribute to remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage dynamics and polarization states over time: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. Bone healing is a complex multicellular dynamic process. While traditional in vitro and in vivo experimentation may capture the behavior of select populations with high resolution, they cannot simultaneously track the behavior of multiple populations. To address this, we have used an integrated coupled ordinary differential equations (ODEs)-based framework describing multiple cellular species to in vivo bone injury data in order to identify and test various hypotheses regarding bone cell populations dynamics. Our approach allowed us to infer several biological insights including, but not limited to,: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. In addition, we further tested the robustness of the mathematical model by comparing simulation results to an independent experimental dataset. Taken together, this novel comprehensive mathematical framework allowed us to identify biological mechanisms that best recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process. Furthermore, our hypothesis testing methodology could be used in other contexts to decipher mechanisms in complex multicellular processes.

Myeloid-derived monocytes/macrophages are key cells for bone remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage population dynamics: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. In order to test various hypotheses regarding bone cell populations dynamics, we have integrated a coupled ordinary differential equations-based framework describing multiple cellular species to in vivo bone injury data. Our approach allowed us to infer several biological insights including: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. Taken together, this mathematical framework allowed us to identify biological mechanisms that recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process.

Mathematically modelling inflammation as a promoter of tumour growth

Inflammation is now known to play a significant role in tumour growth and progression. It is also difficult to adequately quantify systemic inflammation and the resulting localized effects in cancer. Here, we use experimental data to infer the possible contributions of inflammation in a mouse model of cancer. The model is validated by predicting tumour growth under anti-inflammatory treatments, and combination cancer therapies are explored. We then extend the model to consider simultaneous tumour implants at two distinct sites, which experimentally was shown to result in one large and one small tumour. We use this model to examine the role inflammation may play in the growth rate separation. Finally, we use this predictive two-tumour model to explore implications of inflammation on metastases, surgical removal of the primary and adjuvant anti-inflammatory treatments. This work suggests that improved tumour control can be obtained by targeting both the cancer and host, through anti-inflammatory treatments, including reduced metastatic burden post-surgical removal of primary tumours.

The Multiple Dimensions of Networks in Cancer: A Perspective

This perspective article gathers the latest developments in mathematical and computational oncology tools that exploit network approaches for the mathematical modelling, analysis, and simulation of cancer development and therapy design. It instigates the community to explore new paths and synergies under the umbrella of the Special Issue “Networks in Cancer: From Symmetry Breaking to Targeted Therapy”. The focus of the perspective is to demonstrate how networks can model the physics, analyse the interactions, and predict the evolution of the multiple processes behind tumour-host encounters across multiple scales. From agent-based modelling and mechano-biology to machine learning and predictive modelling, the perspective motivates a methodology well suited to mathematical and computational oncology and suggests approaches that mark a viable path towards adoption in the clinic.

Modeling the effects of EMT-immune dynamics on carcinoma disease progression

During progression from carcinoma in situ to an invasive tumor, the immune system is engaged in complex sets of interactions with various tumor cells. Tumor cell plasticity alters disease trajectories via epithelial-to-mesenchymal transition (EMT). Several of the same pathways that regulate EMT are involved in tumor-immune interactions, yet little is known about the mechanisms and consequences of crosstalk between these regulatory processes. Here we introduce a multiscale evolutionary model to describe tumor-immune-EMT interactions and their impact on epithelial cancer progression from in situ to invasive disease. Through simulation of patient cohorts in silico, the model predicts that a controllable region maximizes invasion-free survival. This controllable region depends on properties of the mesenchymal tumor cell phenotype: its growth rate and its immune-evasiveness. In light of the model predictions, we analyze EMT-inflammation-associated data from The Cancer Genome Atlas, and find that association with EMT worsens invasion-free survival probabilities. This result supports the predictions of the model, and leads to the identification of genes that influence outcomes in bladder and uterine cancer, including FGF pathway members. These results suggest new means to delay disease progression, and demonstrate the importance of studying cancer-immune interactions in light of EMT.

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.

Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment

Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known as metastatic blow-up. Recent clinical evidence has shown that the immune response can have strong tumor promoting effects. In this work, we investigate if the pro-tumor effects of the immune response can have a significant contribution to metastatic dormancy and metastatic blow-up. We develop an ordinary differential equation model of the immune-mediated theory of metastasis. We include both anti- and pro-tumor immune effects, in addition to the experimentally observed phenomenon of tumor-induced immune cell phenotypic plasticity. Using geometric singular perturbation analysis, we derive a rather simple model that captures the main processes and, at the same time, can be fully analyzed. Literature-derived parameter estimates are obtained, and model robustness is demonstrated through a time dependent sensitivity analysis. We determine conditions under which the parameterized model can successfully explain both metastatic dormancy and blow-up. The results confirm the significant active role of the immune system in the metastatic process. Numerical simulations suggest a novel measure to predict the occurrence of future metastatic blow-up in addition to new potential avenues for treatment of clinically undetectable micrometastases.

Quantitative Systems Pharmacology Approaches for Immuno-Oncology: Adding Virtual Patients to the Development Paradigm

Drug development in oncology commonly exploits the tools of molecular biology to gain therapeutic benefit through reprograming of cellular responses. In immuno‐oncology (IO) the aim is to direct the patient’s own immune system to fight cancer. After remarkable successes of antibodies targeting PD1/PD‐L1 and CTLA4 receptors in targeted patient populations, the focus of further development has shifted toward combination therapies. However, the current drug‐development approach of exploiting a vast number of possible combination targets and dosing regimens has proven to be challenging and is arguably inefficient. In particular, the unprecedented number of clinical trials testing different combinations may no longer be sustainable by the population of available patients. Further development in IO requires a step change in selection and validation of candidate therapies to decrease development attrition rate and limit the number of clinical trials. Quantitative systems pharmacology (QSP) proposes to tackle this challenge through mechanistic modeling and simulation. Compounds’ pharmacokinetics, target binding, and mechanisms of action as well as existing knowledge on the underlying tumor and immune system biology are described by quantitative, dynamic models aiming to predict clinical results for novel combinations. Here, we review the current QSP approaches, the legacy of mathematical models available to quantitative clinical pharmacologists describing interaction between tumor and immune system, and the recent development of IO QSP platform models. We argue that QSP and virtual patients can be integrated as a new tool in existing IO drug development approaches to increase the efficiency and effectiveness of the search for novel combination therapies.

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."

Lessons from Hippocrates: Time to Change the Cancer Paradigm

The ultimate goal of all medical activity is to restore patients to a state of complete physical, mental, and social wellbeing. In cancer, it is assumed that this can only be obtained through the complete eradication of the tumor burden. So far, this strategy has led to a substantial improvement in cancer survival rates. Despite this, more than 9 million people die from cancer every year. Therefore, we need to accept that our current cancer treatment paradigm is obsolete and must be changed. The new paradigm should reflect that cancer is a systemic disease, which affects an individual patient living in a particular social reality, rather than an invading organism or a mere cluster of mutated cells that need to be eradicated. This Hippocratic holistic view will ultimately lead to an improvement in health and wellbeing in cancer patients. They deserve nothing less.

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.

Immunologic Consequences of Sequencing Cancer Radiotherapy and Surgery

PURPOSE

Early-stage cancers are routinely treated with surgery followed by radiotherapy (SR). Radiotherapy before surgery (RS) has been widely ignored for some cancers. We evaluate overall survival (OS) and disease-free survival (DFS) with SR and RS for different cancer types and simulate the plausibility of RS- and SR-induced antitumor immunity contributing to outcomes.

MATERIALS AND METHODS

We analyzed a SEER data set of early-stage cancers treated with SR or RS. OS and DFS were calculated for cancers with sufficient numbers for statistical power (cancers of lung and bronchus, esophagus, rectum, cervix uteri, corpus uteri, and breast). We simulated the immunologic consequences of SR, RS, and radiotherapy alone in a mathematical model of tumor-immune interactions.

RESULTS

RS improved OS for cancers with low 20-year survival rates (lung: hazard ratio [HR], 0.88; P = .046) and improved DFS for cancers with higher survival (breast: HR = 0.64; P < .001). For rectal cancer, with intermediate 20-year survival, RS improved both OS (HR = 0.89; P = .006) and DFS (HR = 0.86; P = .04). Model simulations suggested that RS could increase OS by eliminating cancer for a broader range of model parameters and radiotherapy-induced antitumor immunity compared with SR for selected parameter combinations. This could create an immune memory that may explain increased DFS after RS for certain cancers.

CONCLUSION

Study results suggest plausibility that radiation to the bulk of the tumor could induce a more robust immune response and better harness the synergy of radiotherapy and antitumor immunity than postsurgical radiation to the tumor bed. This exploratory study provides motivation for prospective evaluation of immune activation of RS versus SR in controlled clinical studies.

Brain Metastases: Insights from Statistical Modeling of Size Distribution

BACKGROUND AND PURPOSE

Brain metastases are a common finding on brain MRI. However, the factors that dictate their size and distribution are incompletely understood. Our aim was to discover a statistical model that can account for the size distribution of parenchymal metastases in the brain as measured on contrast-enhanced MR imaging.

MATERIALS AND METHODS

Tumor volumes were calculated on the basis of measured tumor diameters from contrast-enhanced T1-weighted spoiled gradient-echo images in 68 patients with untreated parenchymal metastatic disease. Tumor volumes were then placed in rank-order distributions and compared with 11 different statistical curve types. The resultant R ² values to assess goodness of fit were calculated. The top 2 distributions were then compared using the likelihood ratio test, with resultant R values demonstrating the relative likelihood of these distributions accounting for the observed data.

RESULTS

Thirty-nine of 68 cases best fit a power distribution (mean R ² = 0.938 ± 0.050), 20 cases best fit an exponential distribution (mean R ² = 0.957 ± 0.050), and the remaining cases were scattered among the remaining distributions. Likelihood ratio analysis revealed that 66 of 68 cases had a positive mean R value (1.596 ± 1.316), skewing toward a power law distribution.

CONCLUSIONS

The size distributions of untreated brain metastases favor a power law distribution. This finding suggests that metastases do not exist in isolation, but rather as part of a complex system. Furthermore, these results suggest that there may be a relatively small number of underlying variables that substantially influence the behavior of these systems. The identification of these variables could have a profound effect on our understanding of these lesions and our ability to treat them.

A mathematical model for the immune-mediated theory of metastasis

Accumulating experimental and clinical evidence suggest that the immune response to cancer is not exclusively anti-tumor. Indeed, the pro-tumor roles of the immune system  -  as suppliers of growth and pro-angiogenic factors or defenses against cytotoxic immune attacks, for example  -  have been long appreciated, but relatively few theoretical works have considered their effects. Inspired by the recently proposed "immune-mediated" theory of metastasis, we develop a mathematical model for tumor-immune interactions at two anatomically distant sites, which includes both anti- and pro-tumor immune effects, and the experimentally observed tumor-induced phenotypic plasticity of immune cells (tumor "education" of the immune cells). Upon confrontation of our model to experimental data, we use it to evaluate the implications of the immune-mediated theory of metastasis. We find that tumor education of immune cells may explain the relatively poor performance of immunotherapies, and that many metastatic phenomena, including metastatic blow-up, dormancy, and metastasis to sites of injury, can be explained by the immune-mediated theory of metastasis. Our results suggest that further work is warranted to fully elucidate the pro-tumor effects of the immune system in metastatic cancer.

Immunomodulatory Effects of Surgery, Pain, and Opioids in Cancer Patients

Surgery is the mainstay of therapy for canine and human solid cancers. Alarmingly, evidence suggests that the process of surgery may exacerbate metastasis and accelerate the kinetics of cancer progression. Understanding the mechanisms by which cancer progression is accelerated as a result of surgery may provide pharmacologic interventions. This review discusses surgery-induced cancer progression. It focuses on immunomodulatory properties of anesthesia and opioids and evidence that studies evaluating the role of opioids in tumor progression are indicated. It concludes by discussing why companion animals with spontaneously arising cancer are an ideal model for clinical trials to investigate this phenomenon.

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.

A novel scoring system predicting survival benefits of palliative primary tumor resection for patients with unresectable metastatic colorectal cancer: A retrospective cohort study protocol

The role of palliative primary tumor resection (PPTR) in improving survival in patients with synchronous unresectable metastatic colorectal cancer (mCRC) is controversial. In this study, we aimed to evaluate whether our novel scoring system could predict survival benefits of PPTR in mCRC patients.In this retrospective cohort study consecutive patients with synchronous mCRC and unresectable metastases admitted to Sir Run Run Shaw Hospital between January 2005 and December 2013 were identified. A scoring system was established by the serum levels of carcinoembryonic antigen (CEA), cancer antigen 19-9 (CA19-9), neutrophil/lymphocyte ratio (NLR), and lactate dehydrogenase (LDH). Patients with scores of 0, 1-2, or 3-4 were considered as being in the low, intermediate, and high score group, respectively. Primary outcome was overall survival (OS).A total of 138 eligible patients were included in the analysis, of whom 103 patients had undergone PPTR and 35 had not. The median OS of the PPTR group was better than that of the Non-PPTR group, with 26.2 and 18.9 months, respectively (P < .01). However, the subgroup of PPTR with a high score (3-4) showed no OS benefit (13.3 months) compared with that of the Non-PPTR group (18.9 months, P = .11). The subgroup of PPTR with a low score (52.1 months) or intermediate score (26.2 months) had better OS than that of the Non-PPTR group (P < .001, P = .017, respectively).A novel scoring system composed of CEA, CA19-9, NLR, and LDH values is a feasible method to evaluate whether mCRC patients would benefit from PPTR. It might guide clinical decision making in selecting patients with unresectable mCRC for primary tumor resection.

Illuminating the Numbers: Integrating Mathematical Models to Optimize Photomedicine Dosimetry and Combination Therapies

Cancer photomedicine offers unique mechanisms for inducing local tumor damage with the potential to stimulate local and systemic anti-tumor immunity. Optically-active nanomedicine offers these features as well as spatiotemporal control of tumor-focused drug release to realize synergistic combination therapies. Achieving quantitative dosimetry is a major challenge, and dosimetry is fundamental to photomedicine for personalizing and tailoring therapeutic regimens to specific patients and anatomical locations. The challenge of dosimetry is perhaps greater for photomedicine than many standard therapies given the complexity of light delivery and light-tissue interactions as well as the resulting photochemistry responsible for tumor damage and drug-release, in addition to the usual intricacies of therapeutic agent delivery. An emerging multidisciplinary approach in oncology utilizes mathematical and computational models to iteratively and quantitively analyze complex dosimetry, and biological response parameters. These models are parameterized by preclinical and clinical observations and then tested against previously unseen data. Such calibrated and validated models can be deployed to simulate treatment doses, protocols, and combinations that have not yet been experimentally or clinically evaluated and can provide testable optimal treatment outcomes in a practical workflow. Here, we foresee the utility of these computational approaches to guide adaptive therapy, and how mathematical models might be further developed and integrated as a novel methodology to guide precision photomedicine.

Investigation of tumor-tumor interactions in a double human cervical carcinoma xenograft model in nude mice

Tumor-tumor distant interactions within one organism are of major clinical relevance determining clinical outcome. To investigate this poorly understood phenomenon, a double human cervical xenograft model in nude mice was developed. A first tumor was induced subcutaneously by injection of human papillomavirus positive cervical carcinoma cells into the mouse lower right flank and 3 weeks later, animals were challenged with the same tumor cell line injected subcutaneously into the upper left flank. These tumors had no direct physical contact and we found no systemic changes induced by the primary tumor affecting the growth of a secondary tumor. However, ablation of the primary tumor by local treatment with cidofovir, a nucleotide analogue with known antiviral and antiproliferative properties, resulted not only in a local antitumor effect but also in a temporary far-reaching effect leading to retarded growth of the challenged tumor. Cidofovir far-reaching effects were linked to a reduced tumor-driven inflammation, to increased anti-tumor immune responses, and could not be enhanced by co-administration with immune stimulating adjuvants. Our findings point to the potential use of cidofovir in novel therapeutic strategies aiming to kill tumor cells as well as to influence the immune system to fight cancer.

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.