Simulating the physiology of athletes during endurance sports events: modelling human energy conversion and metabolism

Abstract

The human physiological system is stressed to its limits during endurance sports competition events. We describe a whole body computational model for energy conversion during bicycle racing. About 23 per cent of the metabolic energy is used for muscle work, the rest is converted to heat. We calculated heat transfer by conduction and blood flow inside the body, and heat transfer from the skin by radiation, convection and sweat evaporation, resulting in temperature changes in 25 body compartments. We simulated a mountain time trial to Alpe d'Huez during the Tour de France. To approach the time realized by Lance Armstrong in 2004, very high oxygen uptake must be sustained by the simulated cyclist. Temperature was predicted to reach 39°C in the brain, and 39.7°C in leg muscle. In addition to the macroscopic simulation, we analysed the buffering of bursts of high adenosine triphosphate hydrolysis by creatine kinase during cyclical muscle activity at the biochemical pathway level. To investigate the low oxygen to carbohydrate ratio for the brain, which takes up lactate during exercise, we calculated the flux distribution in cerebral energy metabolism. Computational modelling of the human body, describing heat exchange and energy metabolism, makes simulation of endurance sports events feasible.

Figure 1.

Scheme of the whole body model of heat transport. (a) The body is divided into six segments: head, trunk, arms, hands, legs and feet. Each segment consists of four layers approximated by concentric cylinders, except the head, which is a sphere. (b) Adapted from Stolwijk [5]. Heat is generated by metabolism, exchanged with the blood perfusing the layer and conducted to adjacent layers. Heat is dissipated from the skin by evaporation, but also by convection and radiation.

Figure 2.

Predictions of the main fates of metabolic energy converted in the muscle during the mountain time trial. (a) The increasing temperatures of leg muscles and brain reflect heat generation. The increasing air velocity across the skin during the time trial leads to significant cooling, but this effect becomes less at steeper slopes, where speed is diminished. (b) Power (in Watts) expended against gravity, air resistance and rolling resistance. The sharp spikes in the power against gravity are caused by the sharp transitions to different grades caused by the low resolution (1 km) by which the slope of the road to Alpe d'Huez was known to us: the cyclist enters a section with a steeper grade with high velocity and is subsequently slowed down by the increased opposing gravitational force. The cyclist finishes after 15.5 km in 39 min 41 s.

Figure 3.

(a) Scheme of the model of the creatine kinase (CK) system. Cell and mitochondrial membranes are indicated. Cr, creatine; PCr, phosphocreatine; Pi, inorganic phosphate; OxPhos, oxidative phosphorylation. (b) Steady-state metabolite concentrations at the end of a 600 s simulation compared with data from cycling exercise experiments at different submaximal workloads [26]. For conversion of metabolite concentrations between model (μmol l⁻¹ cell water) and data (mmol kg⁻¹ dry weight), we assumed an intracellular water content of 3 l kg⁻¹ dry muscle weight [27]. (c) Model prediction of the ATP synthesis time course at 100% (dashed line) and 2% (dotted line) of normal CK activity at a workload of 40% of VO₂max. The forcing function of pulsatile ATP hydrolysis is plotted as a solid line. Note that the last 2 s of a simulation over 600 s are shown ensuring a steady state. (b) Dark grey, data; light grey, model prediction. (c) Dashed line, ATP synthesis, 100% CK; dotted line, ATP synthesis, 2% CK; solid line, ATP hydrolysis.

Figure 4.

Models of carbon metabolism in brain. (a) Simulation of cerebral energy metabolism at rest and (b) during 15 min maximal exercise. Substrate uptake is from Quistorff et al. [44]. Flux values are in mmol min⁻¹ for the whole brain. PPP, pentose phosphate pathway; OxPhos, oxidative phosphorylation; GLC, glucose; PYR, pyruvate; LAC, lactate; GLU, glutamate; GABA, gamma-amino butyric acid; MAL, malate; OAA, oxaloacetate; SUCC, succinate; AKG, alpha-ketoglutarate; CIT, citrate; CoA, coenzyme A; G3P, glyceraldehyde-3-phosphate. Please note that for clarity not all reactions are shown and the metabolites are sometimes balanced by reactions that are not plotted. There is, for instance, a small backflux towards glucose in the upper part of the glycolytic chain in (b).