Modeling of the biomechanical behavior and growth of the human uterus during pregnancy.

Premature birth poses a challenge to public health, with one in ten babies being born prematurely worldwide. The pathological distension of the uterus can create tension in the uterine wall, triggering contractions that may lead to birth, including premature birth. While there has been an increase in the use of computational models to study pregnancy in recent years, ethical challenges have limited research on the mechanical properties of the uterus during gestation. This study proposes a biomechanical model based on a stretch-driven growth mechanism to describe uterine evolution during the second half of the gestational period. The constitutive model employed is anisotropic, reflecting the presence of fibers in uterine tissue, and it is also considered incompressible. The geometric model representing the uterine body was derived from truncated ellipsoids, subject to intrauterine pressure as loading. Simulation results indicate that the proposed model is effective in reproducing growth patterns documented in the literature, such as simultaneous increases in intrauterine volume and uterine tissue volume, accompanied by a reduction in uterine wall thickness within limits reported in experimental data.

The Quixotic Task of Forecasting Peaks of COVID-19: Rather Focus on Forward and Backward Projections.

Over the last months, mathematical models have been extensively used to help control the COVID-19 pandemic worldwide. Although extremely useful in many tasks, most models have performed poorly in forecasting the pandemic peaks. We investigate this common pitfall by forecasting four countries' pandemic peak: Austria, Germany, Italy, and South Korea. Far from the peaks, our models can forecast the pandemic dynamics 20 days ahead. Nevertheless, when calibrating our models close to the day of the pandemic peak, all forecasts fail. Uncertainty quantification and sensitivity analysis revealed the main obstacle: the misestimation of the transmission rate. Inverse uncertainty quantification has shown that significant changes in transmission rate commonly precede a peak. These changes are a key factor in forecasting the pandemic peak. Long forecasts of the pandemic peak are therefore undermined by the lack of models that can forecast changes in the transmission rate, i.e., how a particular society behaves, changes of mitigation policies, or how society chooses to respond to them. In addition, our studies revealed that even short forecasts of the pandemic peak are challenging. Backward projections have shown us that the correct estimation of any temporal change in the transmission rate is only possible many days ahead. Our results suggest that the distance between a change in the transmission rate and its correct identification in the curve of active infected cases can be as long as 15 days. This is intrinsic to the phenomenon and how it affects epidemic data: a new case is usually only reported after an incubation period followed by a delay associated with the test. In summary, our results suggest the phenomenon itself challenges the task of forecasting the peak of the COVID-19 pandemic when only epidemic data is available. Nevertheless, we show that exciting results can be obtained when using the same models to project different scenarios of reduced transmission rates. Therefore, our results highlight that mathematical modeling can help control COVID-19 pandemic by backward projections that characterize the phenomena' essential features and forward projections when different scenarios and strategies can be tested and used for decision-making.