B. Roy Frieden

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A number of successful systemic therapies are available for treatment of disseminated cancers. However, tumor response is often transient, and therapy frequently fails due to emergence of resistant populations. The latter reflects the temporal and spatial heterogeneity of the tumor microenvironment as well as the evolutionary capacity of cancer phenotypes to adapt to therapeutic perturbations. Although cancers are highly dynamic systems, cancer therapy is typically administered according to a fixed, linear protocol. Here we examine an adaptive therapeutic approach that evolves in response to the temporal and spatial variability of tumor microenvironment and cellular phenotype as well as therapy-induced perturbations. Initial mathematical models find that when resistant phenotypes arise in the untreated tumor, they are typically present in small numbers because they are less fit than the sensitive population. This reflects the "cost" of phenotypic resistance such as additional substrate and energy used to up-regulate xenobiotic metabolism, and therefore not available for proliferation, or the growth inhibitory nature of environments (i.e., ischemia or hypoxia) that confer resistance on phenotypically sensitive cells. Thus, in the Darwinian environment of a cancer, the fitter chemosensitive cells will ordinarily proliferate at the expense of the less fit chemoresistant cells. The models show that, if resistant populations are present before administration of therapy, treatments designed to kill maximum numbers of cancer cells remove this inhibitory effect and actually promote more rapid growth of the resistant populations. We present an alternative approach in which treatment is continuously modulated to achieve a fixed tumor population. The goal of adaptive therapy is to enforce a stable tumor burden by permitting a significant population of chemosensitive cells to survive so that they, in turn, suppress proliferation of the less fit but chemoresistant subpopulations. Computer simulations show that this strategy can result in prolonged survival that is substantially greater than that of high dose density or metronomic therapies. The feasibility of adaptive therapy is supported by in vivo experiments. [Cancer Res 2009;69(11):4894-903] Major FindingsWe present mathematical analysis of the evolutionary dynamics of tumor populations with and without therapy. Analytic solutions and numerical simulations show that, with pretreatment, therapy-resistant cancer subpopulations are present due to phenotypic or microenvironmental factors; maximum dose density chemotherapy hastens rapid expansion of resistant populations. The models predict that host survival can be maximized if "treatment-for-cure strategy" is replaced by "treatment-for-stability." Specifically, the models predict that an optimal treatment strategy will modulate therapy to maintain a stable population of chemosensitive cells that can, in turn, suppress the growth of resistant populations under normal tumor conditions (i.e., when therapy-induced toxicity is absent). In vivo experiments using OVCAR xenografts treated with carboplatin show that adaptive therapy is feasible and, in this system, can produce long-term survival.

Given M sampled image values of an incoherent object, what can be deduced as the most likely object? Using a communication-theory model for the process of image formation, we find that the most likely object has a maximum entropy and is represented by a restoring formula that is positive and not band limited. The derivation is an adaptation to optics of a formulation by Jaynes for unbiased estimates of positive probability functions. The restoring formula is tested, via computer simulation, upon noisy images of objects consisting of random impulses. These are found to be well restored, with resolution often exceeding the Rayleigh limit and with a complete absence of spurious detail. The proviso is that the noise in each image input must not exceed about 40% of the signal image. The restoring method is applied to experimental data consisting of line spectra. Results are consistent with those of the computer simulations.

This book develops and applies an analytical approach to deriving the probability laws of science in general. It is called 'extreme physical information' or EPI. EPI is an expression of the imperfection of observation: Owing to random interaction of a subject with its observer and other possible disturbances, its measurement contains less Fisher information than does the subject per se. Moreover, the information loss is an extreme value. An EPI output may alternatively be viewed as the payoff of a zero-sum game of information acquisition between the observer and a 'demon' in subject space. EPI derives, Escher-like, the very probability law that gave rise to the measurement. In applications, EPI is used to derive both existing and new analytical relations governing probability laws of physics, genetics, cancer growth, ecology and economics. This unified approach will be fascinating to students and those who seek a new mathematical tool of research.

This book develops and applies an analytical approach to deriving the probability laws of science in general. It is called 'extreme physical information' or EPI. EPI is an expression of the imperfection of observation: Owing to random interaction of a subject with its observer and other possible disturbances, its measurement contains less Fisher information than does the subject per se. Moreover, the information loss is an extreme value. An EPI output may alternatively be viewed as the payoff of a zero-sum game of information acquisition between the observer and a 'demon' in subject space. EPI derives, Escher-like, the very probability law that gave rise to the measurement. In applications, EPI is used to derive both existing and new analytical relations governing probability laws of physics, genetics, cancer growth, ecology and economics. This unified approach will be fascinating to students and those who seek a new mathematical tool of research