A mathematical model of regional citrate anticoagulation in hemodialysis

Regional citrate anticoagulation (RCA) during hemodialysis (HD) has several advantages over heparin anticoagulation, but calcium (Ca) derangements are a major concern necessitating repeated monitoring of systemic ionized Ca (Ca(2+)). We developed a mathematical model of Ca and citrate (Ci) kinetics during RCA.

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.

Viral load monitoring of antiretroviral therapy, cohort viral load and HIV transmission in Southern Africa: A mathematical modelling analysis

In low-income settings, treatment failure is often identified using CD4 cell count monitoring. Consequently, patients remain on a failing regimen, resulting in a higher risk of transmission. We investigated the benefit of routine viral load monitoring for reducing HIV transmission.

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.

Describing the progression from Chlamydia trachomatis and Neisseria gonorrhoeae to pelvic inflammatory disease: systematic review of mathematical modeling studies

Chlamydia screening is recommended to prevent pelvic inflammatory disease (PID). A systematic review was conducted to determine how the natural history of Chlamydia trachomatis or Neisseria gonorrhoeae infection and progression to PID have been described in mathematical modeling studies.

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.

Subconductance states of Cx30 gap junction channels: data from transfected HeLa cells versus data from a mathematical model

Human HeLa cells expressing mouse connexin30 were used to study the electrical properties of gap junction channel substates. Experiments were performed on cell pairs using a dual voltage-clamp method. Single-channel currents revealed discrete levels attributable to a main state, a residual state, and five substates interposed, suggesting the operation of six subgates provided by the six connexins of a gap junction hemichannel. Substate conductances, gamma(j,substate), were unevenly distributed between the main-state and the residual-state conductance (gamma(j,main state) = 141 pS, gamma(j,residual state) = 21 pS). Activation of the first subgate reduced the channel conductance by approximately 30%, and activation of subsequent subgates resulted in conductance decrements of 10-15% each. Current transitions between the states were fast (<2 ms). Substate events were usually demarcated by transitions from and back to the main state; transitions among substates were rare. Hence, subgates are recruited simultaneously rather than sequentially. The incidence of substate events was larger at larger gradients of V(j). Frequency and duration of substate events increased with increasing number of synchronously activated subgates. Our mathematical model, which describes the operation of gap junction channels, was expanded to include channel substates. Based on the established V(j)-sensitivity of gamma(j,main state) and gamma(j,residual state), the simulation yielded unique functions gamma(j,substate) = f(V(j)) for each substate. Hence, the spacing of subconductance levels between the channel main state and residual state were uneven and characteristic for each V(j).

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.