Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

Effect of pulsatility on the mathematical modeling of rotary blood pumps

In this study, the effect of time derivatives of flow rate and rotational speed was investigated on the mathematical modeling of a rotary blood pump (RBP). The basic model estimates the pressure head of the pump as a dependent variable using measured flow and speed as predictive variables. Performance of the model was evaluated by adding time derivative terms for flow and speed. First, to create a realistic working condition, the Levitronix CentriMag RBP was implanted in a sheep. All parameters from the model were physically measured and digitally acquired over a wide range of conditions, including pulsatile speed. Second, a statistical analysis of the different variables (flow, speed, and their time derivatives) based on multiple regression analysis was performed to determine the significant variables for pressure head estimation. Finally, different mathematical models were used to show the effect of time derivative terms on the performance of the models. In order to evaluate how well the estimated pressure head using different models fits the measured pressure head, root mean square error and correlation coefficient were used. The results indicate that inclusion of time derivatives of flow and speed can improve model accuracy, but only minimally.

Non-fatal cardiovascular outcome in patients with posttraumatic stress symptoms caused by myocardial infarction

Objectives Posttraumatic stress disorder (PTSD) prospectively increases the risk of incident cardiovascular disease (CVD) independent of other risk factors in otherwise healthy individuals. Between 10% and 20% of patients develop PTSD related to the traumatic experience of myocardial infarction (MI). We investigated the hypothesis that PTSD symptoms caused by MI predict adverse cardiovascular outcome. Methods We studied 297 patients (61 ± 10 years, 83% men) who self-rated PTSD symptoms attributable to a previous index MI. Non-fatal CVD-related hospital readmissions (i.e. recurrent MI, elective and non-elective intracoronary stenting, bypass surgery, pacemaker implantation, cardiac arrhythmia, cerebrovascular event) were assessed at follow-up. Cox proportional hazard models controlled for demographic factors, coronary heart disease severity, major CVD risk factors, cardiac medication, and mental health treatment. Results Forty-three patients (14.5%) experienced an adverse event during a mean follow-up of 2.8 years (range 1.3–3.8). A 10 point higher level in the PTSD symptom score (mean 8.8 ± 9.0, range 0–47) revealed a hazard ratio (HR) of 1.42 (95% CI 1.07–1.88) for a CVD-related hospital readmission in the fully adjusted model. A similarly increased risk (HR 1.45, 95% CI 1.07–1.97) emerged for patients with a major or unscheduled CVD-related readmission (i.e. when excluding patients with elective stenting). Conclusions Elevated levels of PTSD symptoms caused by MI may adversely impact non-fatal cardiovascular outcome in post-MI patients independent of other important prognostic factors. The possible importance of PTSD symptoms as a novel prognostic psychosocial risk factor in post-MI patients warrants further study.

Timing of progression from Chlamydia trachomatis infection to pelvic inflammatory disease: a mathematical modelling study

Background Pelvic inflammatory disease (PID) results from the ascending spread of microorganisms from the vagina and endocervix to the upper genital tract. PID can lead to infertility, ectopic pregnancy and chronic pelvic pain. The timing of development of PID after the sexually transmitted bacterial infection Chlamydia trachomatis (chlamydia) might affect the impact of screening interventions, but is currently unknown. This study investigates three hypothetical processes for the timing of progression: at the start, at the end, or throughout the duration of chlamydia infection. Methods We develop a compartmental model that describes the trial structure of a published randomised controlled trial (RCT) and allows each of the three processes to be examined using the same model structure. The RCT estimated the effect of a single chlamydia screening test on the cumulative incidence of PID up to one year later. The fraction of chlamydia infected women who progress to PID is obtained for each hypothetical process by the maximum likelihood method using the results of the RCT. Results The predicted cumulative incidence of PID cases from all causes after one year depends on the fraction of chlamydia infected women that progresses to PID and on the type of progression. Progression at a constant rate from a chlamydia infection to PID or at the end of the infection was compatible with the findings of the RCT. The corresponding estimated fraction of chlamydia infected women that develops PID is 10% (95% confidence interval 7-13%) in both processes. Conclusions The findings of this study suggest that clinical PID can occur throughout the course of a chlamydia infection, which will leave a window of opportunity for screening to prevent PID.

Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study

Background New HIV infections in men who have sex with men (MSM) have increased in Switzerland since 2000 despite combination antiretroviral therapy (cART). The objectives of this mathematical modelling study were: to describe the dynamics of the HIV epidemic in MSM in Switzerland using national data; to explore the effects of hypothetical prevention scenarios; and to conduct a multivariate sensitivity analysis. Methodology/Principal Findings The model describes HIV transmission, progression and the effects of cART using differential equations. The model was fitted to Swiss HIV and AIDS surveillance data and twelve unknown parameters were estimated. Predicted numbers of diagnosed HIV infections and AIDS cases fitted the observed data well. By the end of 2010, an estimated 13.5% (95% CI 12.5, 14.6%) of all HIV-infected MSM were undiagnosed and accounted for 81.8% (95% CI 81.1, 82.4%) of new HIV infections. The transmission rate was at its lowest from 1995–1999, with a nadir of 46 incident HIV infections in 1999, but increased from 2000. The estimated number of new infections continued to increase to more than 250 in 2010, although the reproduction number was still below the epidemic threshold. Prevention scenarios included temporary reductions in risk behaviour, annual test and treat, and reduction in risk behaviour to levels observed earlier in the epidemic. These led to predicted reductions in new infections from 2 to 26% by 2020. Parameters related to disease progression and relative infectiousness at different HIV stages had the greatest influence on estimates of the net transmission rate. Conclusions/Significance The model outputs suggest that the increase in HIV transmission amongst MSM in Switzerland is the result of continuing risky sexual behaviour, particularly by those unaware of their infection status. Long term reductions in the incidence of HIV infection in MSM in Switzerland will require increased and sustained uptake of effective interventions.

Physical activity intensity and surrogate markers for cardiovascular health in adolescents

We examined the impact of physical activity (PA) on surrogate markers of cardiovascular health in adolescents. 52 healthy students (28 females, mean age 14.5 ± 0.7 years) were investigated. Microvascular endothelial function was assessed by peripheral arterial tonometry to determine reactive hyperemic index (RHI). Vagal activity was measured using 24 h analysis of heart rate variability [root mean square of successive normal-to-normal intervals (rMSSD)]. Exercise testing was performed to determine peak oxygen uptake ([Formula: see text]) and maximum power output. PA was assessed by accelerometry. Linear regression models were performed and adjusted for age, sex, skinfolds, and pubertal status. The cohort was dichotomized into two equally sized activity groups (low vs. high) based on the daily time spent in moderate-to-vigorous PA (MVPA, 3,000-5,200 counts(.)min(-1), model 1) and vigorous PA (VPA, >5,200 counts(.)min(-1), model 2). MVPA was an independent predictor for rMSSD (β = 0.448, P = 0.010), and VPA was associated with maximum power output (β = 0.248, P = 0.016). In model 1, the high MVPA group exhibited a higher vagal tone (rMSSD 49.2 ± 13.6 vs. 38.1 ± 11.7 ms, P = 0.006) and a lower systolic blood pressure (107.3 ± 9.9 vs. 112.9 ± 8.1 mmHg, P = 0.046). In model 2, the high VPA group had higher maximum power output values (3.9 ± 0.5 vs. 3.4 ± 0.5 W kg(-1), P = 0.012). In both models, no significant differences were observed for RHI and [Formula: see text]. In conclusion, in healthy adolescents, PA was associated with beneficial intensity-dependent effects on vagal tone, systolic blood pressure, and exercise capacity, but not on microvascular endothelial function.

Creation of Computer Simulation Model for Ecological Consequences Prognosis of Toxic Chemicals Discharge from Sunken on Baltic Sea Bottom Weapons"

This study summarises all the accessible data on old German chemical weapons dumped in the Baltic Sea. Mr. Goncharov formulated a concept of ecological impact evaluation of chemical warfare agents (CWA) on the marine environment and structured a simulation model adapted to the specific character of the hydrological condition and hydrobiological subjects of the Bornholm Deep. The mathematical model he has created describes the spreading of contaminants by currents and turbulence in the near bottom boundary layer. Parameters of CWA discharge through corrosion of canisters were given for various kinds of bottom sediments with allowance for current velocity. He created a method for integral estimations and a computer simulation model and completed a forecast for CWA "Mustard", which showed that in normal hydrometeorological conditions there are local toxic plumes drifting along the bottom for a distance of up to several kilometres. With storm winds the toxic plumes from separate canisters interflow and lengthen and can reach fishery areas near Bornholm Island. When salt water from the North Sea flows in, the length of toxic zones can increase up to and over 100 kilometres and toxic water masses can spread into the northern Baltic. On this basis, Mr. Goncharov drew up recommendations to reduce dangers for human ecology and proposed the creation of a special system for the forecasting and remote sensing of the environmental conditions of CWA burial places.

Impact of left ventricular hypertrophy late after aortic valve replacement for aortic stenosis on cardiovascular morbidity and mortality

AIMS: The goal of this study was to assess the prevalence of left ventricular (LV) hypertrophy in patients with aortic stenosis late (>6 months) after aortic valve replacement and its impact on cardiac-related morbidity and mortality. METHODS AND RESULTS: In a single tertiary centre, echocardiographic data of LV muscle mass were collected. Detailed information of medical history and angiographic data were gathered. Ninety-nine of 213 patients (46%) had LV hypertrophy late (mean 5.8 +/- 5.4 years) after aortic valve replacement. LV hypertrophy was associated with impaired exercise capacity, higher New York Heart Association dyspnoea class, a tendency for more frequent chest pain expressed as higher Canadian Cardiovascular Society class, and more rehospitalizations. 24% of patients with normal LV mass vs. 39% of patients with LV hypertrophy reported cardiac-related morbidity (p = 0.04). In a multivariate logistic regression model, LV hypertrophy was an independent predictor of cardiac-related morbidity (odds ratio 2.31, 95% CI 1.08 to 5.41), after correction for gender, baseline ejection fraction, and coronary artery disease and its risk factors. Thirty seven deaths occurred during a total of 1959 patient years of follow-up (mean follow-up 9.6 years). Age at aortic valve replacement (hazard ratio 1.85, 95% CI 1.39 to 2.47, for every 5 years increase in age), coexisting coronary artery disease at the time of surgery (hazard ratio 3.36, 95% CI 1.31 to 8.62), and smoking (hazard ratio 4.82, 95% CI 1.72 to 13.45) were independent predictors of overall mortality late after surgery, but not LV hypertrophy. CONCLUSIONS: In patients with aortic valve replacement for isolated aortic stenosis, LV hypertrophy late after surgery is associated with increased morbidity.

Predicting asthma control and exacerbations: chronic asthma as a complex dynamic model

PURPOSE OF REVIEW: Predicting asthma episodes is notoriously difficult but has potentially significant consequences for the individual, as well as for healthcare services. The purpose of this review is to describe recent insights into the prediction of acute asthma episodes in relation to classical clinical, functional or inflammatory variables, as well as present a new concept for evaluating asthma as a dynamically regulated homeokinetic system. RECENT FINDINGS: Risk prediction for asthma episodes or relapse has been attempted using clinical scoring systems, considerations of environmental factors and lung function, as well as inflammatory and immunological markers in induced sputum or exhaled air, and these are summarized here. We have recently proposed that newer mathematical methods derived from statistical physics may be used to understand the complexity of asthma as a homeokinetic, dynamic system consisting of a network comprising multiple components, and also to assess the risk for future asthma episodes based on fluctuation analysis of long time series of lung function. SUMMARY: Apart from the classical analysis of risk factor and functional parameters, this new approach may be used to assess asthma control and treatment effects in the individual as well as in future research trials.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.

Effects of an aging vascular model on healthy and diseased hearts

The vitamin D(3) and nicotine (VDN) model is a model of isolated systolic hypertension (ISH) due to arterial calcification raising arterial stiffness and vascular impedance similar to an aged and stiffened arterial tree. We therefore analyzed the impact of this aging model on normal and diseased hearts with myocardial infarction (MI). Wistar rats were treated with VDN (n = 9), subjected to MI by coronary ligation (n = 10), or subjected to a combination of both MI and VDN treatment (VDN/MI, n = 14). A sham-treated group served as control (Ctrl, n = 10). Transthoracic echocardiography was performed every 2 wk, whereas invasive indexes were obtained at week 8 before death. Calcium, collagen, and protein contents were measured in the heart and the aorta. Systolic blood pressure, pulse pressure, thoracic aortic calcium, and end-systolic elastance as an index of myocardial contractility were highest in the aging model group compared with MI and Ctrl groups (P(VDN) < 0.05, 2-way ANOVA). Left ventricular wall stress and brain natriuretic peptide (P(VDNxMI) = not significant) were highest, while ejection fraction, stroke volume, and cardiac output were lowest in the combined group versus all other groups (P(VDNxMI) < 0.05). The combination of ISH due to this aging model and MI demonstrates significant alterations in cardiac function. This model mimics several clinical phenomena of cardiovascular aging and may thus serve to further study novel therapies.

Depression, the metabolic syndrome and cardiovascular risk

BACKGROUND: The relationship between depression and the metabolic syndrome is unclear, and whether metabolic syndrome explains the association between depression and cardiovascular disease (CVD) risk is unknown. METHODS: We studied 652 women who received coronary angiography as part of the Women's Ischemia Syndrome Evaluation (WISE) study and completed the Beck Depression Inventory (BDI). Women who had both elevated depressive symptoms (BDI > or =10) and a previous diagnosis of depression were considered at highest risk, whereas those with one of the two conditions represented an intermediate group. The metabolic syndrome was defined according to the ATP-III criteria. The main outcome was incidence of adverse CVD events (hospitalizations for myocardial infarction, stroke, congestive heart failure, and CVD-related mortality) over a median follow-up of 5.9 years. RESULTS: After adjusting for demographic factors, lifestyle and functional status, both depression categories were associated with about 60% increased odds for metabolic syndrome compared with no depression (p = .03). The number of metabolic syndrome risk factors increased gradually across the three depression categories (p = .003). During follow-up, 104 women (15.9%) experienced CVD events. In multivariable analysis, women with both elevated symptoms and a previous diagnosis of depression had 2.6 times higher risk of CVD. When metabolic syndrome was added to the model, the risk associated with depression only decreased by 7%, and both depression and metabolic syndrome remained significant predictors of CVD. CONCLUSIONS: In women with suspected coronary artery disease, the metabolic syndrome is independently associated with depression but explains only a small portion of the association between depression and incident CVD.

Drug-induced respiratory depression: an integrated model of drug effects on the hypercapnic and hypoxic drive

Drug-induced respiratory depression is a common side effect of the agents used in anesthesia practice to provide analgesia and sedation. Depression of the ventilatory drive in the spontaneously breathing patient can lead to severe cardiorespiratory events and it is considered a primary cause of morbidity. Reliable predictions of respiratory inhibition in the clinical setting would therefore provide a valuable means to improve the safety of drug delivery. Although multiple studies investigated the regulation of breathing in man both in the presence and absence of ventilatory depressant drugs, a unified description of respiratory pharmacodynamics is not available. This study proposes a mathematical model of human metabolism and cardiorespiratory regulation integrating several isolated physiological and pharmacological aspects of acute drug-induced ventilatory depression into a single theoretical framework. The description of respiratory regulation has a parsimonious yet comprehensive structure with substantial predictive capability. Simulations relative to the synergistic interaction of the hypercarbic and hypoxic respiratory drive and the global effect of drugs on the control of breathing are in good agreement with published experimental data. Besides providing clinically relevant predictions of respiratory depression, the model can also serve as a test bed to investigate issues of drug tolerability and dose finding/control under non-steady-state conditions.

Mathematical analysis for perceived annoyance of impulsive sounds in terms of physical factors

From the customer satisfaction point of view, sound quality of any product has become one of the important factors these days. The primary objective of this research is to determine factors which affect the acceptability of impulse noise. Though the analysis is based on a sample impulse sound file of a Commercial printer, the results can be applied to other similar impulsive noise. It is assumed that impulsive noise can be tuned to meet the accepTable criteria. Thus it is necessary to find the most significant factors which can be controlled physically. This analysis is based on a single impulse. A sample impulsive sound file is tweaked for different amplitudes, background noise, attack time, release time and the spectral content. A two level factorial design of experiments (DOE) is applied to study the significant effects and interactions. For each impulse file modified as per the DOE, the magnitude of perceived annoyance is calculated from the objective metric developed recently at Michigan Technological University. This metric is based on psychoacoustic criteria such as loudness, sharpness, roughness and loudness based impulsiveness. Software called ‘Artemis V11.2’ developed by HEAD Acoustics is used to calculate these psychoacoustic terms. As a result of two level factorial analyses, a new objective model of perceived annoyance is developed in terms of above mentioned physical parameters such as amplitudes, background noise, impulse attack time, impulse release time and the spectral content. Also the effects of the significant individual factors as well as two level interactions are also studied. The results show that all the mentioned five factors affect annoyance level of an impulsive sound significantly. Thus annoyance level can be reduced under the criteria by optimizing the levels. Also, an additional analysis is done to study the effect of these five significant parameters on the individual psychoacoustic metrics.