The proportionality constant varied with activity, possibly reflecting differences in the aspects of muscular contraction, fiber types, or mechanical advantage in each activity. It is speculated that a more general relation could be obtained if biomechanical analyses to account for other factors, such as contraction length, were included.

To address the limitations of regression-based performance models, the literature describes a fatigue model that reduces the complexities of motor unit activation into a set of first-order differential equations requiring only a few parameters to capture the global effects of activation physiology (M0: maximal force-generating capacity, F: fatigue rate, R: recovery rate). However, there are no solutions to the general form of the equations, which limits its applicability. We formulate an algorithm that allows the equations to be solved if an arbitrary force profile is specified. Furthermore, we support the validity of the model, applying it to exercises found in the literature including quadriceps contractions (M0=954±326 N, F=2.5±0.4%·s(-1), R=0.3±0.3%·s(-1)), cycling (M0=1095±486 W, F=3.5±0.3%·s(-1), R=1.1±0.3%·s(-1)) and running (M0=9.2±1.2 m·s(-1), F=0.9±0.4%·s(-1), R=1.0±0.3%·s(-1)), where effective muscle forces are converted to cycling power and running speed. The model predicts muscle output for 10 maximum efforts and 32 endurance tests, where the coefficient of determination (R2) ranged from 0.81 to 1.00. These results support the hypothesis found in the literature that motor unit activation and fatigue mechanisms lead to a cumulative muscle fatigue effect that can be observed in exercise performance.

The performance dynamic physiology model (DPM-PE) integrates a modified muscle fatigue model with an exercise physiology model that calculates the transport and delivery of oxygen to working muscles during exposures of oxygen-limiting environments. This mathematical model implements a number of physiologic processes (respiration, circulation, tissue metabolism, diffusion-limited gas transfer at the blood/gas lung interface, and ventilatory control with afferent feedback, central command and humoral chemoreceptor feedback) to replicate the three phases of ventilatory response to a variety of exertion patterns, predict the delivery and transport of oxygen and carbon dioxide from the lungs to tissues, and calculate the amount of aerobic and anaerobic work performed. The ventilatory patterns from passive leg movement, unloaded work, and stepped and ramping loaded work compare well against data. The model also compares well against steady-state ventilation, cardiac output, blood oxygen levels, oxygen consumption, and carbon dioxide generation against a range of exertion levels at sea level and at altitude, thus demonstrating the range of applicability of the exercise model. With the ability to understand and predict gas transport and delivery of oxygen to working muscle tissue for different workloads and environments, the correlation between blood oxygen measures and the recovery factor of the muscle fatigue model was explored. Endurance data sets in normoxia and hypoxia were best replicated using arterial oxygen saturation as the correlate with the recovery factor. This model provides a physiologically based method for predicting physical performance decrement due to oxygen-limiting environments.

BackgroundThis work expands upon a previously developed exercise dynamic physiology model (DPM) with the addition of an anatomic pulmonary system in order to quantify the impact of lung damage on oxygen transport and physical performance decrement.MethodsA pulmonary model is derived with an anatomic structure based on morphometric measurements, accounting for heterogeneous ventilation and perfusion observed experimentally. The model is incorporated into an existing exercise physiology model; the combined system is validated using human exercise data. Pulmonary damage from blast, blunt trauma, and chemical injury is quantified in the model based on lung fluid infiltration (edema) which reduces oxygen delivery to the blood. The pulmonary damage component is derived and calibrated based on published animal experiments; scaling laws are used to predict the human response to lung injury in terms of physical performance decrement.ResultsThe augmented dynamic physiology model (DPM) accurately predicted the human response to hypoxia, altitude, and exercise observed experimentally. The pulmonary damage parameters (shunt and diffusing capacity reduction) were fit to experimental animal data obtained in blast, blunt trauma, and chemical damage studies which link lung damage to lung weight change; the model is able to predict the reduced oxygen delivery in damage conditions. The model accurately estimates physical performance reduction with pulmonary damage.ConclusionsWe have developed a physiologically-based mathematical model to predict performance decrement endpoints in the presence of thoracic damage; simulations can be extended to estimate human performance and escape in extreme situations.

Unlike a statistical approach, a phenomenological model accounts for physiological changes and, therefore, has the potential to not only identify trainees at risk of failing BCT on novel training regimens, but offer guidance to regimen planners on how to change the regimen for maximizing physical performance. This paper is Part I of a 2-part series on physical training outcome predictions.