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Figure 2 | Journal of NeuroEngineering and Rehabilitation

Figure 2

From: Development of a mathematical model for predicting electrically elicited quadriceps femoris muscle forces during isovelocity knee joint motion

Figure 2

A) Schematic representation of a Hill-type model used for modeling the muscle's response to electrical stimulation. The muscle modeled as a linear series spring, linear damper, and a motor. The parallel elastic element was neglected because for the range of motion studied in the current study the passive forces are smaller than the active force. k s is the spring constant of the series element, b is the damping coefficient of the damper, and V is the velocity of the motor. The force exerted by the spring and damper are k s x and b ( y ˙ x ˙ ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOyaiMaeiikaGIafmyEaKNbaiaacqGHsislcuWG4baEgaGaaiabcMcaPaaa@32C7@ , respectively. The velocity of the motor is given by V = y ˙ z ˙ = B C N K M + C N MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOvayLaeyypa0JafmyEaKNbaiaacqGHsislcuWG6bGEgaGaaiabg2da9iabdkeacLqbaoaalaaabaGaem4qam0aaSbaaeaacqWGobGtaeqaaaqaaiabdUealnaaBaaabaGaemyta0eabeaacqGHRaWkcqWGdbWqdaWgaaqaaiabd6eaobqabaaaaaaa@3CA7@ , where B is the constant of proportionality (see text for details). B) Schematic representation of the leg modeled as single rigid body segment (tibia) when subjected to stimulation under isovelocity conditions. In the isovelocity mode, the KinCom arm moves the tibia at a constant angular velocity ( θ ˙ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafqiUdeNbaiaaaaa@2D94@ = constant). θ is the knee flexion angle. L is the distance from the knee joint center to the center of the force transducer placed above the ankle and l is the distance from the knee center of rotation to the center of mass of the tibia. T stim is the torque due to stimulation, F EXT is the force measured by the KinCom dynamometer, mg is the weight of the tibia-foot complex (foot not shown in figure), and H is the resistance moment to knee extension due to visco-elasticity of the musculotendon complex of the knee joint.

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