def isotonic_experiment(muscle_stimulation, loads,
time_param=TimeParameters()):
# Muscle
muscle_parameters = MuscleParameters()
muscle = Muscle(muscle_parameters)
# Initial conditions
x0 = [0] * StatesIsotonic.NB_STATES.value
x0[StatesIsotonic.STIMULATION.value] = 0.
x0[StatesIsotonic.L_CE.value] = muscle.L_OPT
x0[StatesIsotonic.LOAD_POS.value] = muscle.L_OPT + muscle.L_SLACK
x0[StatesIsotonic.LOAD_SPEED.value] = 0.
# Containers
v_ce = []
tendon_force = []
# Integration
pylog.info("Running the experiments (this might take a while)...")
for load in loads:
# New load definition
mass_parameters = MassParameters()
mass_parameters.mass = load
mass = Mass(mass_parameters)
# System definition
sys = IsotonicMuscleSystem()
sys.add_muscle(muscle)
sys.add_mass(mass)
result = sys.integrate(x0=x0,
time=time_param.times,
time_step=time_param.t_step,
time_stabilize=time_param.t_stabilize,
stimulation=muscle_stimulation,
load=load)
# Result processing
if result.l_mtc[-1] > x0[StatesIsotonic.LOAD_POS.value]:
# Extension
index = result.v_ce.argmax()
v_ce.append(result.v_ce.max())
tendon_force.append(result.tendon_force[index])
else:
# Contraction
index = result.v_ce.argmin()
v_ce.append(result.v_ce.min())
tendon_force.append(result.tendon_force[index])
return v_ce, tendon_force
def __init__(self, parameters=None):
super(Mass, self).__init__()
if parameters is None:
pylog.warning('Setting default parameters to mass model.')
self.parameters = MassParameters()
else:
self.parameters = parameters
def plotVceLoad(load,ms=[1.]):
# Defination of muscles
muscle_parameters = MuscleParameters()
mass_parameters = MassParameters()
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# Evalute for a single load
#load = 100.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT,
sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
plt.figure('Max Velocity-Tension curve')
for s in ms:
muscle_stimulation = s
v = []
for l in load:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=l)
# Find the max or min speed achieved
i = np.argmax(np.abs(result.v_ce))
v.append(-result.v_ce[i])
#if result[i].l_mtc < sys.muscle.L_OPT + sys.muscle.L_SLACK:
for i in range(len(v)):
if i >= 1 and v[i]*v[i-1] <=0:
plt.plot(load[i],v[i],color='green', marker='x', linestyle='dashed',
linewidth=2, markersize=12)
plt.plot(load, v,label='maximal speed\nMuscle stimulation: {}'.format(s))
plt.legend()
plt.title('Isotonic muscle experiment\nMax Velocity-Tension curve')
plt.xlabel('load [kg]')
plt.ylabel('CE speed [m/s]')
#axes = plt.gca()
#axes.set_xlim([0.05,0.2])
#axes.set_ylim([0,1700])
plt.grid()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evalute for a single load
load = 100.
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT,
sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
# 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()
# Run 1.d
load = np.arange(0,1000,20)
plotVceLoad(load,[0.1,0.5,1])
def exercise1f():
""" Exercise 1f
What happens to the force-velocity relationship when the stimulation is varied
between [0 - 1]?"""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
# Instantiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evaluate for a single load
load = 100.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 1.25
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# ---------------------------------------------
# maximum force over stimulation
# ---------------------------------------------
# Evaluate for different muscle stimulation
muscle_stimulation = np.arange(0, 1.1, 0.1)
max_active_force = []
max_passive_force = []
max_sum_force = []
# Begin plotting
for s in muscle_stimulation:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=s,
load=load)
if abs(min(result.active_force)) > max(result.active_force):
max_active_force.append(min(result.active_force))
else:
max_active_force.append(max(result.active_force))
if abs(min(result.passive_force)) > max(result.passive_force):
max_passive_force.append(min(result.passive_force))
else:
max_passive_force.append(max(result.passive_force))
max_sum_force.append(max_active_force[-1] + max_passive_force[-1])
plt.figure('Isotonic muscle active force - stimulation [0, 1]')
plt.plot(muscle_stimulation,
max_active_force,
label='maximum active force')
plt.plot(muscle_stimulation,
max_passive_force,
label='maximum passive force')
plt.plot(muscle_stimulation, max_sum_force, label='maximum sum force')
plt.xlabel('Stimulation [-]')
plt.ylabel('Muscle sum forces [N]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# force - velocity over stimulation
# ---------------------------------------------
muscle_stimulation = np.arange(0, 1.1, 0.1)
# Begin plotting
for s in muscle_stimulation:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=s,
load=load)
plt.figure('Isotonic muscle active force - velocity')
plt.plot(result.v_ce[200:-1],
result.active_force[200:-1],
label='stimulation {:0.1f}'.format(s))
plt.figure('Isotonic muscle passive force - velocity')
plt.plot(result.v_ce[200:-1],
result.passive_force[200:-1],
label='stimulation {:0.1f}'.format(s))
plt.figure('Isotonic muscle sum forces - velocity')
plt.plot(result.v_ce[200:-1],
result.active_force[200:-1] + result.passive_force[200:-1],
label='stimulation {:0.1f}'.format(s))
plt.figure('Isotonic muscle active force - velocity')
plt.xlabel('Velocity contractile element [m/s]')
plt.ylabel('Active force [N]')
plt.legend(loc='upper right')
plt.grid()
plt.figure('Isotonic muscle passive force - velocity')
plt.xlabel('Velocity contractile element [m/s]')
plt.ylabel('Passive force [N]')
plt.legend(loc='upper right')
plt.grid()
plt.figure('Isotonic muscle sum forces - velocity')
plt.xlabel('Velocity contractile element [m/s]')
plt.ylabel('Sum forces [N]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# Plot velocity - tension relation
# ---------------------------------------------
muscle_stimulation = np.arange(0, 1.1, 0.25)
load = np.arange(5, 1500, 20)
plt.figure('Velocity - Tension')
# Begin plotting
for s in muscle_stimulation:
(max_vce, active_force) = ex1d_for(sys, x0, time, time_step,
time_stabilize, s, load, False)
plt.plot(load, max_vce, label="stimulation {:0.1f}".format(s))
plt.title('Velocity [m/s] - Load [N]')
plt.xlabel('Load [N]')
plt.ylabel('Velocity [m/s]')
plt.legend(loc='lower right')
plt.grid()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evaluate for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 1.25
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# Set max_vce
max_vce = []
# ---------------------------------------------
# Small load experiment
# ---------------------------------------------
load_table_small = [5, 10, 20, 50, 100]
# Begin plotting
plt.figure('Isotonic muscle experiment - load [10, 200] [N]')
max_vce_small = ex1d_for(sys, x0, time, time_step, time_stabilize,
muscle_stimulation, load_table_small, False)
plt.title('Isotonic muscle experiment - load [5, 140] [N]')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contractile velocity [m/s]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# Big load experiment
# ---------------------------------------------
load_table_big = [150, 200, 220, 250, 500, 1000, 1500]
# Begin plotting
plt.figure('Isotonic muscle experiment - load [150, 1500] [N]')
max_vce += ex1d_for(sys, x0, time, time_step, time_stabilize,
muscle_stimulation, load_table_big, True)
plt.title('Isotonic muscle experiment - load [150, 1500] [N]')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contractile velocity [m/s]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# Plot velocity - tension relation
# ---------------------------------------------
load = np.arange(5, 2500, 200)
(max_vce, active_force) = ex1d_for(sys, x0, time, time_step,
time_stabilize, muscle_stimulation,
load, False)
fig = plt.figure('Velocity - Tension')
ax = fig.add_subplot(111)
# Plot comments and line at 0 value
min_val = 0.0
if min(map(abs, max_vce)) not in max_vce:
min_val = -min(map(abs, max_vce))
else:
min_val = min(map(abs, max_vce))
xy = (load[max_vce.index(min_val)], min_val)
xytext = (load[max_vce.index(min_val)] + 50, min_val)
ax.annotate('load = {:0.1f}'.format(152.2), xy=xy, xytext=xytext)
plt.title('Velocity [m/s] - Tension [N]')
plt.xlabel('Tension [N]')
plt.ylabel('Velocity [m/s]')
plt.grid()
plt.plot(load, max_vce)
plt.plot(load[max_vce.index(min_val)], min_val, 'o')
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evalute for a single load
load = 100.
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.5
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
loads = np.arange(20, 351, 10)
velocities = []
for index, load in enumerate(loads):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
if (result.l_mtc[-1] < sys.muscle.L_OPT + sys.muscle.L_SLACK):
velocities.append(np.max(result.v_ce))
print('max')
else:
velocities.append(np.min(result.v_ce))
print('min')
#Muscle contracile Velocity - Tension (load) relationship
plt.figure('Isotonic muscle experiment')
plt.title('Isotonic muscle experiment')
plt.xlabel('Muscle Contractile Velocity [m/s]')
plt.ylabel('Tension (load) [N]')
plt.plot(velocities, loads)
plt.grid()
#For different stimulations 1.f
muscle_stimulation = np.arange(0, 1.1, 0.2)
plt.figure('Isotonic muscle exp with different stimulations')
plt.title('Isotonic muscle experiment with different stimulations')
for stim in muscle_stimulation:
velocities = []
for index, load in enumerate(loads):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=stim,
load=load)
if (result.l_mtc[-1] < sys.muscle.L_OPT + sys.muscle.L_SLACK):
velocities.append(np.max(result.v_ce))
else:
velocities.append(np.min(result.v_ce))
plt.xlabel('Muscle Contractile Velocity [m/s]')
plt.ylabel('Tension (load) [N]')
plt.plot(velocities, loads)
plt.legend(('0', '0.2', '0.4', '0.6', '0.8', '1.0'))
plt.grid()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.l_opt # To get the muscle optimal length
# Evalute for a single load
load = 250 / 9.81
# Evalute for a single muscle stimulation
muscle_stimulation = 1.0
# Set the initial condition
x0 = [0.0, sys.muscle.l_opt, sys.muscle.l_opt + sys.muscle.l_slack, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.4
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
# 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 contracticle velocity [lopts/s]')
plt.grid()
######################################################################
######################################################################
######################################################################
######################################################################
######################################################################
######################################################################
### code for 1d
pylog.info(
"1d. relationship between muscle contractile velocity and external load"
)
load_start = 1
load_stop = 501
load_step = 10
load_range = np.arange(load_start, load_stop, load_step)
muscle_stimulation = 1.0
vels = []
tendon_forces = []
active_forces = []
passive_forces = []
total_forces = []
for temp_load in load_range:
temp_result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=temp_load)
temp_tendon_force = temp_result.tendon_force[-1]
temp_active_force = temp_result.active_force[-1]
temp_passive_force = temp_result.passive_force[-1]
temp_total_force = temp_active_force + temp_passive_force
tendon_forces = tendon_forces + [temp_tendon_force]
active_forces = active_forces + [temp_active_force]
passive_forces = passive_forces + [temp_passive_force]
total_forces = total_forces + [temp_total_force]
temp_l_mtu = temp_result.l_mtu[-1]
if temp_l_mtu < sys.muscle.l_opt + sys.muscle.l_slack:
vels = vels + [np.min(temp_result.v_ce)]
else:
vels = vels + [np.max(temp_result.v_ce)]
plt.figure(
'1d. Isotonic muscle experiment for tension and contractile velocities'
)
plt.plot(vels, tendon_forces)
plt.plot(vels, load_range)
plt.plot(vels, active_forces)
plt.plot(vels, passive_forces)
plt.plot(vels, total_forces)
plt.title(
'Isotonic muscle experiment for tension and contractile velocities')
plt.xlabel('Muscle contracticle velocity [lopts/s]')
plt.ylabel('Tension [N]')
plt.legend(("Tendon Force", "Load", "Active Force", "Passive Force",
"Total force"))
plt.grid()
plt.show()
######################################################################
######################################################################
######################################################################
######################################################################
######################################################################
######################################################################
### code for 1f
pylog.info(
"1f. relationship between muscle contractile velocity and external load with different stimulations"
)
muscle_stimulations = np.arange(0, muscle_stimulation + 0.1, 0.1)
load_start = 1
load_stop = 501
load_step = 10
load_range = np.arange(load_start, load_stop, load_step)
all_vels = []
all_tendon_forces = []
for temp_muscle_stimulation in muscle_stimulations:
temp_vels = []
temp_tendon_forces = []
for temp_load in load_range:
temp_result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=temp_muscle_stimulation,
load=temp_load)
temp_tendon_force = temp_result.tendon_force[-1]
temp_tendon_forces = temp_tendon_forces + [temp_tendon_force]
temp_l_mtu = temp_result.l_mtu[-1]
if temp_l_mtu < sys.muscle.l_opt + sys.muscle.l_slack:
temp_vels = temp_vels + [np.min(temp_result.v_ce)]
else:
temp_vels = temp_vels + [np.max(temp_result.v_ce)]
all_vels = all_vels + [temp_vels]
all_tendon_forces = all_tendon_forces + [temp_tendon_forces]
plt.figure(
'1f. Isotonic muscle experiment for loads and contractile velocities with different stimulations'
)
for i in range(len(muscle_stimulations)):
plt.plot(all_vels[i], load_range)
plt.title(
'Isotonic muscle experiment for loads and contractile velocities with different stimulations'
)
plt.xlabel('Muscle contracticle velocity [lopts/s]')
plt.ylabel('Tension [N]')
temp_legends = [
'stimulation = ' + format((temp_stimulation), '.1f')
for temp_stimulation in muscle_stimulations
]
plt.legend(temp_legends)
plt.grid()
plt.show()
plt.figure(
'1f. Isotonic muscle experiment for tendon forces and contractile velocities with different stimulations'
)
for i in range(len(muscle_stimulations)):
plt.plot(all_vels[i], all_tendon_forces[i])
plt.title(
'Isotonic muscle experiment for tendon forces and contractile velocities with different stimulations'
)
plt.xlabel('Muscle contracticle velocity [lopts/s]')
plt.ylabel('Tension [N]')
temp_legends = [
'stimulation = ' + format((temp_stimulation), '.1f')
for temp_stimulation in muscle_stimulations
]
plt.legend(temp_legends)
plt.grid()
plt.show()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evalute for a single load
load = 100.
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT,
sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# Run the integration
load_array=np.arange(0.1,3000/sys.mass.parameters.g,5)
vel_ce=[]
act_force_int=[]
stimulation=[0.,0.2,0.4,0.6,0.8,1.]
colors=['r','g','b','c','m','y']
for loadx in load_array:
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=loadx)
if (loadx==150.1 or loadx==155.1):
plt.figure("Single Exp")
plt.title("Result for a single experiment")
plt.plot(result.time,result.v_ce*(-1))
plt.xlabel("Time [s]")
plt.ylabel("Velocity [m/s]")
plt.legend(('Shortening','Lengthening'))
pylog.info(result.l_mtc[-1])
plt.grid()
plt.show()
if result.l_mtc[-1] < ( muscle_parameters.l_opt + muscle_parameters.l_slack):
#pylog.info("min condition")
vel_ce.append(min(result.v_ce[:])*(-1))
act_force_int.append(max(result.active_force))
else:
vel_ce.append(max(result.v_ce[:])*(-1))
act_force_int.append(max(result.active_force))
# pylog.info("max condition")
plt.figure('Isotonic muscle experiment')
plt.plot(vel_ce,load_array*mass_parameters.g)
plt.plot(vel_ce,act_force_int)
plt.title('Isotonic Muscle Experiment')
plt.xlabel('Contractile Element Velocity [m/s]')
plt.ylabel('Force[N]')
plt.legend(("External Load","Internal Active Force"))
plt.grid()
plt.show()
plt.figure('Varying Stimulation')
leg=[]
for i,stim in enumerate(stimulation):
pylog.info("Stim is {}".format(stim))
vel_ce=[]
act_force_int=[]
for loadx in load_array:
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=stim,
load=loadx)
if result.l_mtc[-1] < ( muscle_parameters.l_opt + muscle_parameters.l_slack):
#pylog.info("min condition")
vel_ce.append(min(result.v_ce[:])*(-1))
act_force_int.append(max(result.active_force))
else:
vel_ce.append(max(result.v_ce[:])*(-1))
act_force_int.append(max(result.active_force))
plt.plot(vel_ce,load_array*mass_parameters.g,colors[i],label='Stimulation={}'.format(stim))
plt.plot(vel_ce,act_force_int,colors[i],linestyle=":",label='Stimulation={}'.format(stim))
leg.append(("Load-velocity plot with simulation={}".format(stim)))
leg.append(("Force-velocity with simulation={}".format(stim)))
plt.title('Varying Stimulation')
plt.legend(leg)
plt.xlabel('Contractile Element Velocity [m/s]')
plt.ylabel('Force[N]')
#("Stimulation = 0","Stimulation = 0.2","Stimulation = 0.4","Stimulation = 0.6","Stimulation = 0.8","Stimulation = 1")
plt.grid()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evalute for a single load
#load = 15.
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.35
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
####custom code#####
load_range = np.arange(1, 361, 5)
my_velocity = []
plt.figure('Isotonic muscle experiment')
for load in load_range:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
my_velocity.append(max(abs(result.v_ce)))
i, = np.where(result.v_ce == my_velocity[-1])
if i.shape == (0, ): #checks for negative velocity
my_velocity[-1] *= -1
plt.plot(result.time, result.v_ce, label='Load: %s' % load)
# Plotting
#plt.plot(result.time, result.v_ce)
plt.title('Isotonic muscle experiment')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contractilve velocity')
plt.grid()
plt.figure('Isotonic Experiment')
plt.plot(load_range, my_velocity)
plt.xlabel('Load[Kg]')
plt.ylabel('Maximal Muscle Contractile Velocity[m/s]')
plt.grid()
def exercise1f():
""" Exercise 1f """
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# Velocity-tension curve
# Evalute for various loads
load_min = 1
load_max = 501
N_load = 50
load_list = np.arange(load_min, load_max, (load_max - load_min) / N_load)
# Evalute for various muscle stimulation
N_stim = 4
muscle_stimulation = np.round(np.arange(N_stim) / (N_stim - 1), 2)
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
max_velocity = np.zeros((N_stim, N_load))
tendonF = np.zeros((N_stim, N_load))
for i, stim in enumerate(muscle_stimulation):
for ind_load, load in enumerate(load_list):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=stim,
load=load)
if (result.l_mtc[-1] < (sys.muscle.L_OPT + sys.muscle.L_SLACK)):
max_velocity[i, ind_load] = np.max(-result.v_ce)
else:
max_velocity[i, ind_load] = np.min(-result.v_ce)
tendonF[i, ind_load] = result.tendon_force[-1]
# Plotting
plt.figure('Isotonic Muscle Experiment 1f')
v_min = np.amin(max_velocity)
v_max = np.amax(max_velocity)
for i, stim in enumerate(muscle_stimulation):
plt.plot(max_velocity[i, :] * 100 / -muscle.V_MAX,
tendonF[i, :] * 100 / muscle.F_MAX,
label='Tendon Force - Stimulation = {}'.format(stim))
plt.xlim(v_min * 100 / -muscle.V_MAX, v_max * 100 / -muscle.V_MAX)
plt.ylim(0, 200)
plt.axvline(linestyle='--', color='r', linewidth=2)
plt.text(v_min * 100 / -muscle.V_MAX * 2 / 3,
170,
r'lengthening',
fontsize=16)
plt.text(v_max * 100 / -muscle.V_MAX * 1 / 8,
170,
r'shortening',
fontsize=16)
plt.xlabel('Maximal velocity [% of $V_{max}$]')
plt.ylabel('Tendon Force [% of $F_{max}$]')
plt.title(
'Velocity-tension curves for isotonic muscle experiment with various muscle stimulations'
)
plt.legend()
plt.grid()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Velocity-tension curve
# Evalute for various loads
load_min = 1
load_max = 301
N_load = 50
load_list = np.arange(load_min, load_max, (load_max - load_min) / N_load)
# Evalute for Stimulation = 1.0
stimulation = 1.0
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
max_velocity = np.zeros(N_load)
tendonF = np.zeros(N_load)
for ind_load, load in enumerate(load_list):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=stimulation,
load=load)
if (result.l_mtc[-1] < (sys.muscle.L_OPT + sys.muscle.L_SLACK)):
max_velocity[ind_load] = np.max(-result.v_ce)
else:
max_velocity[ind_load] = np.min(-result.v_ce)
tendonF[ind_load] = result.tendon_force[-1]
# Plotting
plt.figure('Isotonic Muscle Experiment 1d')
v_min = np.amin(max_velocity)
v_max = np.amax(max_velocity)
plt.plot(max_velocity * 100 / -muscle.V_MAX, tendonF * 100 / muscle.F_MAX)
plt.axvline(linestyle='--', color='r', linewidth=2)
plt.text(v_min * 100 / -muscle.V_MAX, 20, r'lengthening', fontsize=14)
plt.text(v_max * 100 / -muscle.V_MAX * 1 / 3,
20,
r'shortening',
fontsize=14)
plt.xlabel('Maximal velocity [% of $V_{max}$]')
plt.ylabel('Tendon Force [% of $F_{max}$]')
plt.title(
'Velocity-tension curve for isotonic muscle experiment (Stimulation = 1.0)'
)
plt.grid()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.l_opt # To get the muscle optimal length
# Evalute for a single load
load = 250/9.81
# Evalute for a single muscle stimulation
muscle_stimulation = 1.0
# Set the initial condition
x0 = [0.0, sys.muscle.l_opt,
sys.muscle.l_opt + sys.muscle.l_slack, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.4
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
load = np.linspace(100/9.81,1700/9.81,50)
Stimu = np.linspace(0,1,6)
Vce = np.zeros((len(load),len(Stimu)))
plt.figure('Isotonix Globale')
for j in range(len(Stimu)):
# Vce = np.empty(len(load))
# Vcemax = np.empty(len(load))
# Vcemin = np.empty(len(load))
for i in range(len(load)):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=Stimu[j],
load=load[i]
)
print(result.l_mtu[-1])
print(sys.muscle.l_opt + sys.muscle.l_slack)
if (result.l_mtu[-1] > sys.muscle.l_opt + sys.muscle.l_slack):
Vce[i,j]=(max(result.v_ce))
else: Vce[i,j] = min(result.v_ce)
Vce[:,j]
plt.plot(Vce[:,j],load, label ="MS %s" %round(Stimu[j],1))
plt.legend(loc = "upper left")
plt.xlabel('Vitesse max [m/s]')
plt.ylabel('Load [kg]')
# Plotting
plt.figure('Isotonic muscle experiment')
#plt.plot(result.time,
# result.v_ce)
plt.plot(Vce,load)
plt.title('Isotonic muscle experiment')
plt.xlabel('Vitesse max [m/s]')
plt.ylabel('Load [kg]')
#plt.xlabel('Time [s]')
#plt.ylabel('Muscle contracticle velocity [lopts/s]')
plt.grid()
#MUSCLE-Force Velocity relationship :
plt.figure('Muscle Force-Velocity')
plt.plot(result.v_ce,result.active_force, label ="Active Force")
plt.plot(result.v_ce,result.active_force+result.passive_force, label = "Passive + Active")
plt.plot(result.v_ce,result.passive_force, label = "Passive Force")
plt.legend(loc = "upper left")
plt.xlabel('Vitesse m')
plt.ylabel('Force')
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
#sys.muscle.L_OPT=0.05
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.25
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal
# Create a V_ce vector
V_ce_1d = np.zeros(100)
PF_ce_1d = np.zeros(100)
AF_ce_1d = np.zeros(100)
# Create load vector
Load = np.linspace(1, 600, num=100)
"""1.d) velocity-tension analysis """
for i in range(0, len(Load)):
# Set the initial condition
x0 = [
muscle_stimulation, sys.muscle.L_OPT,
sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0
]
# Evalute for a single load
load = Load[i]
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
#print(sys.muscle.L_OPT+sys.muscle.L_SLACK)
#print(result.l_mtc[-1]-(sys.muscle.L_OPT+sys.muscle.L_SLACK))
if (result.l_mtc[-1] < sys.muscle.L_OPT + sys.muscle.L_SLACK):
V_ce_1d[i] = min(result.v_ce)
else:
V_ce_1d[i] = max(result.v_ce)
PF_ce_1d[i] = result.passive_force[-1]
AF_ce_1d[i] = result.active_force[-1]
# Plotting
plt.figure('Isotonic muscle experiment')
plt.plot(result.time, result.v_ce)
plt.title('Isotonic muscle experiment')
plt.xlabel('Time [s]')
plt.ylabel('Contractile element velocity')
plt.grid()
# Plot velocity versus tension
plt.figure()
plt.plot(V_ce_1d, Load)
plt.title('Isotonic muscle experiment')
plt.xlabel('Contractile element velocity')
plt.ylabel('Load')
plt.grid()
plt.axvline(0, color='r', linestyle='--')
# Plot velocity versus tension
plt.figure()
plt.plot(V_ce_1d, PF_ce_1d + AF_ce_1d)
#plt.plot(V_ce_1d, PF_ce_1d)
#plt.plot(V_ce_1d, AF_ce_1d, '--')
plt.title('Isotonic muscle experiment')
plt.xlabel('Contractile element velocity')
plt.ylabel('Total Force')
plt.grid()
#plt.legend(['total','passive', 'active'])
plt.axvline(0, color='r', linestyle='--')
""" 1.f) velocity-tension as a function of muscle activation """
# Create solution vector
#R_glob=np.zeros((5,50))
# Create muscle activation vector
dS = np.linspace(0.1, 1, num=5)
# Create a V_ce vector
V_ce = np.zeros((5, 100))
PF_ce = np.zeros((5, 100))
AF_ce = np.zeros((5, 100))
for i in range(0, len(Load)):
for j in range(0, len(dS)):
# Evalute for a single load
load = Load[i]
# Evalute for a single muscle stimulation
muscle_stimulation = dS[j]
# Set the initial condition
x0 = [
muscle_stimulation, sys.muscle.L_OPT,
sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0
]
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
#R_glob[j,i]=result.tendon_force[len(result.tendon_force)-1]
#print(sys.muscle.L_OPT+sys.muscle.L_SLACK)
#print(result.l_mtc[-1]-(sys.muscle.L_OPT+sys.muscle.L_SLACK))
if (result.l_mtc[-1] < sys.muscle.L_OPT + sys.muscle.L_SLACK):
V_ce[j, i] = min(result.v_ce)
else:
V_ce[j, i] = max(result.v_ce)
PF_ce[j, i] = result.passive_force[-1]
AF_ce[j, i] = result.active_force[-1]
# # Plotting
# plt.figure('Isotonic muscle experiment')
# plt.plot(result.time, result.v_ce)
# plt.title('Isotonic muscle experiment')
# plt.xlabel('Time [s]')
# plt.ylabel('Contractile element velocity')
# plt.grid()
# Plot velocity versus tension
plt.figure()
for i in range(0, 5):
plt.plot(V_ce[i, :], PF_ce[i, :] + AF_ce[i, :])
plt.title('Isotonic muscle experiment')
plt.xlabel('Contractile element velocity')
plt.ylabel('Force')
plt.grid()
plt.legend([
'Stimulation = 0.1', 'Stimulation = 0.28', 'Stimulation = 0.46',
'Stimulation = 0.64', 'Stimulation = 0.82', 'Stimulation = 1'
])
