# Minimizing Metastatic Risk in Radiotherapy Fractionation Schedules

Metastasis is the process by which cells from a primary tumor disperse and form new tumors at distant anatomical locations. The treatment and prevention of metastatic cancer remains an extremely challenging problem. In this work, we consider the problem of developing fractionated irradiation schedules that minimize production of metastatic cancer cells. Interestingly we observe that the resulting fractionation schedules are significantly different than those that result from more standard objectives such as minimization of final primary tumor volume. Hypo-fractionation is suggested even in cases when the α/β value of the tumor is large. This work introduces a novel biologically motivated objective function to the radiation optimization community that takes into account metastatic risk instead of the status of the primary tumor.

http://arxiv.org/abs/1312.7337

# Cells Hypothesis

The tumour control probability (TCP) is a formalism derived to compare various treatment regimens of radiation therapy, defined as the probability that given a prescribed dose of radiation, a tumour has been eradicated or controlled. In the traditional view of cancer, all cells share the ability to divide without limit and thus have the potential to generate a malignant tumour. However, an emerging notion is that only a sub-population of cells, the so-called cancer stem cells (CSCs), are responsible for the initiation and maintenance of the tumour. A key implication of the CSC hypothesis is that these cells must be eradicated to achieve cures, thus we define TCP_S as the probability of eradicating CSCs for a given dose of radiation. A cell surface protein expression profile, such as CD44high/CD24low for breast cancer, is often used as a biomarker to monitor CSCs enrichment. However, it is increasingly recognized that not all cells bearing this expression profile are necessarily CSCs, and in particular early generations of progenitor cells may share the same phenotype. Thus, due to the lack of a perfect biomarker for CSCs, we also define a novel measurable TCP_CD+, that is the probability of eliminating or controlling biomarker positive cells. Based on these definitions, we use stochastic methods and numerical simulations to compare the theoretical TCP_S and the measurable TCP_CD+. We also use the measurable TCP to compare the effect of various radiation protocols.

## Wednesday, December 18, 2013

### Radiotherapy planning for glioblastoma based on a tumor growth model: Improving target volume delineation

Jan Unkelbach, Bjoern H. Menze, Ender Konukoglu, Florian Dittmann, Matthieu Le, Nicholas Ayache, Helen A. Shih

Glioblastoma di ffer from many other tumors in the sense that they grow in filtratively into the brain tissue instead of forming a solid tumor mass with a de fined boundary. Only the part of the tumor with high tumor cell density can be localized through imaging directly. In contrast, brain tissue infi ltrated by tumor cells at low density appears normal on current imaging modalities. In current clinical practice, a uniform margin, typically two centimeters, is applied to account for microscopic spread of disease that is not directly assessable through imaging. The current treatment planning procedure can potentially be improved by accounting for the anisotropy of tumor growth, which arises from di fferent factors: Anatomical barriers such as the falx cerebri represent boundaries for migrating tumor cells. In addition, tumor cells primarily spread in white matter and in lfiltrate gray matter at lower rate. We investigate the use of a phenomenological tumor growth model for treatment planning. The model is based on the Fisher-Kolmogorov equation, which formalizes these growth characteristics and estimates the spatial distribution of tumor cells in normal appearing regions of the brain. The target volume for radiotherapy planning can be defi ned as an isoline of the simulated tumor cell density. This paper analyzes the model with respect to implications for target volume de finition and identifi es its most critical components. A retrospective study involving 10 glioblastoma patients treated at our institution has been performed.

To illustrate the main fi ndings of the study, a detailed case study is presented for a glioblastoma located close to the falx. In this situation, the falx represents a boundary for migrating tumor cells, whereas the corpus callosum provides a route for the tumor to spread to the contralateral hemisphere. We further discuss the sensitivity of the model with respect to the input parameters. Correct segmentation of the brain appears to be the most crucial model input. We conclude that the tumor growth model provides a method to account for anisotropic growth patterns of glioma, and may therefore provide a tool to make target delineation more objective and automated.

# Inferring causal models of cancer progression with a shrinkage estimator and probability raising

Existing techniques to reconstruct tree models of progression for accumulative processes such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper we define a novel theoretical framework to reconstruct such models based on the probabilistic notion of causation defined by Suppes, which differ fundamentally from that based on correlation. We consider a general reconstruction setting complicated by the presence of noise in the data, owing to the intrinsic variability of biological processes as well as experimental or measurement errors. To gain immunity to noise in the reconstruction performance we use a shrinkage estimator. On synthetic data, we show that our approach outperforms the state-of-the-art and, for some real cancer datasets, we highlight biologically significant differences revealed by the reconstructed progressions. Finally, we show that our method is efficient even with a relatively low number of samples and its performance quickly converges to its asymptote as the number of samples increases. Our analysis suggests the applicability of the method on small datasets of real patients.

http://arxiv.org/abs/1311.6293

## Tuesday, December 3, 2013

### Most viewed abstracts: inception through November

Taking the idea from Haldane's Sieve I've decided to start a monthly 'most viewed' post.  To start though, I'll list the top 5 viewed posts to date, from our first post on June 19th, 2013.

The number one post actually comprises two abstracts:

### A recent physical approach to angiogenesis modeling: mixture models

http://mathematicaloncology.blogspot.com/2013/06/a-recent-physical-approach-to.html

### Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation

http://mathematicaloncology.blogspot.com/2013/05/modeling-dichotomy-of-immune-response.html

### Cancer initiation with epistatic interactions between driver and passenger mutations

Please, keep spreading the word, and let us know if you find any preprints that we've missed. With +PeerJ, the +bioRxiv, +F1000 and the +arXiv there are more and more out there!

# Investigating the relation between stochastic differentiation and homeostasis in intestinal crypts via multiscale modeling

Alex GraudenziGiulio CaravagnaGiovanni De MatteisMarco Antoniotti

## ABSTRACT

Colorectal tumors originate and develop within intestinal crypts. Even though some of the essential phenomena that characterize crypt structure and dynamics have been effectively described in the past, the relation between the differentiation process and the overall crypt homeostasis is still partially understood. We here investigate this relation and other important biological phenomena by introducing a novel multiscale model that combines a morphological description of the crypt with a gene regulation model: the emergent dynamical behavior of the underlying gene regulatory network drives cell growth and differentiation processes, linking the two distinct spatio-temporal levels. The model relies on a few a priori assumptions, yet accounting for several key processes related to crypt functioning, such as: dynamic gene activation patterns, stochastic differentiation, signaling pathways ruling cell adhesion properties, cell displacement, cell growth, mitosis, apoptosis and the presence of biological noise. We show that this modeling approach captures the major dynamical phenomena that characterize the regular physiology of crypts, such as cell sorting, coordinate migration, dynamic turnover, stem cell niche maintenance and clonal expansion. All in all, the model suggests that the process of stochastic differentiation might be sufficient to drive the crypt to homeostasis, under certain crypt configurations. Besides, our approach allows to make precise quantitative inferences that, when possible, were matched to the current biological knowledge and it permits to investigate the role of gene-level perturbations, with reference to cancer development. We also remark the theoretical framework is general and may applied to different tissues, organs or organisms.

# A multi-phenotypic cancer model with cell plasticity

The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible cell plasticity among cancer cells has received much attention very recently. Here we present a generalized multi-phenotypic cancer model by integrating cell plasticity with the conventional hierarchical structure of cancer cells. Based on our model, we theoretically explain the universality of the phenotypic equilibrium phenomena reported in various cancer cell lines. By applying our model to concrete biological examples with real experimental data, we show that cancer cell plasticity plays an essential role in transient regulation of cancer heterogeneity. Our work may pave the way for modeling and analyzing the cell population dynamics with cell plasticity.

http://arxiv.org/abs/1311.6222

# James P. Brody

Cancers are caused by the accumulation of genetic alterations. Since this accumulation takes time, the incidence of most cancers is thought to increase exponentially with age. However, careful measurements of the age-specific incidence shows that the specific incidence for many forms of cancer rises with age to a maximum, then decreases. This decrease in the age-specific incidence with age is an anomaly. Understanding this anomaly should lead to a better understanding of how tumors develop and grow. Here I derive the shape of the age-specific incidence, showing that it should follow the shape of a Weibull distribution. Measurements indicate that the age-specific incidence for colon cancer does indeed follow a Weibull distribution. This analysis leads to the interpretation that for colon cancer two sub-populations exist in the general population: a susceptible population and an immune population. Colon tumors will only occur in the susceptible population. This analysis is consistent with the developmental origins of disease hypothesis and generalizable to many other common forms of cancer.

## Tuesday, October 22, 2013

### A new pre-print server for biology... AND theoretical oncology!

Sorry for the editorial interjection here, but I've just put a post on my own blog Connecting the Dots, which I think is appropriate for this forum as well.  In short, there is a new pre-print forum coming out for biologically oriented papers called the bioRxiv.  I think it is an excellent opportunity for us theorists to get our work seen by the experimental crowd in our various fields.  Check out my blog post, check out the bioRxiv, and consider putting your work there.

Now... back to our regularly scheduled programming.

Jake

## Wednesday, October 9, 2013

### Accounting for Intrinsic and Extrinsic Randomness in Studying Cancer Cell Population Dynamics

Is cancer growth random and stochastic or ordered and deterministic? Are these ideas mutually exclusive?
Studying the development of malignant tumours, it is important to know and predict the proportions of different cell types in tissue samples. Knowing the expected temporal evolution of the proportion of normal tissue cells, compared to stem-like and non-stem like cancer cells, gives an indication about the progression of the disease and indicates the expected response to interventions with drugs. Such processes have been modeled using Markov processes. An essential step for the simulation of such models is then the determination of state transition probabilities. We here consider the experimentally more realistic scenario in which the measurement of cell population sizes is noisy, leading to a hidden Markov model. In this context, extrinsic randomness is related to noisy measurements, which are used for the estimation of the transition probability matrix. Intrinsic randomness, on the other hand, is here related to the error in estimating the state probability from small cell populations. Using aggregated data of fluorescence-activated cell sorting (FACS) measurement, we develop a minimum mean square error estimator (MMSE) and maximum likelihood (ML) estimator and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes using a transition probability matrix estimated from noisy data. We analyze the properties of two estimators for different noise distributions and prove an optimal solution for Gaussian distributions with the MMSE. Our numerical results show, that for noisy measurements the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach in which measurements are assumed to be noise free.

## Tuesday, October 8, 2013

### Cancer initiation with epistatic interactions between driver and passenger mutations

We investigate the dynamics of cancer initiation in a model with one driver mutation and several passenger mutations. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic background of the cell, in our case on the number of passenger mutations. The passenger mutations themselves have no or only a very small impact on the cell's fitness. This approach is motivated by the Burkitt Lymphoma, where the hallmark mutation, a translocation between the MYC gene and an immunoglobulin gene, alters the rate of apoptosis, but also the proliferation rate of cells. This way we obtain an epistatic fitness landscape, where the fitness of cells with the driver mutation is advantageous only if enough passenger genes have mutated. Otherwise the fitness might even be deleterious. Our analysis is based on an individual cell model in which the cells can divide or undergo apoptosis. In case of division the two daughter cells can mutate. This model shows a very interesting dynamical behavior. Since the driver mutation is deleterious on a background with only a few passenger mutations, there is a long period of stasis in the number of cells until a clone of cells has evolved with enough passenger mutations. Only when the driver mutation occurs in one of those cells, the cell population starts to grow exponentially.

### Global Dormancy of Metastases due to Systemic Inhibition of Angiogenesis

Cancer does not always develop to become a clinically manifest disease. Most of the population actually carries small occult tumors that remain asymptomatic and undetectable. Here, we propose a theoretical study of this phenomenon by defining and simulating a novel mathematical model able to describe the development of a population of tumors at the organism scale. After demonstrating the model can explain experimental data on metastatic development, we go on to test the hypothesis of global dormancy resulting from inhibitory signaling interactions among the tumors. These interactions are targeted against the tumor's vascular support development (angiogenesis), known to be essential for tumor growth, by means of inhibitory molecules released in the circulation. By quantifying their consequences on the establishment of metastases and maintenance of the dormant state, our model shows for the first time how a previously unrecognized phenomenon - systemic inhibition of angiogenesis (SIA) - regulates tumor development. We show SIA alone is not sufficient for global dormancy but can suppress the growth of the total metastatic burden, even to the point of producing an equilibrium state with low and stable total cancerous mass.

Sebastien BenzekryAlberto GandolfiPhilip Hahnfeldt

# A High-Performance Cellular Automaton Model of Tumor Growth with Dynamically Growing Domains

Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but computing performance often counterbalances simplicity. Computationally convenient simulation times can be achieved by choosing appropriate data structures, memory and cell handling as well as domain setup. We propose a cellular automaton model of tumor growth with a domain that expands dynamically as the tumor population increases. We discuss memory access, data structures and implementation techniques that yield high-performance multi-scale Monte Carlo simulations of tumor growth. We present simulation results of the tumor growth model and discuss tumor properties that favor the proposed high-performance design.

## Thursday, September 19, 2013

### A filter-flow perspective of hematogenous metastasis offers a non-genetic paradigm for personalized cancer therapy

This is a rather short paper authored by some of us who maintain Warburg's Lens. The focus is on metastatic spread and how it can be understood from a filter-flow perspective, i.e. how the blood flow and filtration that occurs in capillary beds affects the efficiency of the process. This method builds on the work of Leonard Weiss, who was a leading figure in research into metastatic spread for many years.

Jacob G. Scott, Alexander G. Fletcher, Philip K. Maini, Alexander R. A. Anderson, Philip Gerlee
Research into mechanisms of hematogenous metastasis has largely become genetic in focus, attempting to understand the molecular basis of seed-soil' relationships. Preceding this biological mechanism is the physical process of dissemination of circulating tumour cells (CTCs). We utilize a filter-flow' paradigm to show that assumptions about CTC dynamics strongly affect metastatic efficiency: without data on CTC dynamics, any attempt to predict metastatic spread in individual patients is impossible.

## Tuesday, September 17, 2013

### A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences

In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may be a function of the number of cancer cells. Constant, periodic and impulsive therapies (as well as the non-perturbed system) are investigated both analytically for the general family and, by using the model by Kuznetsov et al. (V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson. Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis. Bulletin of Mathematical Biology 56(2): 295-321, (1994)), via numerical simulations. Simulations seem to show that the shape of the function modeling the therapy is a crucial factor only for very high values of the therapy period $T$, whereas for realistic values of $T$, the eradication of the cancer cells depends on the mean values of the therapy term. Finally, some medical inferences are proposed.

# Mechanical cell-substrate feedback explains pairwise and collective endothelial cell behavior in vitro

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in a extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the mechanisms underlying in vitro angiogenesis are still poorly understood. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and ignore the intermediate organizational levels of the system. Here we show, using a hybrid Cellular Potts and finite-element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation and sprouting from epithelial spheroids. Combining the present, mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.

Arxiv: [PDF

# The Cancer Diaspora: Metastasis beyond the seed and soil hypothesis

Do cancer cells escape their confinement of their original habitat in the primary tumor or are they forced out by ecological changes in their home niche? Describing metastasis in terms of a simple one-way migration of cells from the primary to target organs is an insufficient concept to cover the nuances of cancer spread. A diaspora is the scattering of people away from an established homeland. To date, diaspora has been a uniquely human term utilized by social scientists, however, the application of the diaspora concept to metastasis may yield new biological insights as well as therapeutic paradigms. The diaspora paradigm takes into account and models several variables: the quality of the primary tumor microenvironment, the fitness of individual cancer cell migrants as well as migrant populations, the rate of bidirectional migration of cancer and host cells between cancer sites, and the quality of the target microenvironments to establish metastatic sites. Ecological scientific principles can be applied to the cancer diaspora to develop new therapeutic strategies. For example, ecological traps, habitats that lead to the extinction of a species, can be developed to attract cancer cells to a place where they can be better exposed to treatments or to cells of the immune system for improved antigen presentation. Merging the social science concept of diaspora with ecological and population sciences concepts can inform the cancer field to understand the biology of tumorigenesis and metastasis and inspire new ideas for therapy.

http://arxiv.org/abs/1308.1938

# Spatial evolution of tumors with successive driver mutations

We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor. Each cell division has a chance to give rise to a mutation that activates an additional driver gene. The resulting clone has an enhanced growth rate, which generates a local ensemble of faster growing cells, thereby distorting the spherical shape of the tumor. We derive analytic formulas for the geometric boundary that separates the original cancer clone from the new mutant as well as the expanding frontier of the new mutant. The total number of original cancer cells converges to a constant as time goes to infinity, because this clone becomes enveloped by mutants. We derive formulas for the abundance and diversity of additional driver mutations as function of time. Our model is semi-deterministic: the spatial growth of the various cancer clones follows deterministic equations, but the arrival of a new mutant is a stochastic event.

http://arxiv.org/abs/1308.1564

## Thursday, August 1, 2013

### Reduction of Breast Cancer Relapses with Perioperative Non-Steroidal Anti-Inflammatory Drugs: New Findings and a Review

Reduction of Breast Cancer Relapses with Perioperative Non-Steroidal
Anti-Inflammatory Drugs: New Findings and a Review

Michael Retsky, Romano Demicheli, William JM Hrushesky, Patrice Forget, Marc De Kock, Isaac Gukas, Rick A Rogers, Michael Baum, Vikas Sukhatme and Jayant S Vaidya

Abstract: To explain a bimodal pattern of hazard of relapse among early stage breast cancer patients identified in multiple databases, we proposed that late relapses result from steady stochastic progressions from single dormant malignant cells to avascular micrometastases and then on to growing deposits. However in order to explain early relapses, we had to postulate that something happens at about the time of surgery to provoke sudden exits from dormant phases to active growth
and then to detection. Most relapses in breast cancer are in the early category. Recent data from Forget et al. suggests an unexpected mechanism. They retrospectively studied results from 327 consecutive breast cancer patients comparing various perioperative analgesics and anesthetics in one Belgian hospital and one surgeon. Patients were treated with mastectomy and conventional adjuvant therapy. Relapse hazard updated Sept 2011 are presented. A common Non-Steroidal Anti-Inflammatory Drug (NSAID) analgesic used in surgery produced far superior disease-free survival in the first 5 years
after surgery. The expected prominent early relapse events in months 9-18 are reduced 5-fold. If this observation holds up to further scrutiny, it could mean that the simple use of this safe, inexpensive and effective anti-inflammatory agent at surgery might eliminate early relapses. Transient systemic inflammation accompanying surgery could facilitate angiogenesis of dormant micrometastases, proliferation of dormant single cells, and seeding of circulating cancer stem cells (perhaps in part released from bone marrow) resulting in early relapse and could have been effectively blocked by the perioperative anti-inflammatory agent.

While this paper is not currently available on a server, the author is happy to provide them to interested parties.  If interested, contact Michael Retsky at:
michael.retsky@gmail.com

## Monday, July 29, 2013

### Edge effects in game theoretic dynamics of spatially structured tumours

Edge effects in game theoretic dynamics of spatially structured tumours

Authors: +Artem Kaznatcheev , +Jacob Scott and +David Basanta

Abstract:
Evolutionary game theory has been used to model many situations in ecology
where different species, or different phenotypes within one species, compete
against one another. Of late, this has extended to cancer biology to understand
the dynamics of disease progression as a game between competing cellular
phenotypes. A major assumption in this modeling paradigm is that the population
is inviscid: the probability of a player with a given phenotypic strategy
interacting with another depends exclusively on the respective abundance of
those strategies in the population. While there are scenarios where this
assumption might be useful, in solid tumours, where the populations have
spatial structure, this assumption can yield misleading results. In this study
we use a recently developed mathematical tool, the Ohtsuki-Nowak transform, to
study the effect of interaction neighborhood size on a canonical evolutionary
cancer game: go vs. grow. We show that spatial structure promotes invasive (go)
strategy. By considering the change in neighbourhood size at a boundary we show
an edge effect in solid tumours. This edge effect allows a tumour with no
invasive phenotypes expressed internally to have a polyclonal boundary with
both invasive and non-invasive cells. We focus on evolutionary game dynamics
between competing cancer cells, but we anticipate that our approach can be
extended to games between other types of players where interaction
neighborhoods change at the system boundary.

## Natural selection increases mutational robustness in complex diseases: Mendelian evidence from early versus late onset common diseases

Author: Bora E. Baysal

Background. Natural selection operates on genetically influenced phenotypic variations that confer differential survival or reproductive advantages. Common diseases are frequently associated with increased mortality and disability and complex heritable factors play an important role in their pathogenesis. Hence, common diseases should trigger the process of natural selection with subsequent population genetic response. However, empirical impact of natural selection on genetics of complex diseases is poorly understood. In this paper, I hypothesize that negative selection of diseased individuals leads to systemic genetic differences between common diseases that primarily occur before or during the reproductive years (early onset) and those that occur after the reproductive years (late onset).
Methods. To test this hypothesis, a comprehensive literature survey of highly penetrant (80% or more) nonpleiotropic, nonsyndromic susceptibility genes (hereafter defined as Mendelian phenocopies) was completed for early versus late onset common diseases, organized using the World Health Organization (WHO) ICD-10 classification scheme. An average age at sporadic disease onset of 30 years was selected for dividing early versus late onset common diseases.
Results. Mendelian phenocopies were identified for 16 primarily late onset common diseases from 9 distinct WHO diagnostic categories. Late onset common diseases with Mendelian phenocopies include papillary renal carcinoma, obesity, Alzheimer disease, Parkinson disease, frontotemporal dementia, amyotrophic lateral sclerosis, primary open angle glaucoma, age-related hearing loss, coronary artery disease, stroke, pancreatitis, thrombotic thrombocytopenic purpura, systemic lupus erythematosus, inclusion body myositis, Paget's disease of bone and focal segmental glomerulosclerosis (steroid resistant). In contrast, no Mendelian phenocopy was found for any primarily early onset common disease (p<5.8x10-4). Thus, highly predictive rare variants are present for a subset of late onset common diseases, but not for early onset common diseases.
Discussion. These findings suggest that genetic architecture of early onset common diseases is more robust against the phenotypic expression of highly penetrant predisposing mutations than is the case for late onset common diseases. The primary candidate for increased genetic robustness in early onset common diseases is proposed to be natural selection.

# Forecasts of Cancer and Chronic Patients: Big Data Metrics of Population Health

Chronic diseases and cancer account for over 75 percent of healthcare costs in the US. Increased prevention services and improved primary care are thought to decrease costs. Current models for detecting changes in the health of populations are cumbersome and expensive, and are not sensitive in the short term. In this paper we model population health as a dynamical system to predict the time evolution of the new diagnosis of chronic diseases and cancer. This provides a reliable forecasting tool and a means of measuring short-term changes in the health status of the population resulting from preventive care programs. Twelve month forecasts of cancer and chronic populations were accurate with errors lying between 3 percent and 6 percent. We confirmed what other studies have demonstrated that diabetes patients are at increased cancer risk but, interestingly, we also discovered that all of the studied chronic conditions increased cancer risk just as diabetes did, and by a similar amount. The model(i)yields a new metric for measuring performance of preventive and clinical care programs that can provide timely feedback for quality improvement programs;(ii)helps understand "savings" in the context of preventive care programs and explains how they can be calculated in the short term, even though they materialize only in the long term and(iii)provides an analytic tool and metrics to infer correlations and derive insights on the effect of changes in socio-economic factors affecting population health on improving health and lowering costs of populations.

## Tuesday, July 9, 2013

### Morphological instabilities of stratified epithelia: a mechanical instability in tumour formation

This paper presents biomechanical considerations in tumor formation and metastasis. I wonder how results obtained from such analyses can be addressed experimentally.

# Morphological instabilities of stratified epithelia: a mechanical instability in tumour formation

Interfaces between stratified epithelia and their supporting stromas commonly exhibit irregular shapes. Undulations are particularly pronounced in dysplastic tissues and typically evolve into long, finger-like protrusions in carcinomas. In a previous work (Basan et al., Phys. Rev. Lett. 106, 158101 (2011)), we demonstrated that an instability arising from viscous shear stresses caused by the constant flow due to cell turnover in the epithelium could drive this phenomenon. While interfacial tension between the two tissues as well as mechanical resistance of the stroma tend to maintain a flat interface, an instability occurs for sufficiently large viscosity, cell-division rate and thickness of the dividing region in the epithelium. Here, extensions of this work are presented, where cell division in the epithelium is coupled to the local concentration of nutrients or growth factors diffusing from the stroma. This enhances the instability by a mechanism similar to that of the Mullins-Sekerka instability in single-diffusion processes of crystal growth. We furthermore present the instability for the generalized case of a viscoelastic stroma.

# The waiting time for a second mutation: an alternative to the Moran model

The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the distribution of the waiting time for a second mutation. This models the time of appearance of the first cancerous cell in a tissue. Our model is an alternative to the Moran model with mutations.

## Friday, June 28, 2013

### Quantitative Analysis of the Tumor/Metastasis System and its Optimal Therapeutic Control

This preprint presents a model which looks like a merge of two previous models on different biological scales: one is a tumour growth model by Hahnfeldt et al. the other is a model of metastatic spread in terms of a transport equation originally formulated by Iwata et al. With this new model the authors investigate the efficacy of different schedules for chemotherapy.

# Quantitative Analysis of the Tumor/Metastasis System and its Optimal Therapeutic Control

Sebastien Benzekry (CCSB, INRIA Bordeaux - Sud-Ouest), Dominique Barbolosi (CRO2), Assia Benabdallah (LATP), Florence Hubert (LATP), Philip Hahnfeldt (CCSB)
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments (cytotoxic or anti-angiogenic), in monotherapy or in combination. Quantification of the effect of surgery on the size distribution of metastatic colonies is derived. For systemic therapies, emphasis is placed on the differences between the treatment of an isolated lesion and a population of metastases. Combination therapy is addressed, in particular the problem of the drugs administration sequence. Theoretical optimal schedules are derived that show the superiority of a metronomic administration scheme (defined as a continuous administration of a given amount of drug spread during the whole therapeutic cycle) on a classical Maximum Tolerated Dose scheme (where the dose is given as a few concentrated administrations at the beginning of the cycle), for the total metastatic burden in the organism.

## Tuesday, June 25, 2013

### Maximum Tolerated Dose Versus Metronomic Scheduling in the Treatment of Metastatic Cancers

This paper was posted to the arxiv along with another paper, titled

The authors are clearly interested in the implications of optimal control in the metastatic setting. The paper below leaves me wondering from an evolutionary selection point of view, if metronomic therapy is actually increasing the probability of metastasis.

## Maximum Tolerated Dose Versus Metronomic Scheduling in the Treatment of Metastatic Cancers

Authors
Sébastien Benzekry, Philip Hahnfeldt

Abstract

Although optimal control theory has been used for the theoretical study of anticancerous drugs scheduling optimization,with the aim of reducing the primary tumor volume, the effect on metastases is often ignored. Here, we use a previously published model for metastatic development to define an optimal control problem at the scale of the entire organism of the patient. In silico study of the impact of different scheduling strategies for anti-angiogenic and cytotoxic agents (either in monotherapy or in combination) is performed to compare a low-dose, continuous, metronomic administration scheme with a more classical maximum tolerated dose schedule. Simulation results reveal differences between primary tumor reduction and control of metastases but overall suggest use of the metronomic protocol.

# Moderate stem cell telomere shortening rate postpones cancer onset in stochastic model

Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and, when they reach a critical length, the cell will enter permanent cell cycle arrest - a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably.
Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer free life span before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favour a shorter than optimal average cancer free life span in order to postpone cancer onset until late in life.

# Phylogenetic quantification of intra-tumour heterogeneity

Background: Intra-tumour heterogeneity (ITH) is the result of ongoing evolutionary change within each cancer. The expansion of genetically distinct sub-clonal populations may explain the emergence of drug resistance and if so would have prognostic and predictive utility. However, methods for objectively quantifying ITH have been missing and are particularly difficult to establish in cancers where predominant copy number variation prevents accurate phylogenetic reconstruction owing to horizontal dependencies caused by long and cascading genomic rearrangements.
Results: To address these challenges we present MEDICC, a method for phylogenetic reconstruction and ITH quantification based on a Minimum Event Distance for Intra-tumour Copynumber Comparisons. Using a transducer-based pairwise comparison function we determine optimal phasing of major and minor alleles, as well as evolutionary distances between samples, and are able to reconstruct ancestral genomes. Rigorous simulations and an extensive clinical study show the power of our method, which outperforms state-of-the-art competitors in reconstruction accuracy and additionally allows unbiased numerical quantification of ITH.
Conclusions: Accurate quantification and evolutionary inference are essential to understand the functional consequences of ITH. The MEDICC algorithms are independent of the experimental techniques used and are applicable to both next-generation sequencing and array CGH data.

# Adaptation and learning of molecular networks as a description of cancer development at the systems-level: Potential use in anti-cancer therapies

There is a widening recognition that cancer cells are products of complex developmental processes. Carcinogenesis and metastasis formation are increasingly described as systems-level, network phenomena. Here we propose that malignant transformation is a two-phase process, where an initial increase of system plasticity is followed by a decrease of plasticity at late stages of carcinogenesis as a model of cellular learning. We describe the hallmarks of increased system plasticity of early, tumor initiating cells, such as increased noise, entropy, conformational and phenotypic plasticity, physical deformability, cell heterogeneity and network rearrangements. Finally, we argue that the large structural changes of molecular networks during cancer development necessitate a rather different targeting strategy in early and late phase of carcinogenesis. Plastic networks of early phase cancer development need a central hit, while rigid networks of late stage primary tumors or established metastases should be attacked by the network influence strategy, such as by edgetic, multi-target, or allo-network drugs. Cancer stem cells need special diagnosis and targeting, since their dormant and rapidly proliferating forms may have more rigid, or more plastic networks, respectively. The extremely high ability to change their rigidity/plasticity may be a key differentiating hallmark of cancer stem cells. The application of early stage-optimized anti-cancer drugs to late-stage patients may be a reason of many failures in anti-cancer therapies. Our hypotheses presented here underlie the need for patient-specific multi-target therapies applying the correct ratio of central hits and network influences -- in an optimized sequence.

## Thursday, June 13, 2013

### The time-evolution of DCIS size distributions with applications to breast cancer growth and progression

This paper looks at the growth dynamics of ductal carcinoma in situ (DCIS) in the breast, but instead of focusing on the dynamics of a single tumour the authors derive an equation for the size distribution of DCIS across an entire population. The equation for the size distribution has a stationary solution, and by comparing the analytical expression with data from mammographic screening the parameters of the growth model were estimated.

# The time-evolution of DCIS size distributions with applications to breast cancer growth and progression

Ductal carcinoma {\em in situ} (DCIS) lesions are non-invasive tumours of the breast which are thought to precede most invasive breast cancers (IBC). As individual DCIS lesions are initiated, grow and invade (i.e. become IBC) the size distribution of the DCIS lesions present in a given human population will evolve. We derive a differential equation governing this evolution and show, for given assumptions about growth and invasion, that there is a unique distribution which does not vary with time. Further, we show that any initial distribution converges to this stationary distribution exponentially quickly. It is therefore reasonable to assume that the stationary distribution governs the size of DCIS lesions in human populations which are relatively stable with respect to the determinants of breast cancer. Based on this assumption and the size data of 110 DCIS lesions detected in a mammographic screening program between 1993 and 2000, we produce maximum likelihood estimates for certain growth and invasion parameters. Assuming that DCIS size is proportional to a positive power $p$ of the time since tumour initiation, we estimate $p$ to be 0.50 with a 95% confidence interval of $(0.35, 0.71)$. Therefore we estimate that DCIS lesions follow a square-root growth law and hence that they grow rapidly when small and relatively slowly when large. Our approach and results should be useful for other mathematical studies of cancer, especially those investigating biological mechanisms of invasion.