def exercise1a():
""" Exercise 1a
The goal of this exercise is to understand the relationship
between muscle length and tension.
Here you will re-create the isometric muscle contraction experiment.
To do so, you will have to keep the muscle at a constant length and
observe the force while stimulating the muscle at a constant activation."""
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT]
# x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.5
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Evalute for a single muscle stimulation
muscle_stimulation = np.arange(0, 1., 0.2)
# Several muscle stretch
muscle_stretches = np.arange(0, 0.3, 0.01)
active_active = []
for stim in muscle_stimulation:
active_forces = []
passive_forces = []
total = []
lengths = []
for stretch in muscle_stretches:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=stim,
muscle_length=stretch)
active_forces.append(result.active_force[-1])
passive_forces.append(result.passive_force[-1])
total.append(result.active_force[-1] + result.passive_force[-1])
lengths.append(result.l_ce[-1])
active_active.append(active_forces)
# Plotting
plt.figure('Isometric muscle experiment 1')
plt.plot(lengths, active_forces)
plt.plot(lengths, passive_forces)
plt.plot(lengths, total)
plt.title('Isometric muscle experiment stimulation')
plt.xlabel('Muscle stretch')
plt.ylabel('Muscle force')
plt.legend(('Active', 'Passive', 'Total'))
plt.grid()
plt.show()
# Plotting
plt.figure('Isometric muscle experiment 2')
for i in range(len(muscle_stimulation)):
plt.plot(lengths, active_active[i])
plt.title('Isometric muscle experiment')
plt.xlabel('Muscle stretch')
plt.ylabel('Muscle force')
plt.legend(muscle_stimulation)
plt.grid()
plt.show()
# Plotting
#plt.figure('Isotonic muscle experiment')
#plt.plot(result.time, result.v_ce)
#plt.title('Isotonic muscle experiment')
#plt.xlabel('Time [s]')
#plt.ylabel('Muscle contractilve velocity')
#plt.grid()
#muscle with longer l_opt
muscle.L_OPT = 0.5
muscle_stimulation = 1.
lce = []
totalF = []
activeF = []
passiveF = []
for stretch in muscle_stretches:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=stretch)
activeF.append(result.active_force[-1])
passiveF.append(result.passive_force[-1])
lce.append(result.l_ce[-1])
totalF.append(result.active_force[-1] + result.passive_force[-1])
plt.figure('muscle with l_opt=0.5')
plt.title('muscle with l_opt=0.5')
plt.plot(lce, activeF)
plt.plot(lce, passiveF)
plt.plot(lce, totalF)
plt.xlabel('Muscle Stretch')
plt.ylabel('Force')
plt.ylim((0, 4000))
plt.legend(('Active Force', 'Passive Force', 'Total Force'))
plt.grid()
#muscle with shorter l_opt
t_start = 0.0
t_stop = 1
time_step = 0.005
time = np.arange(t_start, t_stop, time_step)
muscle_stretches = np.arange(0, 0.3, 0.01)
muscle.L_OPT = 0.075
muscle_stimulation = 1.
lce = []
totalF = []
activeF = []
passiveF = []
plt.figure('muscle with l_opt=0.075')
for stretch in muscle_stretches:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=stretch)
activeF.append(result.active_force[-1])
passiveF.append(result.passive_force[-1])
lce.append(result.l_ce[-1])
totalF.append(result.active_force[-1] + result.passive_force[-1])
plt.title('muscle with l_opt=0.075')
plt.plot(lce, activeF)
plt.plot(lce, passiveF)
plt.plot(lce, totalF)
plt.xlabel('Muscle Stretch')
plt.ylabel('Force')
plt.ylim((0, 4000))
plt.legend(('Active Force', 'Passive Force', 'Total Force'))
plt.grid()
def exercise1c():
""" Exercice 1c """
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Force-length curves
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT]
# Set the time for integration
t_start = 0.0
t_stop = 0.2
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
N_stretch = 40
activeF = np.zeros(N_stretch)
passiveF = np.zeros(N_stretch)
tendonF = np.zeros(N_stretch)
lceF = np.zeros(N_stretch)
# Evaluate for various optimal length
l_opt_list = np.array([0.1, 0.3])
# Subplots grid
n_plot = len(l_opt_list)
n_subplot = int((np.sqrt(n_plot - 1)) + 1)
if (n_plot <= n_subplot * (n_subplot - 1)):
fig, axes = plt.subplots(n_subplot, n_subplot - 1)
n_subplot2 = n_subplot - 1
else:
fig, axes = plt.subplots(n_subplot, n_subplot)
n_subplot2 = n_subplot
for i, l_opt in enumerate(l_opt_list):
# Evaluate for various muscle stretch
muscle.L_OPT = l_opt
stretch_min = muscle.L_OPT
stretch_max = muscle.L_OPT * 3
muscle_stretch = np.arange(stretch_min, stretch_max,
(stretch_max - stretch_min) / N_stretch)
for stretch in range(len(muscle_stretch)):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=1.,
muscle_length=muscle_stretch[stretch])
activeF[stretch] = result.active_force[-1]
passiveF[stretch] = result.passive_force[-1]
tendonF[stretch] = result.tendon_force[-1]
lceF[stretch] = result.l_ce[-1]
plt.subplot(n_subplot, n_subplot2, i + 1)
plt.plot(lceF, 100 * activeF / muscle.F_MAX, label='Active Force')
plt.plot(lceF, 100 * passiveF / muscle.F_MAX, label='Passive Force')
plt.plot(lceF, 100 * tendonF / muscle.F_MAX, label='Tendon Force')
plt.axvline(l_opt, linestyle="--", color="r")
plt.xlim([l_opt - 0.3, l_opt + 0.3])
plt.ylim([0, 120])
plt.xlabel('Contractile element length')
plt.ylabel('Force [% of $F_{max}$]')
plt.title('Optimal length = {} [m]'.format(l_opt))
plt.legend()
plt.grid()
plt.suptitle(
'Force-length curves for isometric muscle experiment with various muscle optimal lengths'
)
fig.tight_layout()
