Mathematical Aspects of a New Synergy Theory Applicable to Malstressor-Dominated Mixtures which Include Damage-Ameliorating Countermeasures.

In radiobiology, and throughout translational biology, synergy theories for multi-component agent mixtures use 1-agent dose-effect relations (DERs) to calculate baseline neither synergy nor antagonism mixture DERs. The most used synergy theory, simple effect additivity, is not self-consistent when curvilinear 1-agent DERs are involved, and many alternatives have been suggested. In this paper we present the mathematical aspects of a new alternative, generalized Loewe additivity (GLA).

The circulation stage of the metastatic cascade: A mathematical description and its clinical implications.

Metastatic cascade is a multi-stage process that starts with separation of a cancer cell from the primary tumor and ends with the emergence of a detectable metastasis. In the process the initiator cancer cell enters the circulatory system (intravasates), flows with the blood, and exits the circulation (extravasates) into an organ or tissue. The time period between intravasation and extravasation constitutes the circulation stage of the metastatic cascade.

Tumor control probability in hypofractionated radiotherapy as a function of total and hypoxic tumor volumes.

Clinical studies in the hypofractionated stereotactic body radiotherapy (SBRT) have shown a reduction in the probability of local tumor control with increasing initial tumor volume. In our earlier work, we obtained and tested an analytical dependence of the tumor control probability (TCP) on the total and hypoxic tumor volumes using conventional radiotherapy model with the linear-quadratic (LQ) cell survival. In this work, this approach is further refined and tested against clinical observations for hypofractionated radiotherapy treatment schedules.

The natural history of renal cell carcinoma with pulmonary metastases illuminated through mathematical modeling.

The goal of this study is to uncover some unobservable aspects of the individual-patient natural history of metastatic renal cell carcinoma (RCC) through mathematical modeling. We analyzed four clear cell RCC patients who at the time of primary tumor resection already had pulmonary metastases. Our description of the natural history of cancer in these patients was based on a parameterized version of a previously proposed very general mathematical model adjusted to these clinical cases.

Suppression of Metastasis by Primary Tumor and Acceleration of Metastasis Following Primary Tumor Resection: A Natural Law?

We study metastatic cancer progression through an extremely general individual-patient mathematical model that is rooted in the contemporary understanding of the underlying biomedical processes yet is essentially free of specific biological assumptions of mechanistic nature. The model accounts for primary tumor growth and resection, shedding of metastases off the primary tumor and their selection, dormancy and growth in a given secondary site. However, functional parameters descriptive of these processes are assumed to be essentially arbitrary.

Why statistical inference from clinical trials is likely to generate false and irreproducible results.

One area of biomedical research where the replication crisis is most visible and consequential is clinical trials. Why do outcomes of so many clinical trials contradict each other? Why is the effectiveness of many drugs and other medical interventions so low? Why have prescription medications become the third leading cause of death in the US and Europe after cardiovascular diseases and cancer? In answering these questions, the main culprits identified so far have been various biases and conflicts of interest in planning, execution and analysis of clinical trials as well as reporting their outcomes. In this work, we take an in-depth look at statistical methodology used in planning clinical trials and analyzing trial data.

A quantitative insight into metastatic relapse of breast cancer.

Background: Metastatic relapse is the principal source of breast cancer mortality. This work seeks to uncover unobservable, yet clinically important, aspects of post-surgery metastatic relapse of breast cancer and to quantify effects of surgery on metastatic progression.

Methods: We classified metastases into three categories: (1) solitary cancer cells that were formed before or during surgery and either circulate in blood or are lodged at various secondary sites; (2) dormant or slowly growing avascular metastases; and (3) vascular secondary tumors.

A "universal" model of metastatic cancer, its parametric forms and their identification: what can be learned from site-specific volumes of metastases.

We develop a methodology for estimating unobservable characteristics of the individual natural history of metastatic cancer from the volume of the primary tumor and site-specific volumes of metastases measured before, or shortly after, the start of treatment. In particular, we address the question as to what information about natural history of cancer can and cannot be gained from this type of data. Estimation of the natural history of cancer is based on parameterization of a very general mathematical model of cancer progression accounting for primary tumor growth, shedding of metastases, their selection, latency and growth in a given secondary site.

Uncovering the natural history of cancer from post-mortem cross-sectional diameters of hepatic metastases.

We develop a mathematical and statistical methodology for estimation of important unobservable characteristics of the individual natural history of cancer from a sample of cross-sectional diameters of liver metastases measured at autopsy. Estimation of the natural history of cancer is based on a previously proposed stochastic model of cancer progression tailored to this type of observations. The model accounts for primary tumour growth, shedding of metastases, their selection, latency and growth in a given secondary site.

Optimal schedules of fractionated radiation therapy by way of the greedy principle: biologically-based adaptive boosting.

We revisit a long-standing problem of optimization of fractionated radiotherapy and solve it in considerable generality under the following three assumptions only: (1) repopulation of clonogenic cancer cells between radiation exposures follows linear birth-and-death Markov process; (2) clonogenic cancer cells do not interact with each other; and (3) the dose response function s(D) is decreasing and logarithmically concave. Optimal schedules of fractionated radiation identified in this work can be described by the following 'greedy' principle: give the maximum possible dose as soon as possible. This means that upper bounds on the total dose and the dose per fraction reflecting limitations on the damage to normal tissue, along with a lower bound on the time between successive fractions of radiation, determine the optimal radiation schedules completely.

On the probability of cure for heavy-ion radiotherapy.

The probability of a cure in radiation therapy (RT)-viewed as the probability of eventual extinction of all cancer cells-is unobservable, and the only way to compute it is through modeling the dynamics of cancer cell population during and post-treatment. The conundrum at the heart of biophysical models aimed at such prospective calculations is the absence of information on the initial size of the subpopulation of clonogenic cancer cells (also called stem-like cancer cells), that largely determines the outcome of RT, both in an individual and population settings. Other relevant parameters (e.

Reconstruction of the natural history of metastatic cancer and assessment of the effects of surgery: Gompertzian growth of the primary tumor.

This work deals with retrospective reconstruction of the individual natural history of solid cancer and assessment of the effects of treatment on metastatic progression. This is achieved through a mathematical model of cancer progression accounting for the growth of the primary tumor, shedding of metastases, their dormancy and growth at secondary sites. To describe dynamics of the primary tumor, we used the Gompertz law, a parsimonious model of tumor growth accounting for its saturation.

Dynamics of pathologic clot formation: a mathematical model.

Recent studies have provided evidence of a significant role of the Hageman factor in pathologic clot formation. Since auto-activation of the Hageman factor triggers the intrinsic coagulation pathway, we study the dynamics of pathologic clot formation considering the intrinsic pathway as the predominant mechanism of this process. Our methodological approach to studying the dynamics of clot formation is based on mathematical modelling.

A mechanistic description of radiation-induced damage to normal tissue and its healing kinetics.

We introduce a novel mechanistic model of the yield of tissue damage at the end of radiation treatment and of the subsequent healing kinetics. We find explicit expressions for the total number of functional proliferating cells as well as doomed (functional but non-proliferating) cells as a function of time post treatment. This leads to the possibility of estimating-for any given cohort of patients undergoing radiation therapy-the probability distribution of those kinetic parameters (e.

Seeing the invisible: how mathematical models uncover tumor dormancy, reconstruct the natural history of cancer, and assess the effects of treatment.

The hypothesis of early metastasis was debated for several decades. Dormant cancer cells and surgery-induced acceleration of metastatic growth were first observed in clinical studies and animal experiments conducted more than a century ago; later, these findings were confirmed in numerous modern studies.In this primarily methodological work, we discuss critically important, yet largely unobservable, aspects of the natural history of cancer, such as (1) early metastatic dissemination; (2) dormancy of secondary tumors; (3) treatment-related interruption of metastatic dormancy, induction of angiogenesis, and acceleration of the growth of vascular metastases; and (4) the existence of cancer stem cells.

Optimal screening schedules for prevention of metastatic cancer.

We develop methodological, mathematical, statistical, and computational approaches to constructing schedules of cancer screening that maximize the probability that by the time of primary tumor detection it has not yet metastasized. Solving this problem is based on a comprehensive mechanistic model of cancer progression. We apply the model with realistic parameters and the screening optimization methodology to mammographic screening for breast cancer within the American female population.

Tumor control probability in radiation treatment.

Patients undergoing radiation therapy (and their physicians alike) are concerned with the probability of cure (long-term recurrence-free survival, meaning the absence of a detectable or symptomatic tumor). This is not what current practice categorizes as "tumor control (TC);" instead, TC is taken to mean the extinction of clonogenic tumor cells at the end of treatment, a sufficient but not necessary condition for cure. In this review, we argue that TC thus defined has significant deficiencies.

Effects of Surgery and Chemotherapy on Metastatic Progression of Prostate Cancer: Evidence from the Natural History of the Disease Reconstructed through Mathematical Modeling.

This article brings mathematical modeling to bear on the reconstruction of the natural history of prostate cancer and assessment of the effects of treatment on metastatic progression. We present a comprehensive, entirely mechanistic mathematical model of cancer progression accounting for primary tumor latency, shedding of metastases, their dormancy and growth at secondary sites. Parameters of the model were estimated from the following data collected from 12 prostate cancer patients: (1) age and volume of the primary tumor at presentation; and (2) volumes of detectable bone metastases surveyed at a later time.

Why victory in the war on cancer remains elusive: biomedical hypotheses and mathematical models.

We discuss philosophical, methodological, and biomedical grounds for the traditional paradigm of cancer and some of its critical flaws. We also review some potentially fruitful approaches to understanding cancer and its treatment. This includes the new paradigm of cancer that was developed over the last 15 years by Michael Retsky, Michael Baum, Romano Demicheli, Isaac Gukas, William Hrushesky and their colleagues on the basis of earlier pioneering work of Bernard Fisher and Judah Folkman.

Cell-survival probability at large doses: an alternative to the linear-quadratic model.

A model of irradiated cell survival based on rigorous accounting of microdosimetric effects is developed. The model does not assume that the distribution of lesions is Poisson and is applicable to low, intermediate and high acute doses of low or high LET radiation. For small doses, the model produces the linear-quadratic (LQ) model.

Does extirpation of the primary breast tumor give boost to growth of metastases? Evidence revealed by mathematical modeling.

A comprehensive mechanistic model of cancer natural history was utilized to obtain an explicit formula for the distribution of volumes of detectable metastases in a given secondary site at any time post-diagnosis. This model provided an excellent fit to the volumes of n=31, 20 and 15 bone metastases observed in three breast cancer patients 8 years, 5.5 years and 9 months after primary diagnosis, respectively.

Non-linear dynamics of the complement system activation.

The complement system (CS) plays a prominent role in the immune defense. The goal of this work is to study the dynamics of activation of the classic and alternative CS pathways based on the method of mathematical modeling. The principal difficulty that hinders modeling effort is the absence of the measured values of kinetic constants of many biochemical reactions forming the CS.

Chromosome-specific spatial periodicities in gene expression revealed by spectral analysis.

Recent years have seen an unprecedented surge of research activity in studies of gene expression. This extensive work, however, has been almost uniformly focused on genome-wide gene expression and has largely ignored the fundamental fact that every gene has a specific chromosome location. We propose a novel method of spectral analysis for detecting hidden periodicities in gene expression signals ordered along the length of each chromosome.