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--- neuromuscular_modeling [24.07.2019 22:40] – [Hill-type muscle model] Guoping Zhao
+++ neuromuscular_modeling [27.11.2022 22:58] (aktuell) – Externe Bearbeitung 127.0.0.1
@@ Zeile 62: / Zeile 62: @@
 {{:guro_vtm_parameter.png?200|}}
+===== Neural reflex =====
+The muscle excitation-contraction coupling (ECC) is modelled as (Geyer2003):
+\begin{equation}
+\label{eqn_ecc}
+    \tau \frac{\mathrm{d}A(t)}{\mathrm{d}t} = S(t) - A(t)
+\end{equation}
+where $S(t)$ is the stimulation signal (neural input), $A(t)$ is the muscle activation, and $\tau$ is a time constant. We assume a linear relation between $S$ and the sensory feedback $P$ (i.e. $F_{m}$, $l_{ce}$, $v_{ce}$):
+\begin{equation}
+    \label{eqn_stim}
+    S(t) = \left\{
+        \begin{array}{lr}
+        S_0 & t \leq \Delta t \\
+        S_0 + GP(t-\Delta t)     & t > \Delta t
+        \end{array}
+        \right.
+\end{equation}
+where $S_0$ is the constant stimulation bias, $G$ is the gain factor for different feedback signals, and $\Delta t$ is the sensory feedback time delay. $S(t)$ is saturated in the range of $[0, 1]$. In the implementation, each sensory feedback $P$ signal (i.e. $F_{m}$, $l_{ce}$, $v_{ce}$) is normalized. More specifically, $S(t)$ for each individual feedback pathway (i.e. force feedback (FFB), length feedback (LFB), and velocity feedback (VFB)) is computed as:
+\begin{equation}
+    \label{eqn_stim_fb}
+    S(t) = \left\{
+        \begin{array}{lr}
+        S_0 & t \leq \Delta t \\
+        S_0 + G_F F_m^n (t-\Delta t)     & \text{FFB}, t > \Delta t \\
+        S_0 + G_L l_{ce}^n (t-\Delta t)  & \text{LFB}, t > \Delta t  \\
+        S_0 + G_F v_{ce}^n (t-\Delta t)  & \text{VFB}, t > \Delta t
+        \end{array}
+        \right.
+\end{equation}
+where $F_m^n = F_m/F_{max}$, $l_{ce}^n = l_{ce}/l_{opt}$, and $v_{ce}^n = v_{ce}/v_{max}$. $G_F$, $G_L$, and $G_V$ denote the gain for force, length, and velocity feedback pathway, respectively.
 ===== Matlab implementation =====
+==== MTU ====
+According to the Hill-type muscle equations, we build the MTU model with Matlab simulink (Geyer2010).
+{{:guro_vtm_sim_block.png?200|}}
+The input of the MTU model is the length of the MTU (lmtu), muscle stimulation signal (STIM), and the rest signal (sigRest, rest the integrator when the system state changes (e.g. from flight to stance)). The output signals are the MTU states including muscle force (Fmtu), muscle length (Lce), muscle velocity (Vce), tendon length (Lse), and muscle activation (A).
+{{:guro_vtm_sim_model.png?1000|}}
+==== Reflex ====
+Here's the overview of the simulink model which calculate knee joint torque based on joint angle.
+{{:guro_vtm_sim_torque.png?1000|}}
+With the virtual muscle states from the MTU block, muscle stimulation signal is computed based on the linear combination of muscle force, length and velocity reflexes.
+{{:guro_vtm_sim_reflex.png?1000|}}