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.

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.

Reinfection by untreated partners of people treated for Chlamydia trachomatis and Neisseria gonorrhoeae: mathematical modelling study

OBJECTIVES Reinfection after treatment for Chlamydia trachomatis or Neisseria gonorrhoeae reduces the effect of control interventions. We explored the impact of delays in treatment of current partners on the expected probability of reinfection of index cases using a mathematical model. METHODS We used previously reported parameter distributions to calculate the probability that index cases would be reinfected by their untreated partners. We then assumed different delays between index case and partner treatment to calculate the probabilities of reinfection. RESULTS In the absence of partner treatment, the medians of the expected reinfection probabilities are 19.4% (IQR 9.2-31.6%) for C trachomatis and 12.5% (IQR 5.6-22.2%) for N gonorrhoeae. If all current partners receive treatment 3 days after the index case, the expected reinfection probabilities are 4.2% (IQR 2.1-6.9%) for C trachomatis and 5.5% (IQR 2.6-9.5%) for N gonorrhoeae. CONCLUSIONS Quicker partner referral and treatment can substantially reduce reinfection rates for C trachomatis and N gonorrhoeae by untreated partners. The formula we used to calculate reinfection rates can be used to inform the design of randomised controlled trials of novel partner notification technologies like accelerated partner therapy.

Direct and indirect effects of screening for Chlamydia trachomatis on the prevention of pelvic inflammatory disease: a mathematical modeling study

BACKGROUND Pelvic inflammatory disease (PID) results from the ascending spread of microorganisms, including Chlamydia trachomatis, to the upper genital tract. Screening could improve outcomes by identifying and treating chlamydial infections before they progress to PID (direct effect) or by reducing chlamydia transmission (indirect effect). METHODS We developed a compartmental model that represents a hypothetical heterosexual population and explicitly incorporates progression from chlamydia to clinical PID. Chlamydia screening was introduced, with coverage increasing each year for 10 years. We estimated the separate contributions of the direct and indirect effects of screening on PID cases prevented per 100,000 women. We explored the influence of varying the time point at which clinical PID could occur and of increasing the risk of PID after repeated chlamydial infections. RESULTS The probability of PID at baseline was 3.1% by age 25 years. After 5 years, the intervention scenario had prevented 187 PID cases per 100,000 women and after 10 years 956 PID cases per 100,000 women. At the start of screening, most PID cases were prevented by the direct effect. The indirect effect produced a small net increase in PID cases, which was outweighed by the effect of reduced chlamydia transmission after 2.2 years. The later that progression to PID occurs, the greater the contribution of the direct effect. Increasing the risk of PID with repeated chlamydial infection increases the number of PID cases prevented by screening. CONCLUSIONS This study shows the separate roles of direct and indirect PID prevention and potential harms, which cannot be demonstrated in observational studies.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Transmission dynamics of Chlamydia trachomatis affect the impact of screening programmes

To assess the impact of screening programmes in reducing the prevalence of Chlamydia trachomatis, mathematical and computational models are used as a guideline for decision support. Unfortunately, large uncertainties exist about the parameters that determine the transmission dynamics of C. trachomatis. Here, we use a SEIRS (susceptible-exposed-infected-recovered-susceptible) model to critically analyze the turnover of C. trachomatis in a population and the impact of a screening programme. We perform a sensitivity analysis on the most important steps during an infection with C. trachomatis. Varying the fraction of the infections becoming symptomatic as well as the duration of the symptomatic period within the range of previously used parameter estimates has little effect on the transmission dynamics. However, uncertainties in the duration of temporary immunity and the asymptomatic period can result in large differences in the predicted impact of a screening programme. We therefore analyze previously published data on the persistence of asymptomatic C. trachomatis infection in women and estimate the mean duration of the asymptomatic period to be longer than anticipated so far, namely 433 days (95% CI: 420-447 days). Our study shows that a longer duration of the asymptomatic period results in a more pronounced impact of a screening programme. However, due to the slower turnover of the infection, a substantial reduction in prevalence can only be achieved after screening for several years or decades.

Towards More Robust Estimates of the Transmissibility of Chlamydia trachomatis

There is a lack of a common concept on how to estimate transmissibility of Chlamydia trachomatis from cross-sectional sexual partnership studies. Using a mathematical model that takes into account the dynamics of chlamydia transmission and sexual partnership formation, we report refined estimates of chlamydia transmissibility in heterosexual partnerships.

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.

Cost effectiveness of home based population screening for Chlamydia trachomatis in the UK: economic evaluation of chlamydia screening studies (ClaSS) project

OBJECTIVE: To investigate the cost effectiveness of screening for Chlamydia trachomatis compared with a policy of no organised screening in the United Kingdom. DESIGN: Economic evaluation using a transmission dynamic mathematical model. SETTING: Central and southwest England. PARTICIPANTS: Hypothetical population of 50,000 men and women, in which all those aged 16-24 years were invited to be screened each year. MAIN OUTCOME MEASURES: Cost effectiveness based on major outcomes averted, defined as pelvic inflammatory disease, ectopic pregnancy, infertility, or neonatal complications. RESULTS: The incremental cost per major outcome averted for a programme of screening women only (assuming eight years of screening) was 22,300 pounds (33,000 euros; $45,000) compared with no organised screening. For a programme screening both men and women, the incremental cost effectiveness ratio was approximately 28,900 pounds. Pelvic inflammatory disease leading to hospital admission was the most frequently averted major outcome. The model was highly sensitive to the incidence of major outcomes and to uptake of screening. When both were increased the cost effectiveness ratio fell to 6200 pound per major outcome averted for screening women only. CONCLUSIONS: Proactive register based screening for chlamydia is not cost effective if the uptake of screening and incidence of complications are based on contemporary empirical studies, which show lower rates than commonly assumed. These data are relevant to discussions about the cost effectiveness of the opportunistic model of chlamydia screening being introduced in England.

Individual and population level effects of partner notification for Chlamydia trachomatis

Partner notification (PN or contact tracing) is an important aspect of treating bacterial sexually transmitted infections (STIs), such as Chlamydia trachomatis. It facilitates the identification of new infected cases that can be treated through individual case management. PN also acts indirectly by limiting onward transmission in the general population. However, the impact of PN, both at the level of individuals and the population, remains unclear. Since it is difficult to study the effects of PN empirically, mathematical and computational models are useful tools for investigating its potential as a public health intervention. To this end, we developed an individual-based modeling framework called Rstisim. It allows the implementation of different models of STI transmission with various levels of complexity and the reconstruction of the complete dynamic sexual partnership network over any time period. A key feature of this framework is that we can trace an individual's partnership history in detail and investigate the outcome of different PN strategies for C. trachomatis. For individual case management, the results suggest that notifying three or more partners from the preceding 18 months yields substantial numbers of new cases. In contrast, the successful treatment of current partners is most important for preventing re-infection of index cases and reducing further transmission of C. trachomatis at the population level. The findings of this study demonstrate the difference between individual and population level outcomes of public health interventions for STIs.

Screening and treatment to prevent sequelae in women with Chlamydia trachomatis genital infection: how much do we know?

Background. An important question for chlamydia control programs is the extent to which finding and treating prevalent, asymptomatic Chlamydia trachomatis genital infection reduces reproductive sequelae in infected women. Methods. We reviewed the literature to critically evaluate evidence on the effect of chlamydia screening on development of sequelae in infected women. Results. Two randomized controlled trials of 1-time screening for chlamydial infection—in a Seattle-area health maintenance organization and a Danish school district—revealed that screening was associated with an ∼50% reduction in the incidence of pelvic inflammatory disease over the following year. However, both of these trials had methodological issues that may have affected the magnitude of observed screening benefits and might limit generalizability to other populations. A large, nonrandomized cohort of chlamydia screening among US Army recruits, although limited by lack of outpatient data, did not find a benefit of similar magnitude to the randomized trials. Methodological limitations restrict valid conclusions about individual benefits of screening using data from historical cohorts and ecological studies. We identified no trials directly evaluating the effect of chlamydia screening on subclinical tubal inflammation or damage, ectopic pregnancy, or tubal factor infertility and no studies addressing the effects of >1 round of screening, the optimal frequency of screening, or the benefits of screening for repeat infections. Conclusions. Additional studies of the effectiveness of chlamydia screening would be valuable; feasible study designs may depend on the degree to which screening programs are already established. In addition, better natural history data on the timing of tubal inflammation and damage after C. trachomatis infection and development of more accurate, noninvasive tools to assess chlamydial sequelae are essential to informing chlamydia control efforts.

Risk of sequelae after Chlamydia trachomatis genital infection in women

Chlamydia trachomatis infection, the most common reportable disease in the United States, can lead to pelvic inflammatory disease (PID), infertility, ectopic pregnancy, and chronic pelvic pain. Although C. trachomatis is identified among many women who receive a diagnosis of PID, the incidence and timing of PID and long-term sequelae from an untreated chlamydial infection have not been fully determined. This article examines evidence reviewed as part of the Centers for Disease Control and Prevention Chlamydia Immunology and Control Expert Advisory Meeting; 24 reports were included. We found no prospective studies directly assessing risk of long-term reproductive sequelae, such as infertility, after untreated C. trachomatis infection. Several studies assessed PID diagnosis after untreated chlamydial infection, but rates varied widely, making it difficult to determine an overall estimate. In high-risk settings, 2%-5% of untreated women developed PID within the approximately 2-week period between testing positive for C. trachomatis and returning for treatment. However, the rate of PID progression in the general, asymptomatic population followed up for longer periods appeared to be low. According to the largest studies, after symptomatic PID of any cause has occurred, up to 18% of women may develop infertility. In several studies, repeated chlamydial infection was associated with PID and other reproductive sequelae, although it was difficult to determine whether the risk per infection increased with each recurrent episode. The present review critically evaluates this body of literature and suggests future research directions. Specifically, prospective studies assessing rates of symptomatic PID, subclinical tubal damage, and long-term reproductive sequelae after C. trachomatis infection; better tools to measure PID and tubal damage; and studies on the natural history of repeated chlamydial infections are needed.

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.

Transmission of Chlamydia trachomatis through sexual partnerships: a comparison between three individual-based models and empirical data

Chlamydia trachomatis is the most common bacterial sexually transmitted infection (STI) in many developed countries. The highest prevalence rates are found among young adults who have frequent partner change rates. Three published individual-based models have incorporated a detailed description of age-specific sexual behaviour in order to quantify the transmission of C. trachomatis in the population and to assess the impact of screening interventions. Owing to varying assumptions about sexual partnership formation and dissolution and the great uncertainty about critical parameters, such models show conflicting results about the impact of preventive interventions. Here, we perform a detailed evaluation of these models by comparing the partnership formation and dissolution dynamics with data from Natsal 2000, a population-based probability sample survey of sexual attitudes and lifestyles in Britain. The data also allow us to describe the dispersion of C. trachomatis infections as a function of sexual behaviour, using the Gini coefficient. We suggest that the Gini coefficient is a useful measure for calibrating infectious disease models that include risk structure and highlight the need to estimate this measure for other STIs.