Fig 1.
Diagram of the simulation workflows.
Computed inverse kinematics, inverse dynamics, muscle-tendon length, and moment arms are inputs for all the simulation workflows. In simulation GEN, the performance criterion is the sum of squared muscle activations, the muscle force (FM) is the product of the maximum isometric force () and the muscle activation (a), force-velocity (fv), active force-length (fl) and passive force-length (fp) relationships, and tendon force is the product of the maximum isometric force and the tendon force-length (ft) relationship. In simulation PAS, passive force-length relationship (
) is updated based on the calibration of passive joint angle-moment relationships in the generic musculoskeletal model. In simulation TEN, the tendon force-length relationship (
) is updated based on personalized tendon stiffness values. In simulation EMG, the performance criterion incorporates a term to track experimental EMGs.
Fig 2.
Metabolic rates in the soleus at different levels of muscle activations during shortening, isometric, and concentric contractions (first row), and metabolic (), work (
), and heat (
) rates during walking (second and thrid row).
Metabolic rates were computed using six models: Umberger et al. [14] (UM03), Bhargava et al. [12] (BH04), Houdijk et al. [15] (HO06), Lichtwark and Wilson [16] (LW07), Umberger [17] (UM10), and Uchida et al. [18] (UC16). The ratio of slow twitch muscle fiber, muscle mass, optimal fiber length, and maximum voluntary contraction is assumed as 0.8, 0.48 kg, 4.5 cm, and 10 [optimal fiber lengths/second], respectively. Simulated muscle metabolic rate as computed from one representative subject walking at preferred speed.
Fig 3.
Computed and experimental muscle excitations and fiber lengths.
Muscle excitations of biceps femoris long head (BF), semitendinosus (ST), vastus lateralis (VL), vastus medialis (VM), tibialis anterior (TA), gastrocnemius lateralis (GL), gastrocnemius medialis (GM) and soleus (SO) during the gait cycle at preferred walking speed (PWS) (left) and normalized fiber lengths of vastus lateralis, gastrocnemius lateralis, gastrocnemius medialis, and soleus during the gait cycle across walking speeds with four simulation workflows: Minimal muscle effort with generic passive force (GEN), with calibrated passive force (PAS), with calibrated passive force and personalized tendon stiffness (TEN), and EMG-informed with calibrated passive force and personalized tendon stiffness (EMG). Simulated muscle excitations and normalized fiber lengths represent the average values among all subjects. Measured EMGs represented the average values among all subjects and were scaled using optimization variables in EMG. Experimental values of fiber lengths were obtained by digitalizing previously reported experimental findings using ultrasound in vastus lateralis [42,43], gastrocnemius lateralis [44,46], gastrocnemius medialis [45] and soleus [47]. Experimental fiber lengths were normalized based on average values reported from a muscle architecture data set [52] when not otherwise reported in experimental studies. Horizontal lines above muscle excitations indicate on/off timing for EMG signals, defined as >50% excitation.
Fig 4.
Quantitative differences between computed and experimental muscle excitations, fiber lengths, and whole-body average metabolic rates.
Correlation coefficient r and rmse (column 1) between computed and experimental muscle excitations and fiber lengths, and differences between estimated and experimental metabolic whole-body average metabolic rates (columns 2–4, W/kg) with four simulation workflows: Minimal muscle effort with generic passive force (GEN), with calibrated passive force (PAS), with calibrated passive force and personalized tendon stiffness (TEN), and EMG-informed with calibrated passive force and personalized tendon stiffness (EMG), using six metabolic energy models: Umberger et al. [14] (UM03), Bhargava et al. [12] (BH04), Houdijk et al. [15] (HO06), Lichtwark and Wilson [16] (LW07), Umberger [17] (UM10), and Uchida et al. [18] (UC16). Bar plots shown mean value and one standard deviation computed among all subjects and walking trials.
Fig 5.
Repeated measures correlation between estimated and experimental whole-body average metabolic rates.
Repeated measures correlation between estimated and experimental whole-body average metabolic rate [W/kg] over a range of metabolic demand with four simulation workflows: Minimal muscle effort with generic passive force (GEN), with calibrated passive force (PAS), with calibrated passive force and personalized tendon stiffness (TEN), and EMG-informed with calibrated passive force and personalized tendon stiffness (EMG), using six metabolic energy models: Umberger et al. [14] (UM03), Bhargava et al. [12] (BH04), Houdijk et al. [15] (HO06), Lichtwark and Wilson [16] (LW07), Umberger [17] (UM10), and Uchida et al. [18] (UC16). Each color represents an individual subject. An ideal relationship, equivalent to y = x is illustrated as a dotted line. For each simulation workflow and metabolic energy model, the slope m, correlation coefficient r, and p-value of the null hypothesis that no correlation between estimated and experimental metabolic rate exists are shown as means of all subjects.
Fig 6.
Estimated metabolic rates among the simulation workflows.
Estimation of metabolic rates in one leg at preferred walking speeds with four simulation workflows: Minimal muscle effort with generic passive force (GEN), with calibrated passive force (PAS), with calibrated passive force and personalized tendon stiffness (TEN), and EMG-informed with calibrated passive force and personalized tendon stiffness (EMG), using six metabolic energy models: Umberger et al. [14] (UM03), Bhargava et al. [12] (BH04), Houdijk et al. [15] (HO06), Lichtwark and Wilson [16] (LW07), Umberger [17] (UM10), and Uchida et al. [18] (UC16). The estimated metabolic rate represented the average values among all subjects, scaled by their mass. Statistically significant differences (SnPM test, p<0.05) are shown in horizontal lines above each figure. They indicate differences between workflows GEN and PAS (brown), between workflows PAS and TEN (purple), and between workflows TEN and EMG (cyan). The vertical line represented the toe-off event.
Fig 7.
Estimated metabolic rates of muscle function groups.
Estimation of metabolic rates in the muscle function groups [W/kg] at preferred walking speed with the simulation workflow based on minimal muscle effort with calibrated passive force and personalized tendon stiffness (TEN), using six metabolic energy models: Umberger et al. [14] (UM03), Bhargava et al. [12] (BH04), Houdijk et al. [15] (HO06), Lichtwark and Wilson (LW07) [16], Umberger [17] (UM10), and Uchida et al. [18] (UC16). The estimated metabolic rates represented the average values among all subjects, scaled by their mass. The vertical line represented the toe-off event.
Fig 8.
Estimated whole-body metabolic rates across walking speeds.
Estimation of the whole-body metabolic rates [W/kg] at 55% PWS (light grey), 100% PWS (dark grey), and 145% PWS (black) with the simulation workflow based on minimal muscle effort with calibrated passive force and personalized tendon stiffness (TEN), using six metabolic energy models: Umberger et al. [14] (UM03), Bhargava et al. [12] (BH04), Houdijk et al. [15] (HO06), Lichtwark and Wilson [16] (LW07), Umberger [17] (UM10), and Uchida et al. [18] (UC16). The estimated metabolic rates represented the average values among all subjects, scaled by their mass. The vertical line represented the toe-off event across walking speeds.
Fig 9.
Estimated relative cost of gait phases.
Cost of the stance and swing phase relative to the total energy cost in a gait cycle during preferred walking speed [left] and vs. walking speeds [right] (in percentage) with the simulation workflow based on minimal muscle effort with calibrated passive force and personalized tendon stiffness (TEN), using six metabolic energy models: Umberger et al. [14] (UM03), Bhargava et al. [12] (BH04), Houdijk et al. [15] (HO06), Lichtwark and Wilson [16] (LW07), Umberger [17] (UM10), and Uchida et al. [18] (UC16). Pie chart areas are scaled based on the total energy cost. Individual subjects are illustrated in different colors, and the slope and correlation coefficient from repeated measures correlation is indicated. The P-value was <0.05 for all correlations.