Distinguishing the effects of convective and diffusive O₂ delivery on VO₂ on-kinetics in skeletal muscle contracting at moderate intensity

Abstract

With current techniques, experimental measurements alone cannot characterize the effects of oxygen blood-tissue diffusion on muscle oxygen uptake (Vo₂) kinetics in contracting skeletal muscle. To complement experimental studies, a computational model is used to quantitatively distinguish the contributions of convective oxygen delivery, diffusion into cells, and oxygen utilization to Vo₂ kinetics. The model is validated using previously published experimental Vo₂ kinetics in response to slowed blood flow (Q) on-kinetics in canine muscle (τQ = 20 s, 46 s, and 64 s) [Goodwin ML, Hernández A, Lai N, Cabrera ME, Gladden LB. J Appl Physiol. 112:9-19, 2012]. Distinctive effects of permeability-surface area or diffusive conductance (PS) and Q on Vo₂ kinetics are investigated. Model simulations quantify the relationship between PS and Q, as well as the effects of diffusion associated with PS and Q dynamics on the mean response time of Vo₂. The model indicates that PS and Q are linearly related and that PS increases more with Q when convective delivery is limited by slower Q dynamics. Simulations predict that neither oxygen convective nor diffusive delivery are limiting Vo₂ kinetics in the isolated canine gastrocnemius preparation under normal spontaneous conditions during transitions from rest to moderate (submaximal) energy demand, although both operate close to the tipping point.

Keywords: diffusion; modeling; permeability-surface area; tipping point; transport.

Fig. 1.

Model simulation (lines) of skeletal muscle blood flow dynamics in response to contraction experiments under 3 conditions: CT20, EX45, and EX70. The vertical line denotes the time of transition between rest and contraction.

Fig. 2.

Experimental data (points) and model simulations (lines) of muscle C_a−v^T(t) (A) and V̇o₂(t) (B) in response to contraction experiments at 60% V̇o_{2 peak} from Goodwin et al. (11). Model simulations were obtained using previous monoexponential PS parameter values of PS_S = 200 l·l⁻¹·min⁻¹ and τ_PS = 20 s (44).

Fig. 3.

Experimental data (points) and model simulations (lines) of muscle C_a−v^T(t) (A) and V̇o₂(t) (B) in response to contraction experiments at 60% V̇o_{2 peak} from Goodwin et al. (11). Model simulations were obtained using PS linearly related to Q with optimally estimated η = 3.3 l·100 g·ml⁻¹·l⁻¹ from EX70.

Fig. 4.

Experimental data (points) and model simulations (lines) of muscle C_a−v^T(t) (A) and V̇o₂(t) (B) in response to contraction experiments at 60% V̇o_{2 peak} from Goodwin et al. (11). Model simulations were obtained using PS linearly related to Q with optimally estimated η = 3.3 l·100 g·ml⁻¹·l⁻¹ for EX70, η = 2.7 l·100 g·ml⁻¹·l⁻¹ for EX45, and η = 2.4 l·100 g·ml⁻¹·l⁻¹ for CT20.

Fig. 5.

Model simulations of the increase of J_O2^b,c (A) and PS (B) during contraction, and the optimally fitted relationships between Q and PS (C) for case 3.

Fig. 6.

Model predictions (lines) of the effect of τ_Q on MRT(V̇o₂). From experimental data, MRT(V̇o₂) calculated by Goodwin et al. (11) shown as closed squares. Dotted line monoexponential PS function with τ_PS = 20 s and PS_S = 200 l l⁻¹ min⁻¹. Solid and dashed lines with PS linearly related to Q and η = 3.3 and 2.4 l 100 g ml⁻¹ l⁻¹, respectively.

Fig. 7.

Model predictions of the effect of τ_PS on MRT(V̇o₂). Solid line with PS_S = 170 l·l⁻¹·min⁻¹; dashed line with PS_S increased by 30%; dotted line with PS_S decreased by 30%.

Fig. 8.

Model predictions of the effect of τ_PS on MRT(V̇o₂). A: solid line with τ_Q = 20 s; dashed line with τ_Q = 45 s; dotted line with τ_Q = 70 s. B: solid line with V_max,OxP = 10.4 mM/min; dashed line with V_max,OxP increased by 30%; dotted line with V_max,OxP decreased by 30%.