Results of an analysis of sensitivity of length–tension curves to errors in parameters
| (A) Effects of parameter errors on length–tension curves and maximal strains of MTU, muscle fascicles and tendon . | . | . | . | . | . | . |
|---|---|---|---|---|---|---|
| ag×1.05 | ag×0.95 | kg×1.05 | kg×0.95 | lG×1.05 | lG×0.95 | |
| Changes in the length–tension curves* | 6.1 | 4.5 | 1.2 | 4.6 | 4.8 | 2.3 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | –2, 9, –3 | –4, 10, –4 | n/a | n/a | –6, 2, –6 | n/a |
| ap×1.05 | ap×0.95 | kp×1.05 | kp×0.95 | θ P×1.05 | θ P×0.95 | |
| Changes in the length–tension curves* | 3.4 | 4.6 | 3.2 | 3.6 | 3.9 | 2.4 |
| Changes in strains of muscle–tendon unit, fascicles and tendon,respectively† | –2, 9, –2 | n/a | 2, –15, 2 | 1, –8, 1 | 4, –30, 4 | n/a |
| ad×1.05 | ad×0.95 | kd×1.05 | kd×0.95 | θ D×1.05 | θ D×0.95 | |
| Changes in the length–tension curves* | 6.4 | 5.3 | 5.4 | 8.9 | 2.8 | 6.0 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | –2, 9, –2 | –2, 8, –2 | –3, 10, –3 | n/a | –1, 7, –1 | 0, 0, 0 |
| (A) Effects of parameter errors on length–tension curves and maximal strains of MTU, muscle fascicles and tendon . | . | . | . | . | . | . |
|---|---|---|---|---|---|---|
| ag×1.05 | ag×0.95 | kg×1.05 | kg×0.95 | lG×1.05 | lG×0.95 | |
| Changes in the length–tension curves* | 6.1 | 4.5 | 1.2 | 4.6 | 4.8 | 2.3 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | –2, 9, –3 | –4, 10, –4 | n/a | n/a | –6, 2, –6 | n/a |
| ap×1.05 | ap×0.95 | kp×1.05 | kp×0.95 | θ P×1.05 | θ P×0.95 | |
| Changes in the length–tension curves* | 3.4 | 4.6 | 3.2 | 3.6 | 3.9 | 2.4 |
| Changes in strains of muscle–tendon unit, fascicles and tendon,respectively† | –2, 9, –2 | n/a | 2, –15, 2 | 1, –8, 1 | 4, –30, 4 | n/a |
| ad×1.05 | ad×0.95 | kd×1.05 | kd×0.95 | θ D×1.05 | θ D×0.95 | |
| Changes in the length–tension curves* | 6.4 | 5.3 | 5.4 | 8.9 | 2.8 | 6.0 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | –2, 9, –2 | –2, 8, –2 | –3, 10, –3 | n/a | –1, 7, –1 | 0, 0, 0 |
| (B) Effects of biases in measured passive ankle torques . | . | . | . | . |
|---|---|---|---|---|
| Raw torque increased 2% | Raw torque decreased 2% | Raw torque increased 5% | Raw torque decreased 5% | |
| Changes in the length–tension curve* | 0.9 | 1.7 | 4.2 | 2.9 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | n/a | 0, 0, 0 | 3, –24, 3 | –1, 5, –1 |
| (C) Effects of biases in measured footplate torques and calculating foot torques | ||||
| Footplate torque increased 5%; foot torque increased 25% | Footplate torque decreased 5%; foot torque increased 25%; | Footplate torque increased 5% foot torque increased 25% | Footplate torque increased 5%; foot torque increased 25% | |
| Changes in the length–tension curve* | 1.4 | 3.4 | 3.0 | 3.4 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | n/a | n/a | 3, –3, 3 | 2, –20, 2 |
| (B) Effects of biases in measured passive ankle torques . | . | . | . | . |
|---|---|---|---|---|
| Raw torque increased 2% | Raw torque decreased 2% | Raw torque increased 5% | Raw torque decreased 5% | |
| Changes in the length–tension curve* | 0.9 | 1.7 | 4.2 | 2.9 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | n/a | 0, 0, 0 | 3, –24, 3 | –1, 5, –1 |
| (C) Effects of biases in measured footplate torques and calculating foot torques | ||||
| Footplate torque increased 5%; foot torque increased 25% | Footplate torque decreased 5%; foot torque increased 25%; | Footplate torque increased 5% foot torque increased 25% | Footplate torque increased 5%; foot torque increased 25% | |
| Changes in the length–tension curve* | 1.4 | 3.4 | 3.0 | 3.4 |
| Changes in strains of the muscle–tendon unit, fascicles and tendon,respectively† | n/a | n/a | 3, –3, 3 | 2, –20, 2 |
Sensitivity was tested by adding errors to the passive length–tension curve of one randomly selected subject. Errors were added to each of the nine estimated model parameters (±5%), raw passive ankle torque data(±2% and 5%) and the weight torques due to the footplate (±5%)and the foot (±25%)
Changes in length–tension curves were calculated by root-mean-square estimates of the curves and expressed as a percentage of maximal control passive tension
Changes in strains of the muscle–tendon unit, muscle fascicles and tendon are expressed as deviations from the control values of strain calculated for this randomly chosen subject, which are 21%, 82% and 14% for the muscle–tendon unit, muscle fascicles and tendon, respectively. Minus and plus signs indicate that the new strain values are lower or higher than control values, respectively. n/a indicates that the new values of slack length of the muscle–tendon unit are shorter than the shortest length;therefore, it was not possible to use Eqn 3 to calculate slack length of the fascicles