Comparative analysis of the spatial distribution of brain metastases across several primary cancers using machine learning and deep learning models.

OBJECTIVE: Brain metastases (BM) are associated with poor prognosis and increased mortality rates, making them a significant clinical challenge. Studying BMs can aid in improving early detection and monitoring. Systematic comparisons of anatomical distributions of BM from different primary cancers, however, remain largely unavailable. METHODS: To test the hypothesis that anatomical BM distributions differ based on primary cancer type, we analyze the spatial coordinates of BMs for five different primary cancer types along principal component (PC) axes. The dataset includes 3949 intracranial metastases, labeled by primary cancer types and with six features. We employ PC coordinates to highlight the distinctions between various cancer types. We utilized different Machine Learning (ML) algorithms (RF, SVM, TabNet DL) models to establish the relationship between primary cancer diagnosis, spatial coordinates of BMs, age, and target volume. RESULTS: Our findings revealed that PC1 aligns most with the Y axis, followed by the Z axis, and has minimal correlation with the X axis. Based on PC1 versus PC2 plots, we identified notable differences in anatomical spreading patterns between Breast and Lung cancer, as well as Breast and Renal cancer. In contrast, Renal and Lung cancer, as well as Lung and Melanoma, showed similar patterns. Our ML and DL results demonstrated high accuracy in distinguishing BM distribution for different primary cancers, with the SVM algorithm achieving 97% accuracy using a polynomial kernel and TabNet achieving 96%. The RF algorithm ranked PC1 as the most important discriminating feature. CONCLUSIONS: In summary, our results support accurate multiclass ML classification regarding brain metastases distribution.

A quantitative characterization of the spatial distribution of brain metastases from breast cancer and respective molecular subtypes.

PURPOSE: Brain metastases (BM) remain a significant cause of morbidity and mortality in breast cancer (BC) patients. Specific factors promoting the process of BM and predilection for selected neuro-anatomical regions remain unknown, yet may have major implications for prevention or treatment. Anatomical spatial distributions of BM from BC suggest a predominance of metastases in the hindbrain and cerebellum. Systematic approaches to quantifying BM location or location-based analyses based on molecular subtypes, however, remain largely unavailable. METHODS: We analyzed stereotactic Cartesian coordinates derived from 134 patients undergoing gamma- knife radiosurgery (GKRS) for treatment of 407 breast cancer BMs to quantitatively study BM spatial distribution along principal component axes and by intrinsic molecular subtype (ER, PR, Herceptin). We used kernel density estimators (KDE) to highlight clustering and distribution regions in the brain, and we used the metric of mutual information (MI) to tease out subtle differences in the BM distributions associated with different molecular subtypes of BC. BM location maps according to vascular and anatomical distributions using Cartesian coordinates to aid in systematic classification of tumor locations were additionally developed. RESULTS: We corroborated that BC BMs show a consistent propensity to arise posteriorly and caudally, and that Her2+ tumors are relatively more likely to arise medially rather than laterally. To compare the distributions among varying BC molecular subtypes, the mutual information metric reveal that the ER-PR-Her2+ and ER-PR-Her2- subtypes show the smallest amount of mutual information and are most molecularly distinct. The kernel density contour plots show a propensity for triple negative BC to arise in more superiorly or cranially situated BMs. CONCLUSIONS: We present a novel and shareable workflow for characterizing and comparing spatial distributions of BM which may aid in identifying therapeutic or diagnostic targets and interactions with the tumor microenvironment. Further characterization of these patterns with larger multi-institutional data-sets may have major impacts on treatment or management of cancer patients.

Prediction of Metastatic Patterns in Bladder Cancer: Spatiotemporal Progression and Development of a Novel, Web-based Platform for Clinical Utility.

BACKGROUND: Bladder cancer (BCa), the sixth commonest cancer in the USA, is highly lethal when metastatic. Spatial and temporal patterns of patient-specific metastatic spread are deemed random and unpredictable. Whether BCa metastatic patterns can be quantified and predicted more accurately is unknown. OBJECTIVE: To develop a web-based calculator for forecasting metastatic progression in individual BCa patients. DESIGN SETTING AND PARTICIPANTS: We used a prospectively collected longitudinal dataset of 3503 BCa patients who underwent a radical cystectomy following diagnosis and were enrolled continuously. We subdivided patients by their pathologic subgroup stages of organ confined (OC), extravesical (EV), and node positive (N+). We illustrated metastatic pathway progression using color-coded, circular, tree ring diagrams. We created a dynamical, data-visualization, web-based platform that displays temporal, spatial, and Markov modeling figures with predictive capability. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: Patients underwent history and physical examination, serum studies, and liver function tests. Surveillance follow-up included computed tomography scans, chest x-rays, and radiographic evaluation of the reservoir and upper tracts, with bone scans performed only if clinically indicated. Outcomes were measured by time to clinical recurrence and overall or progression-free survival. RESULTS AND LIMITATIONS: Metastases developed in 29% of patients (n = 812; median follow-up 15.3 yr), with 5-yr overall survival of 20.2%, compared with 78.6% in those without metastases (n = 1983; median follow-up 10.9 yr). The three commonest sites of spread at the time of first progression were bone (n = 214; 26.4%), pelvis (n = 194; 23.9%), and lung (n = 194; 23.9%). The order and frequency of these sites vary when divided by pathologic subgroup stages of OC (lung [n = 65; 25.1%], urethra [n = 45; 17.4%], and bone [n = 29; 11.2%]), EV (pelvis [n = 63; 33.0%], bone [n = 45; 23.6%], and lung [n = 29; 15.2%]), and N+ (bone [n = 111; 30.7%], retroperitoneum [n = 70; 19.3%], and pelvis [n = 60; 16.6%]). Markov chain modeling indicated a higher probability of spread from bladder to bone (15.5%), pelvis (14.7%), and lung (14.2%). CONCLUSIONS: Our web-based calculator allows real-time analyses in the clinic based on individual patient-specific demographic and cancer data elements. For contrasting subgroups, the models indicated differences in Markov transition probabilities. Spatiotemporal patterns of BCa metastasis and sites of spread indicated underlying organotropic mechanisms in the prediction of response. This recognition opens the possibility of organ site-specific therapeutic targeting in the oligometastatic BCa setting. In the precision medicine era, visualization of complex, time-resolved clinical data will enhance management of postoperative metastatic BCa patients. PATIENT SUMMARY: We developed a web-based calculator to forecast metastatic progression for individual bladder cancer (BCa) patients, based on the clinical and demographic information obtained at diagnosis. This can help in predicting disease status and survival, and improving management in postoperative metastatic BCa patients. TAKE HOME MESSAGE: Future pathways of metastatic progression for individual bladder cancer patients can be determined based on currently available clinical and demographic information obtained at diagnosis. In focused subgroups of patients, these metastatic spread patterns can also portend disease status and survival.

Are Adaptive Chemotherapy Schedules Robust? A Three-Strategy Stochastic Evolutionary Game Theory Model.

We investigate the robustness of adaptive chemotherapy schedules over repeated cycles and a wide range of tumor sizes. Using a non-stationary stochastic three-component fitness-dependent Moran process model (to track frequencies), we quantify the variance of the response to treatment associated with multidrug adaptive schedules that are designed to mitigate chemotherapeutic resistance in an idealized (well-mixed) setting. The finite cell (N tumor cells) stochastic process consists of populations of chemosensitive cells, chemoresistant cells to drug 1, and chemoresistant cells to drug 2, and the drug interactions can be synergistic, additive, or antagonistic. Tumor growth rates in this model are proportional to the average fitness of the tumor as measured by the three populations of cancer cells compared to a background microenvironment average value. An adaptive chemoschedule is determined by using the N→∞ limit of the finite-cell process (i.e., the adjusted replicator equations) which is constructed by finding closed treatment response loops (which we call evolutionary cycles) in the three component phase-space. The schedules that give rise to these cycles are designed to manage chemoresistance by avoiding competitive release of the resistant cell populations. To address the question of how these cycles perform in practice over large patient populations with tumors across a range of sizes, we consider the variances associated with the approximate stochastic cycles for finite N, repeating the idealized adaptive schedule over multiple periods. For finite cell populations, the distributions remain approximately multi-Gaussian in the principal component coordinates through the first three cycles, with variances increasing exponentially with each cycle. As the number of cycles increases, the multi-Gaussian nature of the distribution breaks down due to the fact that one of the three sub-populations typically saturates the tumor (competitive release) resulting in treatment failure. This suggests that to design an effective and repeatable adaptive chemoschedule in practice will require a highly accurate tumor model and accurate measurements of the sub-population frequencies or the errors will quickly (exponentially) degrade its effectiveness, particularly when the drug interactions are synergistic. Possible ways to extend the efficacy of the stochastic cycles in light of the computational simulations are discussed.

Use of Wearable Activity Tracker in Patients With Cancer Undergoing Chemotherapy: Toward Evaluating Risk of Unplanned Health Care Encounters.

PURPOSE: Unplanned health care encounters (UHEs) such as emergency room visits can occur commonly during cancer chemotherapy treatments. Patients at an increased risk of UHEs are typically identified by clinicians using performance status (PS) assessments based on a descriptive scale, such as the Eastern Cooperative Oncology Group (ECOG) scale. Such assessments can be bias prone, resulting in PS score disagreements between assessors. We therefore propose to evaluate PS using physical activity measurements (eg, energy expenditure) from wearable activity trackers. Specifically, we examined the feasibility of using a wristband (band) and a smartphone app for PS assessments. METHODS: We conducted an observational study on a cohort of patients with solid tumor receiving highly emetogenic chemotherapy. Patients were instructed to wear the band for a 60-day activity-tracking period. During clinic visits, we obtained ECOG scores assessed by physicians, coordinators, and patients themselves. UHEs occurring during the activity-tracking period plus a 90-day follow-up period were later compiled. We defined our primary outcome as the percentage of patients adherent to band-wear ≥ 80% of 10 am to 8 pm for ≥ 80% of the activity-tracking period. In an exploratory analysis, we computed hourly metabolic equivalent of task (MET) and counted 10 am to 8 pm hours with > 1.5 METs as nonsedentary physical activity hours. RESULTS: Forty-one patients completed the study (56.1% female; 61.0% age 40-60 years); 68% were adherent to band-wear. ECOG score disagreement between assessors ranged from 35.3% to 50.0%. In our exploratory analysis, lower average METs and nonsedentary hours, but not higher ECOG scores, were associated with higher 150-day UHEs. CONCLUSION: The use of a wearable activity tracker is generally feasible in a similar population of patients with cancer. A larger randomized controlled trial should be conducted to confirm the association between lower nonsedentary hours and higher UHEs.

Quantified Kinematics to Evaluate Patient Chemotherapy Risks in Clinic.

PURPOSE: Performance status (PS) is a key factor in oncologic decision making, but conventional scales used to measure PS vary among observers. Consumer-grade biometric sensors have previously been identified as objective alternatives to the assessment of PS. Here, we investigate how one such biometric sensor can be used during a clinic visit to identify patients who are at risk for complications, particularly unexpected hospitalizations that may delay treatment or result in low physical activity. We aim to provide a novel and objective means of predicting tolerability to chemotherapy. METHODS: Thirty-eight patients across three centers in the United States who were diagnosed with a solid tumor with plans for treatment with two cycles of highly emetogenic chemotherapy were included in this single-arm, observational prospective study. A noninvasive motion-capture system quantified patient movement from chair to table and during the get-up-and-walk test. Activity levels were recorded using a wearable sensor over a 2-month period. Changes in kinematics from two motion-capture data points pre- and post-treatment were tested for correlation with unexpected hospitalizations and physical activity levels as measured by a wearable activity sensor. RESULTS: Among 38 patients (mean age, 48.3 years; 53% female), kinematic features from chair to table were the best predictors for unexpected health care encounters (area under the curve, 0.775 ± 0.029) and physical activity (area under the curve, 0.830 ± 0.080). Chair-to-table acceleration of the nonpivoting knee (t = 3.39; P = .002) was most correlated with unexpected health care encounters. Get-up-and-walk kinematics were most correlated with physical activity, particularly the right knee acceleration (t = -2.95; P = .006) and left arm angular velocity (t = -2.4; P = .025). CONCLUSION: Chair-to-table kinematics are good predictors of unexpected hospitalizations, whereas the get-up-and-walk kinematics are good predictors of low physical activity.

OrgDyn: feature- and model-based characterization of spatial and temporal organoid dynamics.

SUMMARY: Organoid model systems recapitulate key features of mammalian tissues and enable high throughput experiments. However, the impact of these experiments may be limited by manual, non-standardized, static or qualitative phenotypic analysis. OrgDyn is an open-source and modular pipeline to quantify organoid shape dynamics using a combination of feature- and model-based approaches on time series of 2D organoid contour images. Our pipeline consists of (i) geometrical and signal processing feature extraction, (ii) dimensionality reduction to differentiate dynamical paths, (iii) time series clustering to identify coherent groups of organoids and (iv) dynamical modeling using point distribution models to explain temporal shape variation. OrgDyn can characterize, cluster and model differences among unique dynamical paths that define diverse final shapes, thus enabling quantitative analysis of the molecular basis of tissue development and disease. AVAILABILITY AND IMPLEMENTATION: https://github.com/zakih/organoidDynamics (BSD 3-Clause License). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Towards Multidrug Adaptive Therapy.

A new ecologically inspired paradigm in cancer treatment known as "adaptive therapy" capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent "cycles" of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary "absorbing region" reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy. SIGNIFICANCE: Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.

Prediction of Bone Metastasis in Inflammatory Breast Cancer Using a Markov Chain Model.

BACKGROUND: Inflammatory breast cancer (IBC) is a rare yet aggressive variant of breast cancer with a high recurrence rate. We hypothesized that patterns of metastasis differ between IBC and non-IBC. We focused on the patterns of bone metastasis throughout disease progression to determine statistical differences that can lead to clinically relevant outcomes. Our primary outcome of this study is to quantify and describe this difference with a view to applying the findings to clinically relevant outcomes for patients. SUBJECTS, MATERIALS, AND METHODS: We retrospectively collected data of patients with nonmetastatic IBC (n = 299) and non-IBC (n = 3,436). Probabilities of future site-specific metastases were calculated. Spread patterns were visualized to quantify the most probable metastatic pathways of progression and to categorize spread pattern based on their propensity to subsequent dissemination of cancer. RESULTS: In patients with IBC, the probabilities of developing bone metastasis after chest wall, lung, or liver metastasis as the first site of progression were high: 28%, 21%, and 21%, respectively. For patients with non-IBC, the probability of developing bone metastasis was fairly consistent regardless of initial metastasis site. CONCLUSION: Metastatic patterns of spread differ between patients with IBC and non-IBC. Selection of patients with IBC with known liver, chest wall, and/or lung metastasis would create a population in whom to investigate effective methods for preventing future bone metastasis. IMPLICATIONS FOR PRACTICE: This study demonstrated that the patterns of metastasis leading to and following bone metastasis differ significantly between patients with inflammatory breast cancer (IBC) and those with non-IBC. Patients with IBC had a progression pattern that tended toward the development of bone metastasis if they had previously developed metastases in the liver, chest wall, and lung, rather than in other sites. Selection of patients with IBC with known liver, chest wall, and/or lung metastasis would create a population in whom to investigate effective methods for preventing future bone metastasis.

Machine learning models for predicting post-cystectomy recurrence and survival in bladder cancer patients.

Currently in patients with bladder cancer, various clinical evaluations (imaging, operative findings at transurethral resection and radical cystectomy, pathology) are collectively used to determine disease status and prognosis, and recommend neoadjuvant, definitive and adjuvant treatments. We analyze the predictive power of these measurements in forecasting two key long-term outcomes following radical cystectomy, i.e., cancer recurrence and survival. Information theory and machine learning algorithms are employed to create predictive models using a large prospective, continuously collected, temporally resolved, primary bladder cancer dataset comprised of 3503 patients (1971-2016). Patient recurrence and survival one, three, and five years after cystectomy can be predicted with greater than 70% sensitivity and specificity. Such predictions may inform patient monitoring schedules and post-cystectomy treatments. The machine learning models provide a benchmark for predicting oncologic outcomes in patients undergoing radical cystectomy and highlight opportunities for improving care using optimal preoperative and operative data collection.

Cellular interactions constrain tumor growth.

A tumor is made up of a heterogeneous collection of cell types, all competing on a fitness landscape mediated by microenvironmental conditions that dictate their interactions. Despite the fact that much is known about cell signaling, cellular cooperation, and the functional constraints that affect cellular behavior, the specifics of how these constraints (and the range over which they act) affect the macroscopic tumor growth laws that govern total volume, mass, and carrying capacity remain poorly understood. We develop a statistical mechanics approach that focuses on the total number of possible states each cell can occupy and show how different assumptions on correlations of these states give rise to the many different macroscopic tumor growth laws used in the literature. Although it is widely understood that molecular and cellular heterogeneity within a tumor is a driver of growth, here we emphasize that focusing on the functional coupling of states at the cellular level is what determines macroscopic growth characteristics.

Capitalizing on competition: An evolutionary model of competitive release in metastatic castration resistant prostate cancer treatment.

The development of chemotherapeutic resistance resulting in tumor relapse is largely the consequence of the mechanism of competitive release of pre-existing resistant tumor cells selected for regrowth after chemotherapeutic agents attack the previously dominant chemo-sensitive population. We introduce a prisoner's dilemma game theoretic mathematical model based on the replicator of three competing cell populations: healthy (cooperators), sensitive (defectors), and resistant (defectors) cells. The model is shown to recapitulate prostate-specific antigen measurement data from three clinical trials for metastatic castration-resistant prostate cancer patients treated with 1) prednisone, 2) mitoxantrone and prednisone and 3) docetaxel and prednisone. Continuous maximum tolerated dose schedules reduce the sensitive cell population, initially shrinking tumor burden, but subsequently "release" the resistant cells from competition to re-populate and re-grow the tumor in a resistant form. The evolutionary model allows us to quantify responses to conventional (continuous) therapeutic strategies as well as to design adaptive strategies.These novel adaptive strategies are robust to small perturbations in timing and extend simulated time to relapse from continuous therapy administration.

Low-dimensional dynamical characterization of human performance of cancer patients using motion data.

BACKGROUND: Biomechanical characterization of human performance with respect to fatigue and fitness is relevant in many settings, however is usually limited to either fully qualitative assessments or invasive methods which require a significant experimental setup consisting of numerous sensors, force plates, and motion detectors. Qualitative assessments are difficult to standardize due to their intrinsic subjective nature, on the other hand, invasive methods provide reliable metrics but are not feasible for large scale applications. METHODS: Presented here is a dynamical toolset for detecting performance groups using a non-invasive system based on the Microsoft Kinect motion capture sensor, and a case study of 37 cancer patients performing two clinically monitored tasks before and after therapy regimens. Dynamical features are extracted from the motion time series data and evaluated based on their ability to i) cluster patients into coherent fitness groups using unsupervised learning algorithms and to ii) predict Eastern Cooperative Oncology Group performance status via supervised learning. FINDINGS: The unsupervised patient clustering is comparable to clustering based on physician assigned Eastern Cooperative Oncology Group status in that they both have similar concordance with change in weight before and after therapy as well as unexpected hospitalizations throughout the study. The extracted dynamical features can predict physician, coordinator, and patient Eastern Cooperative Oncology Group status with an accuracy of approximately 80%. INTERPRETATION: The non-invasive Microsoft Kinect sensor and the proposed dynamical toolset comprised of data preprocessing, feature extraction, dimensionality reduction, and machine learning offers a low-cost and general method for performance segregation and can complement existing qualitative clinical assessments.

Chemotherapeutic Dose Scheduling Based on Tumor Growth Rates Provides a Case for Low-Dose Metronomic High-Entropy Therapies.

We extended the classical tumor regression models such as Skipper's laws and the Norton-Simon hypothesis from instantaneous regression rates to the cumulative effect over repeated cycles of chemotherapy. To achieve this end, we used a stochastic Moran process model of tumor cell kinetics coupled with a prisoner's dilemma game-theoretic cell-cell interaction model to design chemotherapeutic strategies tailored to different tumor growth characteristics. Using the Shannon entropy as a novel tool to quantify the success of dosing strategies, we contrasted MTD strategies as compared with low-dose, high-density metronomic strategies (LDM) for tumors with different growth rates. Our results show that LDM strategies outperformed MTD strategies in total tumor cell reduction. This advantage was magnified for fast-growing tumors that thrive on long periods of unhindered growth without chemotherapy drugs present and was not evident after a single cycle of chemotherapy but grew after each subsequent cycle of repeated chemotherapy. The evolutionary growth/regression model introduced in this article agrees well with murine models. Overall, this model supports the concept of designing different chemotherapeutic schedules for tumors with different growth rates and develops quantitative tools to optimize these schedules for maintaining low-volume tumors. Cancer Res; 77(23); 6717-28. ©2017 AACR.

Development of metastatic brain disease involves progression through lung metastases in EGFR mutated non-small cell lung cancer.

Lung cancer is often classified by the presence of oncogenic drivers, such as epidermal growth factor receptor (EGFR), rather than patterns of anatomical distribution. While metastatic spread may seem a random and unpredictable process, we explored the possibility of using its quantifiable nature as a measure of describing and comparing different subsets of disease. We constructed a database of 664 non-small cell lung cancer (NSCLC) patients treated at the University of Southern California Norris Comprehensive Cancer Center and the Los Angeles County Medical Center. Markov mathematical modeling was employed to assess metastatic sites in a spatiotemporal manner through every time point in progression of disease. Our findings identified a preferential pattern of primary lung disease progressing through lung metastases to the brain amongst EGFR mutated (EGFR m) NSCLC patients, with exon 19 deletions or exon 21 L858R mutations, as compared to EGFR wild type (EGFR wt). The brain was classified as an anatomic "sponge", with a higher ratio of incoming to outgoing spread, for EGFR m NSCLC. Bone metastases were more commonly identified in EGFR wt patients. Our study supports a link between the anatomical and molecular characterization of lung metastatic cancer. Improved understanding of the differential biology that drives discordant patterns of anatomic spread, based on genotype specific profiling, has the potential to improve personalized oncologic care.

The prisoner's dilemma as a cancer model.

Tumor development is an evolutionary process in which a heterogeneous population of cells with different growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to recreate some of the emergent features of such a developing complex ecosystem? What is a tumor doing before we can detect it? We outline a mathematical model, driven by a stochastic Moran process, in which cancer cells and healthy cells compete for dominance in the population. Each are assigned payoffs according to a Prisoner's Dilemma evolutionary game where the healthy cells are the cooperators and the cancer cells are the defectors. With point mutational dynamics, heredity, and a fitness landscape controlling birth and death rates, natural selection acts on the cell population and simulated 'cancer-like' features emerge, such as Gompertzian tumor growth driven by heterogeneity, the log-kill law which (linearly) relates therapeutic dose density to the (log) probability of cancer cell survival, and the Norton-Simon hypothesis which (linearly) relates tumor regression rates to tumor growth rates. We highlight the utility, clarity, and power that such models provide, despite (and because of) their simplicity and built-in assumptions.

AN EVOLUTIONARY MODEL OF TUMOR CELL KINETICS AND THE EMERGENCE OF MOLECULAR HETEROGENEITY DRIVING GOMPERTZIAN GROWTH.

We describe a cell-molecular based evolutionary mathematical model of tumor development driven by a stochastic Moran birth-death process. The cells in the tumor carry molecular information in the form of a numerical genome which we represent as a four-digit binary string used to differentiate cells into 16 molecular types. The binary string is able to undergo stochastic point mutations that are passed to a daughter cell after each birth event. The value of the binary string determines the cell fitness, with lower fit cells (e.g. 0000) defined as healthy phenotypes, and higher fit cells (e.g. 1111) defined as malignant phenotypes. At each step of the birth-death process, the two phenotypic sub-populations compete in a prisoner's dilemma evolutionary game with the healthy cells playing the role of cooperators, and the cancer cells playing the role of defectors. Fitness, birth-death rates of the cell populations, and overall tumor fitness are defined via the prisoner's dilemma payoff matrix. Mutation parameters include passenger mutations (mutations conferring no fitness advantage) and driver mutations (mutations which increase cell fitness). The model is used to explore key emergent features associated with tumor development, including tumor growth rates as it relates to intratumor molecular heterogeneity. The tumor growth equation states that the growth rate is proportional to the logarithm of cellular diversity/heterogeneity. The Shannon entropy from information theory is used as a quantitative measure of heterogeneity and tumor complexity based on the distribution of the 4-digit binary sequences produced by the cell population. To track the development of heterogeneity from an initial population of healthy cells (0000), we use dynamic phylogenetic trees which show clonal and sub-clonal expansions of cancer cell sub-populations from an initial malignant cell. We show tumor growth rates are not constant throughout tumor development, and are generally much higher in the subclinical range than in later stages of development, which leads to a Gompertzian growth curve. We explain the early exponential growth of the tumor and the later saturation associated with the Gompertzian curve which results from our evolutionary simulations using simple statistical mechanics principles related to the degree of functional coupling of the cell states. We then compare dosing strategies at early stage development, mid-stage (clinical stage), and late stage development of the tumor. If used early during tumor development in the subclinical stage, well before the cancer cell population is selected for growth, therapy is most effective at disrupting key emergent features of tumor development.

Critical behavior of subcellular density organization during neutrophil activation and migration.

Physical theories of active matter continue to provide a quantitative understanding of dynamic cellular phenomena, including cell locomotion. Although various investigations of the rheology of cells have identified important viscoelastic and traction force parameters for use in these theoretical approaches, a key variable has remained elusive both in theoretical and experimental approaches: the spatiotemporal behavior of the subcellular density. The evolution of the subcellular density has been qualitatively observed for decades as it provides the source of image contrast in label-free imaging modalities (e.g., differential interference contrast, phase contrast) used to investigate cellular specimens. While these modalities directly visualize cell structure, they do not provide quantitative access to the structures being visualized. We present an established quantitative imaging approach, non-interferometric quantitative phase microscopy, to elucidate the subcellular density dynamics in neutrophils undergoing chemokinesis following uniform bacterial peptide stimulation. Through this approach, we identify a power law dependence of the neutrophil mean density on time with a critical point, suggesting a critical density is required for motility on 2D substrates. Next we elucidate a continuum law relating mean cell density, area, and total mass that is conserved during neutrophil polarization and migration. Together, our approach and quantitative findings will enable investigators to define the physics coupling cytoskeletal dynamics with subcellular density dynamics during cell migration.

Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites.

BACKGROUND: Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although patterns of spread may superficially seem random and unpredictable, we explored the possibility that this is not the case. AIMS: Develop a Markov based model of breast cancer progression that has predictive capability. METHODS: On the basis of a longitudinal data set of 446 breast cancer patients, we created a Markov chain model of metastasis that describes the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Progression is modeled as a random walk on a directed graph, where nodes represent anatomical sites where tumors can develop. RESULTS: We quantify how survival depends on the location of the first metastatic site for different patient subcategories. In addition, we classify metastatic sites as "sponges" or "spreaders" with implications regarding anatomical pathway prediction and long-term survival. As metastatic tumors to the bone (main spreader) are most prominent, we focus in more detail on differences between groups of patients who form subsequent metastases to the lung as compared with the liver. CONCLUSIONS: We have found that spatiotemporal patterns of metastatic spread in breast cancer are neither random nor unpredictable. Furthermore, the novel concept of classifying organ sites as sponges or spreaders may motivate experiments seeking a biological basis for these phenomena and allow us to quantify the potential consequences of therapeutic targeting of sites in the oligometastatic setting and shed light on organotropic aspects of the disease.

Entropy, complexity, and Markov diagrams for random walk cancer models.

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.