Mechanical power output during stretch–shortening cycles of rat medial gastrocnemius muscle: Influence of various muscle length trajectories

Figures

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  Fig 1. An example of a work loop. In a work loop, MTC force is plotted against MTC length (change). The area enclosed by the work loop represents the net mechanical work produced during a full cycle (C), which is the sum of the positive mechanical work during MTC shortening (A) and the negative mechanical work during MTC lengthening (B). The arrows indicate the direction of the work loop over time.

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  Fig 2. Representation of the parameterisation of stretch–shortening cycles. Tshort and Tlength denote the shortening and lengthening durations, respectively, of either the muscle-tendon-complex (MTC) or the muscle fibres. FTS denotes the fraction of the cycle time spent shortening. In the example shown, the MTC/muscle fibres shorten 65% of the cycle duration (i.e., FTS = 0.65).

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  Fig 3. Representation of the experimental setup that provided full control of MTC length and stimulation while measuring m. gastrocnemius medialis (GM) force. GM was carefully exposed from its surrounding tissue and positioned in the setup such that GM pulled in its natural direction, while the femur and foot were securely fixated. The distal end of the calcaneal tendon was connected to a motor via a steel rod. The distal tendon of m. gastrocnemius lateralis and m. plantaris was connected to a second motor. A cuff-electrode was placed on n. ischiadicus. N. peroneus, n. suralis and the branch of n. ischiadicus innervating m. gastrocnemius lateralis and m. soleus were cut such that only GM was innervated.

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  Fig 4. Representation of experimentally investigated SSCs. Thirteen combinations of cycle frequency and FTS were tested at two distinct MTC length excursions (4 mm and 8 mm), resulting in a total of 26 experimental SSC conditions.

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  Fig 5. Experimentally measured influence of cycle frequency and FTS on AMPO. AMPO as a function of cycle frequency, with a fixed FTS of 0.5 at an MTC length excursion of 4 mm (A) and 8 mm (B). AMPO as a function of FTS, with a fixed cycle frequency of 3 Hz at an MTC length excursion of 4 mm (C) and 8 mm (D). Each combination of cycle frequency, FTS and MTC length excursion was performed twice. The first trial with suboptimal muscle stimulation duration and the second trial with an improved muscle stimulation duration.

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  Fig 6. Comparison of experimentally measured and predicted SEE force over time. Predicted SEE force over time was derived using a Hill MTC-type model, with experimentally measured MTC length and stimulation over time as inputs. Predicted SEE force closely matched experimentally measured SEE force during activation but was slightly higher than experimentally measured during relaxation SEE force in most conditions. Top: MTC length over time. Second: Muscle stimulation over time, with maximal stimulation during the periods indicated by the black bars and no stimulation elsewhere. Third: SEE force over time. Bottom: SEE force as a function of MTC length (‘the work loop’). A) SSC with a cycle frequency of 3 Hz, an FTS of 0.5 and an MTC length excursion of 4 mm. B) SSC with a cycle frequency of 2 Hz, an FTS of 0.5 and an MTC length excursion of 8 mm.

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  Fig 7. Comparison of experimentally measured and predicted AMPO. Measured AMPO was derived from experimentally observed MTC length and GM force. Predicted AMPO was derived using a Hill MTC-type model, with experimentally measured MTC length and stimulation over time as inputs to predict GM force. Each dot represents AMPO of one full cycle where muscle stimulation was present, such that there are three dots for each experimental SSC condition. The nearly perfect correlation demonstrates that a Hill-type MTC model can accurately predict the influence of MTC length and stimulation over time on AMPO.

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  Fig 8. Predicted maximally attainable AMPO as a function of cycle frequency and MTC length excursion, shown for four distinct FTS values. The maximally attainable AMPO (in mW), averaged across three rats, is depicted as contour lines. The open triangles indicate the location of peak AMPO at each FTS corresponding to the optimal combination of cycle frequency and MTC length excursion for each FTS, with the corresponding peak AMPO labelled at the top-left of the triangle.

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  Fig 9. Predicted interrelationships between cycle frequency (CF), FTS, MTC length excursion (ΔLMTC) and the maximally attainable AMPO. These plots collectively illustrate how cycle frequency, FTS, and MTC length excursion interact to maximise AMPO under different conditions. This figure presents a 3x3 grid of plots created by imposing one SSC parameter at a time while optimising the two other SSC parameters to maximise AMPO. In the first column, cycle frequency was imposed, and AMPO (A1) was maximised by identifying the optimal FTS (A2) and MTC length excursion (A3) at each cycle frequency. In the second column, FTS was imposed, and AMPO (A1) was maximised by identifying the optimal MTC length excursion (B2) and cycle frequency (B3) at each FTS. In the third column, MTC length excursion was imposed, and AMPO (C1) was maximised by identifying the optimal cycle frequency (C2) and FTS (C3) at each MTC length excursion. For all columns, muscle stimulation onset time and duration were optimised to maximise AMPO.

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  Fig 10. Predicted CE behaviour for maximally attainable AMPO, shown at three distinct cycle frequencies for rat 1. CE length (A), CE force (B), CE velocity (C) and instantaneous mechanical power output (IMPO) (D) as a function of normalised time (i.e., time divided by the cycle duration). CE stimulation was maximal during the period indicated by the coloured bars and fully off elsewhere. The right labels depict the normalised values, where CE length and CE velocity are normalised to optimum CE length, CE force is normalised to maximal isometric CE force and IMPO is normalised to the product of optimum CE length and maximal isometric CE force. Based on CE length and force over time, and the SEE properties, the MTC length over time can be calculated. The resulting MTC length over time substantially differs between a typical SEE slack length of 28 mm (E) and a short SEE slack length of 3 mm (F).