Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid-dynamics model of the pulmonary circulation

Stochastic modeling of obesity status in United States adults using Markov Chains: A nationally representative analysis of population health data from 2017-2020

Importance

The prevalence of obesity among United States adults has increased from 34.9% in 2013-2014 to 42.8% in 2017-2018. Developing methods to model the increase of obesity over-time is a necessity to know how to accurately quantify its cost and to develop solutions to combat this national public health emergency.

Methods

A cross-sectional cohort study using the publicly available National Health and Nutrition Examination Survey (NHANES 2017-2020) was conducted in individuals who completed the weight questionnaire and had accurate data for both weight at the time of survey and weight 10 years ago. To model the dynamics of obesity, a Markov transition state matrix was created, which allowed for the analysis of weight transitions over time. Bootstrap simulation was incorporated to account for uncertainty and generate multiple simulated datasets, providing a more robust estimation of the prevalence and trends in obesity within the cohort.

Results

Of the 6146 individuals who met the inclusion criteria, 3024 (49%) individuals were male and 3122 (51%) were female. There were 2252 (37%) White individuals, 1257 (20%) Hispanic individuals, 1636 (37%) Black individuals, and 739 (12%) Asian individuals. The average BMI was 30.16 (SD = 7.15), the average weight was 83.67 kilos (SD = 22.04), and the average weight change was a 3.27 kg (SD = 14.97) increase in body weight. A total of 2411 (39%) individuals lost weight, and 3735 (61%) individuals gained weight. 87 (1%) individuals were underweight (BMI <18.5), 2058 (33%) were normal weight (18.5 ≤ BMI <25), 1376 (22%) were overweight (25 ≤ BMI <30) and 2625 (43%) were in the obese category (BMI >30).

Conclusion

United States adults are at risk of transitioning from normal weight to the overweight or obese category. Markov modeling combined with bootstrap simulations can accurately model long-term weight status.

Inverse problems in blood flow modeling: A review

Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.