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ABSTRACT: Background. HPV infection frequently induces hyper-proliferation of epithelial cells leading to both benign (warts) and malignant tumors (cervical cancer). We seek to understand how HPV may achieve these changes by modulating cellular population dynamics. Furthermore, HPV lesion progression is generally understood as a series of molecular changes. As a complement to this approach, we investigate the role of phenotypic changes produced by natural selection during lesion progression.Methods. We develop and numerically analyze spatially and evolutionarily explicit mathematical models of HPV-induced epithelial lesions.Results. Infection of basal cells is a requirement for persistent infection. 2) Increasing the maximum tissue density at which HPV infected cells can divide and decreasing infected cell migration rate leads to large increases in the number of HPV infected cells and consequently virions shed from the skin surface per day. 3) Evolution by natural selection in an autonomous population of cells leads to qualitatively similar tissue changes as those observed during lesion progression.Conclusions. HPV modulates cell population dynamics, which can be characterized by specific ecological parameters. As an unintended consequence, this ecological strategy of the virus may be successfully co-opted by autonomous host cells and play a role in lesion progression.
The Journal of Infectious Diseases 04/2013; · 6.41 Impact Factor
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Yuhua Gu,
Virendra Kumar,
Lawrence O Hall,
Dmitry B Goldgof,
Ching-Yen Li,
René Korn,
Claus Bendtsen,
Emmanuel Rios Velazquez,
Andre Dekker,
Hugo Aerts,
Philippe Lambin,
Xiuli Li,
Jie Tian, Robert A Gatenby,
Robert J Gillies
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ABSTRACT: A single click ensemble segmentation (SCES) approach based on an existing "Click&Grow" algorithm is presented. The SCES approach requires only one operator selected seed point as compared with multiple operator inputs, which are typically needed. This facilitates processing large numbers of cases. Evaluation on a set of 129 CT lung tumor images using a similarity index (SI) was done. The average SI is above 93% using 20 different start seeds, showing stability. The average SI for 2 different readers was 79.53%. We then compared the SCES algorithm with the two readers, the level set algorithm and the skeleton graph cut algorithm obtaining an average SI of 78.29%, 77.72%, 63.77% and 63.76% respectively. We can conclude that the newly developed automatic lung lesion segmentation algorithm is stable, accurate and automated.
Pattern Recognition 03/2013; 46(3):692-702. · 2.29 Impact Factor
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ABSTRACT: Living cells are spatially bounded, low entropy systems that, although far from thermodynamic equilibrium, have persisted for billions of years. Schrödinger, Prigogine, and others explored the physical principles of living systems primarily in terms of the thermodynamics of order, energy, and entropy. This provided valuable insights, but not a comprehensive model. We propose the first principles of living systems must include: (1) Information dynamics, which permits conversion of energy to order through synthesis of specific and reproducible, structurally-ordered components; and (2) Nonequilibrium thermodynamics, which generate Darwinian forces that optimize the system.Living systems are fundamentally unstable because they exist far from thermodynamic equilibrium, but this apparently precarious state allows critical response that includes: (1) Feedback so that loss of order due to environmental perturbations generate information that initiates a corresponding response to restore baseline state. (2) Death due to a return to thermodynamic equilibrium to rapidly eliminate systems that cannot maintain order in local conditions. (3) Mitosis that rewards very successful systems, even when they attain order that is too high to be sustainable by environmental energy, by dividing so that each daughter cell has a much smaller energy requirement. Thus, nonequilibrium thermodynamics are ultimately responsible for Darwinian forces that optimize system dynamics, conferring robustness sufficient to allow continuous existence of living systems over billions of years.
Bulletin of Mathematical Biology 02/2013; · 1.85 Impact Factor
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ABSTRACT: PURPOSE: Measurement variance affects the clinical effectiveness of PET-based measurement as a semiquantitative imaging biomarker for cancer response in individual patients and for planning clinical trials. In this study, we measured test-retest reproducibility of SUV measurements under clinical practice conditions and recorded recognized deviations from protocol compliance. METHODS: Instrument performance calibration, display, and analyses conformed to manufacture recommendations. Baseline clinical F-FDG PET/CT examinations were performed and then repeated at 1 to 7 days. Intended scan initiation uptake period was to repeat the examinations at the same time for each study after injection of 12 mCi FDG tracer. Avidity of uptake was measured in 62 tumors in 21 patients as SUV for maximum voxel (SUVmax) and for a mean of sampled tumor voxels (SUVmean). RESULTS: The range of SUVmax and SUVmean was 1.07 to 21.47 and 0.91 to 14.69, respectively. Intraclass correlation coefficient between log of SUVmax and log of SUVmean was 0.93 (95% confidence interval [CI], 0.88-0.95) and 0.92 (95% CI, 0.87-0.95), respectively.Correlation analysis failed to show an effect on uptake period variation on SUV measurements between the 2 examinations, suggesting additional sources of noise.The threshold criteria for relative difference from baseline for the 95% CI were ±49% or ±44% for SUVmax or SUVmean, respectively. CONCLUSIONS: Variance of SUV for FDG-PET/CT in current clinical practice in a single institution was greater than expected when compared with benchmarks reported under stringent efficacy study settings. Under comparable clinical practice conditions, interpretation of changes in tumor avidity in individuals and assumptions in planning clinical trials may be affected.
Clinical nuclear medicine 01/2013; · 3.92 Impact Factor
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ABSTRACT: The evolutionary process has been modelled in many ways using both stochastic
and deterministic models. We develop an algebraic model of evolution in a
population of asexually reproducing organisms in which we represent a
stochastic walk in phenotype space, constrained to the edges of an underlying
graph representing the genotype, with a time-homogeneous Markov Chain. We show
its equivalence to a more standard, explicit stochastic model and show the
algebraic model's superiority in computational efficiency. Because of this
increase in efficiency, we offer the ability to simulate the evolution of much
larger populations in more realistic genotype spaces. Further, we show how the
algebraic properties of the Markov Chain model can give insight into the
evolutionary process and allow for analysis using familiar linear algebraic
methods.
01/2013;
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Veronica Estrella,
Tingan Chen,
Mark Lloyd,
Jonathan Wojtkowiak,
Heather H Cornnell,
Arig Ibrahim-Hashim,
Kate Bailey,
Yoganand Balagurunathan,
Jennifer M Rothberg,
Bonnie F Sloane,
Joseph Johnson, Robert A Gatenby,
Robert J Gillies
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ABSTRACT: The pH of solid tumors is acidic due to increased fermentative metabolism and poor perfusion. It has been hypothesized that acid pH promotes local invasive growth and metastasis. The hypothesis that acid mediates invasion proposes that H+ diffuses from the proximal tumor microenvironment into adjacent normal tissues where it causes tissue remodeling that permits local invasion. In the current work, tumor invasion and peritumoral pH were monitored over time using intravital microscopy. In every case, the peritumoral pH was acidic and heterogeneous and the regions of highest tumor invasion corresponded to areas of lowest pH. Tumor invasion did not occur into regions with normal or near-normal pHe. Immunohistochemical analyses revealed that cells in the invasive edges expressed the glucose transporter GLUT-1 and the sodium-hydrogen exchanger NHE-1, both of which were associated with peritumoral acidosis. In support of the functional importance of our findings, oral administration of sodium bicarbonate was sufficient to increase peritumoral pH and inhibit tumor growth and local invasion in a preclinical model, supporting the acid-mediated invasion hypothesis.
Cancer Research 01/2013; · 7.86 Impact Factor
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ABSTRACT: We apply competition colonization tradeoff models to tumor growth and invasion dynamics to explore the hypothesis that varying selection forces will result in predictable phenotypic differences in cells at the tumor invasive front compared to those in the core. Spatially, ecologically, and evolutionarily explicit partial differential equation models of tumor growth confirm that spatial invasion produces selection pressure for motile phenotypes. The effects of the invasive phenotype on normal adjacent tissue determine the patterns of growth and phenotype distribution. If tumor cells do not destroy their environment, colonizer and competitive phenotypes coexist with the former localized at the invasion front and the latter, to the tumor interior. If tumors cells do destroy their environment, then cell motility is strongly selected resulting in accelerated invasion speed with time. Our results suggest that the widely observed genetic heterogeneity within cancers may not be the stochastic effect of random mutations. Rather, it may be the consequence of predictable variations in environmental selection forces and corresponding phenotypic adaptations.
Frontiers in oncology. 01/2013; 3:45.
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ABSTRACT: Chemotherapy for metastatic cancer commonly fails due to evolution of drug resistance in tumor cells. Here, we view cancer treatment as a game in which the oncologists choose a therapy and tumors 'choose' an adaptive strategy. We propose the oncologist can gain an upper hand in the game by choosing treatment strategies that anticipate the adaptations of the tumor. In particular, we examine the potential benefit of exploiting evolutionary tradeoffs in tumor adaptations to therapy. We analyze a math model where cancer cells face tradeoffs in allocation of resistance to two drugs. The tumor 'chooses' its strategy by natural selection and the oncologist chooses her strategy by solving a control problem. We find that when tumor cells perform best by investing resources to maximize response to one drug the optimal therapy is a time-invariant delivery of both drugs simultaneously. However, if cancer cells perform better using a generalist strategy allowing resistance to both drugs simultaneously, then the optimal protocol is a time varying solution in which the two drug concentrations negatively covary. However, drug interactions can significantly alter these results. We conclude that knowledge of both evolutionary tradeoffs and drug interactions is crucial in planning optimal chemotherapy schedules for individual patients.
Physical Biology 11/2012; 9(6):065007. · 2.60 Impact Factor
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ABSTRACT: Many cancers adapt to chemotherapeutic agents by upregulating membrane efflux pumps that export drugs from the cytoplasm, but this response comes at an energetic cost. In breast cancer patients, expression of these pumps is low in tumors before therapy but increases after treatment. While the evolution of therapeutic resistance is virtually inevitable, proliferation of resistant clones is not, suggesting strategies of adaptive therapy. Chemoresistant cells must consume excess resources to maintain resistance mechanisms, so adaptive therapy strategies explicitly aim to maintain a stable population of therapy-sensitive cells to suppress growth of resistant phenotypes through intratumoral competition. We employed computational models parameterized by in vitro experiments to illustrate the efficacy of such approaches. Here we show that low doses of verapamil and 2-deoxyglucose, to accentuate the cost of resistance and to decrease energy production, respectively, could suppress the proliferation of drug-resistant clones in vivo. Compared to compared to standard high dose density treatment, the novel treatment we developed achieved a 2- to 10-fold increase in time to progression in tumor models. Our findings challenge the existing flawed paradigm of maximum dose treatment, a strategy that inevitably produces drug resistance which can be avoided by the adaptive therapy strategies we describe.
Cancer Research 10/2012; · 7.86 Impact Factor
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Virendra Kumar,
Yuhua Gu,
Satrajit Basu,
Anders Berglund,
Steven A Eschrich,
Matthew B Schabath,
Kenneth Forster,
Hugo J W L Aerts,
Andre Dekker,
David Fenstermacher,
Dmitry B Goldgof,
Lawrence O Hall,
Philippe Lambin,
Yoganand Balagurunathan, Robert A Gatenby,
Robert J Gillies
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ABSTRACT: "Radiomics" refers to the extraction and analysis of large amounts of advanced quantitative imaging features with high throughput from medical images obtained with computed tomography, positron emission tomography or magnetic resonance imaging. Importantly, these data are designed to be extracted from standard-of-care images, leading to a very large potential subject pool. Radiomics data are in a mineable form that can be used to build descriptive and predictive models relating image features to phenotypes or gene-protein signatures. The core hypothesis of radiomics is that these models, which can include biological or medical data, can provide valuable diagnostic, prognostic or predictive information. The radiomics enterprise can be divided into distinct processes, each with its own challenges that need to be overcome: (a) image acquisition and reconstruction, (b) image segmentation and rendering, (c) feature extraction and feature qualification and (d) databases and data sharing for eventual (e) ad hoc informatics analyses. Each of these individual processes poses unique challenges. For example, optimum protocols for image acquisition and reconstruction have to be identified and harmonized. Also, segmentations have to be robust and involve minimal operator input. Features have to be generated that robustly reflect the complexity of the individual volumes, but cannot be overly complex or redundant. Furthermore, informatics databases that allow incorporation of image features and image annotations, along with medical and genetic data, have to be generated. Finally, the statistical approaches to analyze these data have to be optimized, as radiomics is not a mature field of study. Each of these processes will be discussed in turn, as well as some of their unique challenges and proposed approaches to solve them. The focus of this article will be on images of non-small-cell lung cancer.
Magnetic Resonance Imaging 08/2012; 30(9):1234-48. · 1.99 Impact Factor
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ABSTRACT: All malignant cancers, whether inherited or sporadic, are fundamentally governed by Darwinian dynamics. The process of carcinogenesis requires genetic instability and highly selective local microenvironments, the combination of which promotes somatic evolution. These microenvironmental forces, specifically hypoxia, acidosis and reactive oxygen species, are not only highly selective, but are also able to induce genetic instability. As a result, malignant cancers are dynamically evolving clades of cells living in distinct microhabitats that almost certainly ensure the emergence of therapy-resistant populations. Cytotoxic cancer therapies also impose intense evolutionary selection pressures on the surviving cells and thus increase the evolutionary rate. Importantly, the principles of Darwinian dynamics also embody fundamental principles that can illuminate strategies for the successful management of cancer.
Nature Reviews Cancer 06/2012; 12(7):487-93. · 29.54 Impact Factor
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ABSTRACT: Hypoxia and acidosis develop in in situ tumors as cellular expansion increases the diffusion distance of substrates and metabolites from blood vessels deep to the basement membrane. Prior studies of breast and cervical cancer revealed that cellular adaptation to microenvironmental hypoxia and acidosis is associated with the transition from in situ to invasive cancer. We hypothesized that decreased acidosis in intraductal tumors would alter environmental selection pressures for acid adapted phenotypes and delay or prevent evolution to invasive cancer.
A total of 37 C57BL/6 TRAMP mice were randomized to a control group or to 1 of 4 treatment groups. In the latter groups 200 mM sodium bicarbonate were added to drinking water starting between ages 4 and 10 weeks.
In all 18 controls prostate cancer developed that was visible on 3-dimensional ultrasound at a mean age of 13 weeks. They died within 52 weeks (median 37). When sodium bicarbonate therapy commenced before age 6 weeks in 10 mice, all reached senescence (age 76 weeks) without radiographic evidence of prostate cancer. Histological sections of the prostates in this cohort showed hyperplasia but no cancer in 70% of mice and minimal well differentiated cancer in the remainder. When therapy commenced after age 6 weeks in 9 mice, prostate cancer development was no different from that in controls.
Immunohistochemical staining for carbonic anhydrase 9 in regions of ductal hyperplasia showed increased expression in controls vs the early treatment group. Regional pH perturbation in in situ tumors may be a simple, inexpensive and effective cancer prevention strategy.
The Journal of urology 06/2012; 188(2):624-31. · 4.02 Impact Factor
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ABSTRACT: Although many anticancer therapies are successful in killing a large percentage of tumor cells when initially administered, the evolutionary dynamics underpinning tumor progression mean that, often, resistance is an inevitable outcome. Research in the field of ecology suggests that an evolutionary double bind could be an effective way to treat tumors. In an evolutionary double bind two therapies are used in combination such that evolving resistance to one leaves individuals more susceptible to the other. In this paper we present a general evolutionary game theory framework of a double bind to study the effect that such an approach would have in cancer. Furthermore we use this mathematical framework to understand recent experimental results that suggest a synergistic effect between a p53 cancer vaccine and chemotherapy. Our model recapitulates the latest experimental data and provides an explanation for its effectiveness based on the commensalistic relationship between the tumor phenotypes.
Molecular Pharmaceutics 02/2012; 9(4):914-21. · 4.78 Impact Factor
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ABSTRACT: We address the ecological and evolutionary dynamics of human papillomavirus (HPV) that lead to the dichotomy between high-risk (HR) and low-risk (LR) types. We hypothesize that HPV faces an evolutionary tradeoff between persistence and per-contact transmission probability. High virion production enhances transmissibility but also provokes an immune response leading to clearance and limited persistence. Alternatively, low virion production increases persistence at the cost of diminished transmission probability per sexual contact. We propose that LR HPV types use the former strategy and that HR types use the latter. Sexual behaviors in a host population determine the success of each strategy.
We develop an evolutionary model of HPV epidemiology, which includes host sexual behavior, and we find evolutionarily stable strategies of HPV.
A slow turnover of sexual partners favors HR HPV, whereas high frequency of partner turnover selects for LR. When both sexual behaviors exist as subcultures in a population, disruptive selection can result in the coevolution and ecological coexistence of both HR and LR HPV types.
Our results indicate that the elimination of HR HPV through vaccines may alter the evolutionary trajectory of the remaining types and promote evolution of new HR HPV types.
The Journal of Infectious Diseases 11/2011; 205(2):272-9. · 6.41 Impact Factor
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ABSTRACT: The tumor microenvironment is acidic as a consequence of upregulated glycolysis and poor perfusion and this acidity, in turn, promotes invasion and metastasis. We have recently demonstrated that chronic consumption of sodium bicarbonate increased tumor pH and reduced spontaneous and experimental metastases. This occurred without affecting systemic pH, which was compensated. Additionally, these prior data did not rule out the possibility that bicarbonate was working though effects on carbonic anhydrase, and not as a buffer per se. Here, we present evidence that chronic ingestion of a non-volatile buffer, 2-imidazole-1-yl-3-ethoxycarbonylpropionic acid (IEPA) with a pK (a) of 6.9 also reduced metastasis in an experimental PC3M prostate cancer mouse model. Animals (n = 30) were injected with luciferase expressing PC3M prostate cancer cells either subcutaneously (s.c., n = 10) or intravenously (i.v., n = 20). Four days prior to inoculations, half of the animals for each experiment were provided drinking water containing 200 mM IEPA buffer. Animals were imaged weekly to follow metastasis, and these data showed that animals treated with IEPA had significantly fewer experimental lung metastasis compared to control groups (P < 0.04). Consistent with prior work, the pH of treated tumors was elevated compared to controls. IEPA is observable by in vivo magnetic resonance spectroscopy and this was used to measure the presence of IEPA in the bladder, confirming that it was orally available. The results of this study indicate that metastasis can be reduced by non-volatile buffers as well as bicarbonate and thus the effect appears to be due to pH buffering per se.
Clinical and Experimental Metastasis 08/2011; 28(8):841-9. · 3.52 Impact Factor
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ABSTRACT: Disseminated cancer remains a largely fatal disease. While systemic therapy can have some initial success, it is rarely durable. Typically, populations of cancer cells resistant to therapy emerge quickly requiring progressively less effective second, third, and fourth line therapies until the patient succumbs. Cancer cells possess a large repertoire of heritable phenotypic strategies that can be used to confer resistance to one or more therapeutic drugs. In addition, environmental factors such as ischemia and hypoxia can reduce therapeutic effects by limiting drug delivery or toxicity. Here, we use a fitness generating function (G-function) approach to model tumor response with respect to evolutionary adaptation and microenvironmental conditions in response to various therapeutic strategies. We examine tumor cell death and the evolution of resistance in single and two drug therapies as well as alternative "evolutionary" approaches. We demonstrate that even monotherapy would be highly successful in the absence of tumor evolution or environmentally mediated resistance. However, environmental and evolutionary factors dramatically reduce the effectiveness of therapy. Two-drug therapy in which adaptation requires two different phenotypic changes will maximally reduce tumor size and delay onset of resistance, but actual eradication of the tumor population is rare. We demonstrate that multiagent therapies in which the first drug both achieves tumor cell toxicity and drives phenotypic adaptation that renders the cell more vulnerable to a second therapy can be highly successful in maintaining durable tumor control. Examples of clinical trials that exploit these results are presented. We conclude that the development of more lethal (cytotoxic) drugs is not likely to fundamentally change the outcome of therapy. Instead, new approaches that incorporate evolutionary strategies into target and drug selection are needed.
Molecular Pharmaceutics 08/2011; 8(6):2094-100. · 4.78 Impact Factor
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ABSTRACT: Interactions between cancer cells and their microenvironment are crucial for promoting tumor growth and invasiveness. In the tumor adaptive landscape model, hypoxic and acidic microenvironmental conditions reduce the fitness of cancer cells and significantly restrict their proliferation. This selects for enhanced motility as cancer cells may evolve an invasive phenotype if the consequent cell movement is rewarded by proliferation. Here, we used an integrative approach combining a mathematical tumor adaptive landscape model with experimental studies to examine the evolutionary dynamics that promote an invasive cancer phenotype. Computer simulation results hypothesized an explicit coupling of motility and proliferation in cancer cells. The mathematical modeling results were also experimentally examined by selecting Panc-1 cells with enhanced motility on a fibroblast-derived 3-dimensional matrix for cells that move away from the unfavorable metabolic constraints. After multiple rounds of selection, the cells that adapted through increased motility were characterized for their phenotypic properties compared with stationary cells. Microarray and gene depletion studies showed the role of Rho-GDI2 in regulating both cell movement and proliferation. Together, this work illustrates the partnership between evolutionary mathematical modeling and experimental validation as a potentially useful approach to study the complex dynamics of the tumor microenvironment.
Cancer Research 08/2011; 71(20):6327-37. · 7.86 Impact Factor
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Academic radiology 08/2011; 18(8):929-31. · 2.09 Impact Factor
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ABSTRACT: We show that any convex K-dimensional system has a level of order R that is proportional to its level of Fisher information I. The proportionality constant is 1/8 the square of the longest chord connecting two surface points of the system. This result follows solely from the requirement that R decrease under small perturbations caused by a coarse graining of the system. The form for R is generally unitless, allowing the order for different phenomena, or different representations (e.g., using time vs frequency) of a given phenomenom, to be compared objectively. Order R is also invariant to uniform magnification of the system. The monotonic contraction properties of R and I define an arrow of time and imply that they are entropies, in addition to their usual status as informations. This also removes the need for data, and therefore an observer, in derivations of nonparticipatory phenomena that utilize I. Simple graphical examples of the new order measure show that it measures as well the level of "complexity" in the system. Finally, an application to cell growth during enforced distortion shows that a single hydrocarbon chain can be distorted into a membrane having equal order or complexity. Such membranes are prime constituents of living cells.
Physical Review E 07/2011; 84(1 Pt 1):011128. · 2.26 Impact Factor
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ABSTRACT: We propose that the drivers of carcinogenesis lie more in the adaptive changes that are enabled by local or systemic alterations of tissue architecture than in the genetic changes observed in cancer cells. A full understanding of cancer biology and therapy through a cataloguing of the cancer genome is unlikely unless it is integrated into an evolutionary and ecological context.
Nature Reviews Cancer 04/2011; 11(4):237-8. · 29.54 Impact Factor
