We computationally evaluated the contribution of fiber type composition and fiber type-specific parameters to spatial heterogeneity of tissue oxygenation. These parameters include: fiber type-dependent oxygen consumption (Mc
), oxygen diffusivity in fiber (DO2
), myoglobin concentration (CMb
), fiber size, and number of capillaries around a fiber (NCAF). To understand the effects of each factor separately as well as their combined effects, we ran a series of computational experiments to examine the heterogeneity of oxygen distribution in skeletal muscle during exercise in different muscle geometries (G1–G4) and with scenarios varying a number of the other factors under consideration (S1–S5). The annotations for each simulation are summarized in . For example, G3S1 refers to G3 geometry (non-uniform fiber size and uniform capillary distribution) with scenario S1 (uniform Mc
, and CMb
). The corresponding microvascular and fiber structures are shown in (G1), 1D (G2), 2C (G3) and 2D (G4), representing the same location in networks (z
400 µm). The three-dimensional geometry of G1 is shown in and that of G3 in . The number of capillaries around a fiber (NCAF) for each of the simulation geometries is shown in Table S1. In the following sections, we report the mean and the coefficient of variation (CV) of the tissue oxygen profile as a measure of the heterogeneity in the tissue for each simulation.
List of simulation annotations.
It is worth noting that microvascular hemodynamics is a well-known important determinant of tissue oxygenation and it is not the focus of this study. Our blood flow simulations suggest that these vascular networks in two geometries (G1 and G2) share similar distribution patterns of blood flow velocity and hematocrit, and have similar total blood volume flow rates (see Table S2 and Fig. S1
). In addition, vascular networks G3 and G4 share similar microvascular blood flow and red blood cell distribution (Table S2 and Fig. S2
Capillary distribution is an important determinant of oxygen distribution
For the G1 and G2 geometries (uniform fiber size; ) we first computed the steady-state tissue oxygen distribution without consideration for fiber type composition, not varying O2 consumption rates, O2 diffusivities, and myoglobin concentrations in different fiber types. In other words, uniform fibers with the same parameters: volume-averaged Mc (3.34, 6.68, 10.02×10−4 mlO2 ml−1 s−1 for low, moderate, high intensity exercise), DO2 (1.72×10−5 mlO2 ml−1 s−1), and CMb (5.7×10−3 mlO2 ml−1 s−1) were used for every fiber in the simulation. In this case, with light intensity exercise, an increase in the heterogeneity of microvascular structure (G2 compared to G1), and therefore in the heterogeneity of oxygen supply, is predicted to lead to a slight increase in the heterogeneity of O2 (CVG1S1: 0.09, CVG2S1: 0.10) and a slight lowering of mean tissue PO2 level (PG1S1: 28.9 mmHg, PG2S1: 27.6 mmHg) ( and ). In exercise of moderate or high intensity, the increase in oxygen consumption levels causes even greater heterogeneity. When capillaries are non-uniformly distributed around the fibers (, solid lines), the variation further increases; mean PO2 levels decrease from 17.4 to 15.1 mmHg (moderate intensity exercise), and from 8.84 to 6.82 mmHg (high intensity exercise). These results indicate that capillary distribution in muscle tissue affects non-uniform oxygen distribution and heterogeneity.
PO2 histograms for muscle geometries with uniform-size fibers under exercising conditions.
Effects of fiber type properties on oxygen (PO2) distribution.
Fiber type composition does not contribute significantly to oxygen distribution
We then computed steady-state tissue oxygen distribution in geometries G1 and G2 when fiber type composition and varying Mc, DO2, and CMb in different fiber types (fiber type-specific parameters shown in ) are considered; in other words, all fiber-type-specific parameters except for size. The simulation results with fiber type composition considered (scenario S2) were compared to uniform properties (scenario S1) (). shows the histogram of muscle fiber PO2 in two muscle geometries (G1 and G2). summarizes the key characteristics from all the simulation results of PO2 distribution under different intensities of exercise in G1 and G2.
At all levels of exercise, the difference in oxygen distribution between the heterogeneous fiber-type specific parameters (S2) and the uniform fiber parameters (S1, control cases) is minimal (, red vs. black lines). This includes the mean, range and variance of oxygen levels and the portion of tissue that is hypoxic, i.e. with PO2<1 or 2% (). For example, compared to the control cases with uniform fiber properties (i.e. G1S1, G2S1), the effect of fiber type composition on oxygen spatial heterogeneity and mean PO2 level is small when muscles are stimulated with light or moderate exercise intensity (e.g., for light exercise, CV for the geometry with uniform capillary distribution, CVG1S2/S1: ~0.09, CV for the geometry with fiber-type-specific capillary distribution, CVG2S2/S1: ~0.10, PG1S2/S1: ~28.9 mmHg, PG2S2/S1: ~27.6 mmHg). Under high intensity exercise conditions, oxygen spatial heterogeneity changes slightly compared to control cases (i.e. G1S1, G2S1) (CVG1S2/S1: 0.56 vs. 0.59; CVG2S2/S1 : 0.65 vs. 0.68) and mean PO2 remains at the same levels (PO2 G1S2/S1: 8.8 vs. 8.5 mmHg, high;PO2 G2S2/S1: 6.8 vs. 6.6 mmHg, high). The oxygen distribution is much more dependent on capillary distribution (, solid vs. dotted lines) than on heterogeneity of fiber properties (, red vs. black lines).
Non-uniform fiber size significantly enhances the heterogeneity in oxygen distribution
To investigate the effect of fiber size on oxygen distribution in the EDL, we constructed geometries G3 and G4 (), with non-uniform size fibers within the same dimension cuboid (358×233×800 µm3) and the same total fiber volume (79%) as G1 and G2 (). We first compared the tissue PO2 profile in geometry G3S1 with heterogeneous fiber sizes to the profile in geometry G1S1 with homogeneous fiber sizes. Both of them use uniform fiber type properties (scenario S1, i.e., Mc, DO2, CMb) and have uniform capillary distribution. Our oxygen transport simulation results suggest that fiber size distribution in muscle geometry plays an important role in determining tissue oxygen profile and spatial heterogeneity. shows that PO2 in heterogeneous fiber size geometry is much more broadly distributed compared to the control case (i.e., G1S1) with uniform size fiber under all exercise conditions (G3S1 vs. G1S1, black dashed lines in vs. ; 3D graphical representation shown in ). Heterogeneous fiber size distribution shifts tissue PO2 to lower values (mean PO2 from 28.9 to 26.5 mmHg, light exercise; 17.1 vs. 13.6 mmHg, moderate; 8.84 vs. 6.96 mmHg, high), and increases its spatial heterogeneity (0. 09 vs. 0.14, light; 0.26 vs. 0.42, moderate; 0.56 vs. 0.71, high). Under high intensity exercise conditions, the proportion of hypoxic tissue is much larger than in control case (18% vs. 7%).
PO2 histograms for muscle geometries with non-uniform-size fibers under exercise conditions.
3D PO2 distribution in skeletal muscle.
We further examined the effects of fiber-type-specific properties on oxygen distribution in the non-uniform size fiber geometries (geometries G3 and G4, results in and ). Conclusions similar to those described above can be drawn from these data. First, oxygen distribution is sensitive to local capillary distribution around the fibers. However, their effects are different from previous case with uniform size fiber distribution (, solid vs. dashed lines). With fiber-type-dependent capillary distribution (smaller fibers have more adjacent capillaries), the coefficients of variation of the tissue PO2 profiles under light exercise conditions are slightly decreased compared to the tissue with uniform capillary distribution (CV: 0.14 vs. 0.12, light; 0.42 vs. 0.42, moderate), and their mean PO2 levels shift to slightly lower values (PO2: 26.47 vs. 26.09 mmHg, light; 13.56 vs. 12.54 mmHg). Second, with the consideration of all fiber type properties (scenario S2) and fiber size, tissue PO2 profiles do not change significantly from tissue PO2 profiles computed using the uniform fiber properties. This conclusion is based on the comparisons of tissues PO2 in geometries with uniform/non-uniform capillary distribution in and three-dimensional graphical representation in . There are only slight differences between black and red lines (including dashed and solid cases) at all exercise intensities, with one exception: under high intensity exercise and with fiber-type-specific capillary distribution, heterogeneous fiber type composition increases spatial heterogeneity (CV: 0.81 vs. 1.00) and reduces its tissue PO2 level (PO2: 5.93 vs. 3.22 mmHg).
Effects of fiber type properties and fiber size on oxygen (PO2) distribution.
We further studied the distribution of average PO2 for each fiber from three fiber type groups under various cases (). This shows that under light intensity exercise, the difference in average fiber PO2 level among the three fiber type groups is low. With the increase of exercise intensity (to moderate and high intensity), fibers of type I have higher local oxygenation levels than types IIa and IIb. With fiber-type specific capillary distribution (G4 vs. G3), the oxygenation levels increase for oxidative fibers type I and type IIa, but decrease for type IIb. Therefore, at high intensity exercise conditions, the difference of PO2 levels between fiber type IIb and fiber type I increased significantly, suggesting that local oxygen supply matches local demand well for oxidative fiber but not glycolytic fiber in exercise. Greater heterogeneity of average PO2 level in each fiber type was also observed for higher exercise intensities and with capillary heterogeneity.
Distribution of average PO2 levels of individual fibers in skeletal muscle under exercise conditions.
Fiber-type-specific Mc and DO2, but not CMb, cause greater heterogeneity in oxygen distribution
We next investigated the contribution of the heterogeneity of each fiber-type-dependent variable by itself (Mc
, and CMb
) to tissue PO2
spatial heterogeneity. To do this, we performed simulations for the non-uniform fiber size geometry with alterations of the factor to be considered (scenarios S3–S5; see for a detailed description). Control cases were simulated with uniform fiber properties for comparison. , , and show the simulation results for the effects of Mc
heterogeneity in different fiber types. The results indicate that the heterogeneity of Mc
in different fiber types (, black vs. red lines) will shift mean PO2
levels to lower values (e.g. G3S1 vs. G3S3, 26.5 vs. 25.4 mmHg, light; 13.6 vs. 12.3 mmHg, moderate; 6.9 vs. 5.9 mmHg, high; ), and increase its spatial heterogeneity at all exercise conditions (e.g. G3S1 vs. G3S3, 0.10 vs. 0.16, light; 0.29 vs. 0.48, moderate; 0.65 vs. 0.80, high; ). shows that the tissue oxygen levels are distributed in a much broader range. Incorporation of heterogeneity of oxygen diffusivity in different fiber types (, black vs. red lines) also affects tissue oxygen profiles. The PO2
spatial heterogeneity increased significantly for both G3 (dashed lines) and G4 (solid lines) geometries. However, incorporation of heterogeneity of oxygen diffusivity in different fiber types causes a small increase in the mean PO2
level (e.g., G3S1vs G3S4, 26.5 vs. 27.5 mmHg, light; 13.6 vs. 15.04 mmHg, moderate; 6.9 vs. 7.6 mmHg, high; ). Lastly, comparison of simulation results for G3 and G4 geometries with incorporation of myoglobin concentration variation in different fiber types (, black vs. red lines) to control cases indicates that the contribution of CMb
heterogeneity to PO2
spatial heterogeneity is small ( and ). Further investigation of the sensitivity of PO2
profile to myoglobin-facilitated diffusion by using a much smaller DMb
/s, i.e. 7 orders of magnitude lower) shows that the tissue PO2
profile with no myoglobin-facilitated diffusion does not deviate significantly from control cases at all exercise conditions (Fig. S3
Effects of variation of oxygen consumption rate in different fiber types on PO2 histograms.
Effects of variation of oxygen diffusivity in different fiber types on PO2 histograms.
Effects of variation of myoglobin concentration in different fiber types on PO2 histograms.
Effects of heterogeneities of Mc, DO2, and CMb on oxygen (PO2) distribution.