Prostate cancer is commonly treated by a form of hormone therapy called androgen suppression. This form of treatment, while successful at reducing the cancer cell population, adversely affects quality of life and typically leads to a recurrence of the cancer in an androgen-independent form. Intermittent androgen suppression aims to alleviate some of these adverse affects by cycling the patient on and off treatment. Clinical studies have suggested that intermittent therapy is capable of maintaining androgen dependence over multiple treatment cycles while increasing quality of life during off-treatment periods. This paper presents a mathematical model of prostate cancer to study the dynamics of androgen suppression therapy and the production of prostate-specific antigen (PSA), a clinical marker for prostate cancer. Preliminary models were based on the assumption of an androgen-independent (AI) cell population with constant net growth rate. These models gave poor accuracy when fitting clinical data during simulation. The final model presented hypothesizes an AI population with increased sensitivity to low levels of androgen. It also hypothesizes that PSA production is heavily dependent on androgen. The high level of accuracy in fitting clinical data with this model appears to confirm these hypotheses, which are also consistent with biological evidence.
Carotid artery aneurysms account for 4% of peripheral aneurysms and may present as a neck mass, with hemispheric ischaemic symptoms, or with symptoms secondary to local compression. This case explores the presentation, investigations and management of a presumed mycotic common carotid artery aneurysm in a 77-year-old male, which was repaired using end-to-end interposition vein graft using long saphenous vein. This report discusses the aetiology, presentation and surgical management for carotid artery aneurysms, as well as focusing on that of the rare mycotic carotid artery aneurysm.
Abstract Background Intermittent androgen deprivation therapy (IADT) is an attractive treatment approach for biochemically recurrent prostate cancer (PCa), whereby cycling treatment on and off can reduce cumulative dose, limit toxicities, and delay development of treatment resistance. To optimize treatment within the context of ongoing intratumoral evolution, underlying mechanisms of resistance and actionable biomarkers need to be identified. Methods We have developed a quantitative framework to simulate enrichment of prostate cancer stem cell (PCaSC) dynamics during treatment as a plausible mechanism of resistance evolution. Results Simulated dynamics of PCaSC and non-stem cancer cells demonstrate that stem cell proliferation patterns correlate with longitudinal serum prostate-specific antigen (PSA) measurements in 70 PCa patients undergoing multiple cycles of IADT. By learning the dynamics from each treatment cycle, individual model simulations predict evolution of resistance in the subsequent IADT cycle with a sensitivity and specificity of 57% and 94%, respectively and an overall accuracy of 90%. Additionally, we evaluated the potential benefit of docetaxel for IADT in biochemically recurrent PCa. Model simulations based on response dynamics from the first IADT cycle identify patients who would or would not benefit from concurrent docetaxel in subsequent cycles. Conclusion Our results demonstrate the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics continuously updated with each treatment cycle. Translational Relevance Compared to continuous androgen deprivation therapy, intermittent androgen deprivation (IADT) has been shown to reduce toxicity and delay time to progression in prostate cancer. While numerous mathematical models have been developed to study the response to both continuous and intermittent androgen deprivation, very few have identified actionable biomarkers of resistance and exploited them to predict how patients will or will not respond to subsequent treatment. Here, we identify prostate-specific antigen (PSA) dynamics as the first such biomarker. Mechanistic mathematical modeling of prostate cancer stem cell dynamics that dictate prostate-specific antigen serum levels predicts individual responses to IADT with 90% overall accuracy and can be used to develop patient-specific adaptive treatment protocols, and potentially identify patients that may benefit from concurrent chemotherapy. Model results demonstrate the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics continuously updated with each treatment cycle.
Chronic hepatitis B (HBV) infection is a major cause of human suffering, and a number of mathematical models have examined the within-host dynamics of the disease. Most previous models assumed that infected hepatocytes do not proliferate; however, the effect of HBV infection on hepatocyte proliferation is controversial, with conflicting data showing both induction and inhibition of proliferation. With a family of ordinary differential equation (ODE) models, we explored the dynamical impact of proliferation among HBV-infected hepatocytes. Here, we show that infected hepatocyte proliferation in this class of models generates a threshold that divides the dynamics into two categories. Sufficiently compromised proliferation in infected cells produces complex dynamics characterized by oscillating viral loads, whereas higher proliferation generates straightforward dynamics that always results in chronic infection, sometimes with liver failure. A global stability result of the liver failure state was included as it is unique to this class of models. Finally, the model analysis motivated a testable biological hypothesis: Healthy hepatocytes are present in chronic HBV infection if and only if the proliferation of infected hepatocytes is severely impaired.
Natural selection among tumor cell clones is thought to produce hallmark properties of malignancy. Efforts to understand evolution of one such hallmark—the angiogenic switch—has suggested that selection for angiogenesis can “run away” and generate a hypertumor, a form of evolutionary suicide by extreme vascular hypo- or hyperplasia. This phenomenon is predicted by models of tumor angiogenesis studied with the techniques of adaptive dynamics. These techniques also predict that selection drives tumor proliferative potential towards an evolutionarily stable strategy (ESS) that is also convergence-stable. However, adaptive dynamics are predicated on two key assumptions: (i) no more than two distinct clones or evolutionary strategies can exist in the tumor at any given time; and (ii) mutations cause small phenotypic changes. Here we show, using a stochastic simulation, that relaxation of these assumptions has no effect on the predictions of adaptive dynamics in this case. In particular, selection drives proliferative potential towards, and angiogenic potential away from, their respective ESSs. However, these simulations also show that tumor behavior is highly contingent on mutational history, particularly for angiogenesis. Individual tumors frequently grow to lethal size before the evolutionary endpoint is approached. In fact, most tumor dynamics are predicted to be in the evolutionarily transient regime throughout their natural history, so that clinically, the ESS is often largely irrelevant. In addition, we show that clonal diversity as measured by the Shannon Information Index correlates with the speed of approach to the evolutionary endpoint. This observation dovetails with results showing that clonal diversity in Barrett's esophagus predicts progression to malignancy.
Secondary-charged-pion multiplicity distributions of interactions of 40-GeV/c ..pi../sup -/ mesons with several nucleons in the carbon nucleus are presented. Average ..pi../sup + -/-meson multiplicities of ..pi../sup -/(mN/sub p/) interactions with m=2, 3, and 4 are presented. The results are compared with cascade- and Glauber-model calculations. The results > or =1.50 +- 0.03 is obtained for the average number of interactions.
Long-lived marine megavertebrates (e.g. sharks, turtles, mammals, and seabirds) are inherently vulnerable to anthropogenic mortality. Although some mathematical models have been applied successfully to manage these animals, more detailed treatments are often needed to assess potential drivers of population dynamics. In particular, factors such as age-structure, density-dependent feedbacks on reproduction, and demographic stochasticity are important for understanding population trends, but are often difficult to assess. Lemon sharks ( Negaprion brevirostris ) have a pelagic adult phase that makes them logistically difficult to study. However, juveniles use coastal nursery areas where their densities can be high. Thus, we use a stage-structured, Markov-chain stochastic model to describe lemon shark population dynamics from a 17-year longitudinal dataset at a coastal nursery area at Bimini, Bahamas. We found that the interaction between delayed breeding and demographic stochasticity accounts for 33 to 49% of the variance. Demographic stochasticity contributed all random effects in this model, suggesting that the existence of unmodeled environmental factors may be driving the majority of interannual population fluctuations. In addition, we are able to use our model to estimate the natural mortality rate of older age classes of lemon sharks that are difficult to study. Further, we use our model to examine what effect the length of a time series plays on deciphering ecological patterns. We find that — even with a relatively long time series — our sampling still misses important rare events. Our approach can be used more broadly to infer population dynamics of other large vertebrates in which age structure and demographic stochasticity are important.
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