Note
Go to the end to download the full example code.
Spinal Network Simulation with Systematic Tendon Tap Protocol#
This example demonstrates complete spinal reflex network modeling with a comprehensive tendon tap protocol that systematically varies mechanical perturbations, fusimotor drive, and cortical activity. This sophisticated experimental design reveals how the nervous system modulates stretch reflex gain.
Learning Objectives#
This example teaches the following key concepts in neuromuscular control:
Reflex Gain Modulation: How fusimotor (gamma) drive amplifies stretch reflex sensitivity - Compare motor neuron responses across different gamma levels (0→100 pps) - Observe how higher gamma drive increases spindle sensitivity and reflex output
Sensory Pathway Timing: Why different feedback pathways activate at different times - Spindle-driven pathways (Ia, II → gII) respond immediately to muscle stretch - Force-driven pathways (Ib → gIb) respond later after muscle contraction builds force
Reflex-Voluntary Interaction: How cortical commands interact with spinal reflexes - Phase 1: Isolated reflex responses (no cortical drive) - Phase 2: Reflex modulation during voluntary contraction (with cortical drive) - Observe how background muscle activity affects reflex sensitivity
Closed-loop Biomechanics: How muscle forces create movement that feeds back to sensors - Joint dynamics convert muscle torque into motion - Motion changes muscle length/velocity, affecting spindle feedback - Creates realistic proprioceptive-motor coupling
Experimental Protocol (5-second, 2-phase design):
Phase 1 (0-2.5s): Reflex Gain Modulation - Triangular tendon taps every 0.5s with increasing amplitude (50%, 60%, 70%, 80%)
Triangular waveform: Linear ramp up to peak (50ms) → linear ramp down (50ms)
Total duration: 100ms per tap
Mimics realistic tendon tap dynamics with stretch and release phases
Stepwise increasing gamma drive starting at 0.75s (0→25→50→75→100 pps)
No cortical drive (isolated reflex testing)
Phase 2 (2.5-5s): Reflex-Voluntary Interaction - Repeat triangular tap pattern (50%, 60%, 70%, 80%) - Repeat gamma drive pattern (0→25→50→75→100 pps) - Sinusoidal cortical drive (38±1 Hz at 1 Hz) recruiting ~75% of motor neurons
Note
This example builds upon all previous examples and demonstrates how the complete neuromuscular system functions as an integrated network:
Motor neuron pool: α-motoneurons controlling a single muscle (from examples 01-02)
Muscle model: Hill-type muscle model with realistic force generation (from examples 02, 06)
Proprioceptive feedback: Muscle spindles and Golgi tendon organs (from examples)
Spinal interneurons: Group II and Group Ib interneurons for reflex modulation
Joint dynamics: Closed-loop biomechanical control with realistic inertia and damping
Descending drive: Cortical control signals for voluntary movement (from example 01)
Important
Spinal Reflex Networks are the fundamental control circuits that coordinate muscle activity. Key physiological concepts demonstrated:
Stretch reflex: Muscle spindles provide length/velocity feedback for posture control
Force feedback: Golgi tendon organs monitor muscle tension for protective reflexes
Closed-loop control: Joint mechanics influence neural activity through proprioception
Motor control: Integration of descending commands with sensory feedback
Scientific Background#
The spinal cord contains intricate neural circuits that process sensory information and generate appropriate motor responses. This example models several key components:
Muscle Spindles: Specialized sensory organs that detect muscle length and velocity changes, providing Group Ia (velocity-sensitive) and Group II (length-sensitive) afferent signals.
Golgi Tendon Organs: Force-sensitive receptors that monitor muscle tension and provide Group Ib afferent feedback for protective reflexes.
Spinal Interneurons: The model includes two key inhibitory interneuron populations:
Group II interneurons (gII): Process Group II spindle afferents (length-sensitive). In this model, they provide inhibitory feedback to motor neurons, representing one component of the complex Group II pathway (which can be excitatory or inhibitory depending on context).
Group Ib interneurons (gIb): Receive input from Golgi tendon organs and provide autogenic inhibition - force-dependent negative feedback that protects against excessive muscle tension. Classic Ib inhibitory pathway.
Joint Dynamics: Realistic biomechanical modeling of joint inertia, damping, and muscle-generated torques creates the closed-loop system where neural activity affects movement, which in turn affects sensory feedback.
Import Libraries#
from pathlib import Path
import joblib
import matplotlib.pyplot as plt
import numpy as np
import quantities as pq
from neuron import h
from myogen import load_nmodl_mechanisms
from myogen.simulator.neuron.joint_dynamics import JointDynamics
from myogen.simulator.neuron.muscle import HillModel
from myogen.simulator.neuron.network import Network
from myogen.simulator.neuron.populations import (
AffIa__Pool,
AffIb__Pool,
AffII__Pool,
AlphaMN__Pool,
DescendingDrive__Pool,
GIb__Pool,
GII__Pool,
)
from myogen.simulator.neuron.proprioception import (
GolgiTendonOrganModel,
SpindleModel,
)
from myogen.simulator.neuron.simulation_runner import SimulationRunner
from myogen.utils.plotting import (
plot_gto_dynamics,
plot_membrane_potentials,
plot_muscle_dynamics,
plot_raster_spikes,
plot_spindle_dynamics,
)
Load NEURON Mechanisms and Dependencies#
Load the compiled NMODL mechanisms required for biophysical neuron modeling and load results from previous examples that serve as inputs to this simulation.
# Load NEURON mechanisms
load_nmodl_mechanisms()
# Setup results directory
save_path = Path(r"./results")
save_path.mkdir(exist_ok=True)
recruitment_thresholds = joblib.load(save_path / "thresholds.pkl")
print("(OK) Loaded recruitment thresholds from example 00")
(OK) Loaded recruitment thresholds from example 00
Define Simulation Parameters#
These parameters control the temporal and spatial resolution of the simulation, as well as the physiological characteristics of the neural populations and mechanical system.
# Temporal parameters - high resolution for accurate neural integration
dt = 0.005 * pq.ms # Integration timestep with units
tstop = 5e3 # 5e3 # ms - Total simulation duration (5s for comprehensive protocol)
time = np.arange(0, tstop, dt.magnitude) # Time vector (use magnitude for numpy)
print("Simulation parameters:")
print(f"\tDuration: {tstop} ms")
print(f"\tTimestep: {dt} ms")
print(f"\tTime samples: {len(time)}")
Simulation parameters:
Duration: 5000.0 ms
Timestep: 0.005 ms ms
Time samples: 1000000
Define Neural Population Sizes#
Population sizes are based on physiological estimates from cat and human studies. These numbers represent typical motor pool compositions for a single muscle.
# Afferent populations (sensory input)
# Based on Banks et al. (2006, 2015) for distal upper-limb muscles
nIa = 73 # Group Ia afferents from muscle spindles (velocity-sensitive)
nII = 80 # Group II afferents from muscle spindles (length-sensitive) - 110% of Ia
nIb = 58 # Group Ib afferents from Golgi tendon organs (force-sensitive) - 80% of Ia
# Interneuron populations (spinal processing)
# Note: Interneuron:MN ratio is ~10:1 in spinal cord. Group II/Ib INs are a subset.
# Using ~50% of afferent count as a reasonable estimate for convergent interneurons.
ngII = 120 # Group II interneurons (process spindle feedback from 80 II afferents)
ngIb = 145 # Group Ib interneurons (process force feedback from 58 Ib afferents)
# Motor neurons (output to muscles)
nType1 = 102 # Type I motor neurons (slow, fatigue-resistant)
nType2 = 18 # Type II motor neurons (fast, fatigue-prone)
naMN = nType1 + nType2 # Total α-motoneurons per muscle
# Descending drive (cortical input)
nDD = 400 # Total descending drive neurons (increased for more drive)
DDorder = (
5 # Poisson process order for realistic spike patterns (higher order = more regular spiking)
)
print("Neural population sizes:")
print(f"\t- α-Motoneurons: {naMN} ({nType1} Type I, {nType2} Type II)")
print(f"\t- Ia afferents: {nIa}")
print(f"\t- II afferents: {nII}")
print(f"\t- Ib afferents: {nIb}")
print(f"\t- Interneurons: {ngII + ngIb}")
print(f"\t- Descending drive: {nDD}")
Neural population sizes:
- α-Motoneurons: 120 (102 Type I, 18 Type II)
- Ia afferents: 73
- II afferents: 80
- Ib afferents: 58
- Interneurons: 265
- Descending drive: 400
Define Descending Drive Pattern#
Two-phase pattern: Phase 1 (0-2500ms): No cortical drive (reflex testing with varying gamma) Phase 2 (2500-5000ms): Sinusoidal cortical drive (reflex modulation during voluntary contraction)
# Phase 1: No cortical drive
# Phase 2: 1 Hz sinusoidal drive with bias to recruit ~75% of MN population
DDdrive = np.zeros_like(time)
cortical_start_time = 2500 # ms
# Parameters for sinusoidal drive
bias_hz = 40 # Bias for robust motor neuron recruitment (increased from 75 for ~20 pps firing)
amplitude_hz = 1 # Oscillation amplitude (±5 Hz around bias)
frequency_hz = 1.0 # 1 Hz oscillation
# Apply sinusoidal drive from 2.5s onwards
mask = time >= cortical_start_time
DDdrive[mask] = bias_hz + amplitude_hz * np.sin(
2 * np.pi * frequency_hz * (time[mask] - cortical_start_time) / 1000.0
)
print("Descending drive pattern:")
print("\t- Phase 1 (0-2.5s): No cortical drive")
print(f"\t- Phase 2 (2.5-5s): Sinusoidal drive ({bias_hz}±{amplitude_hz} Hz at {frequency_hz} Hz)")
print(f"\t (Drive range: {bias_hz - amplitude_hz}-{bias_hz + amplitude_hz} Hz)")
Descending drive pattern:
- Phase 1 (0-2.5s): No cortical drive
- Phase 2 (2.5-5s): Sinusoidal drive (40±1 Hz at 1.0 Hz)
(Drive range: 39-41 Hz)
Define Fusimotor Drive#
Fusimotor neurons control the sensitivity of muscle spindles by adjusting the tension in intrafusal muscle fibers. Stepwise increasing gamma drive demonstrates how fusimotor activity modulates stretch reflex gain.
Pattern: Increases every 0.5s starting at 0.75s, resets at 2.5s Steps: 0 → 25 → 50 → 75 → 100 pps (then repeat)
# Time points for stepwise gamma drive
# Phase 1: 0→0.75s (wait)→1.25s→1.75s→2.25s (steps every 0.5s)
# Phase 2: 2.5s (reset)→3.25s (wait 0.75s)→3.75s→4.25s→4.75s (steps every 0.5s)
gamma_times = np.array([0, 750, 1250, 1750, 2250, 2500, 3250, 3750, 4250, 4750, 5000])
gamma_values = np.array([0, 25, 50, 75, 100, 0, 25, 50, 75, 100, 100])
# Create stepwise gamma drive arrays using proper step function (not interpolation!)
gDyn = np.zeros_like(time)
gStat = np.zeros_like(time)
# Phase 1: Steps every 0.5s starting at 0.75s
gDyn[(time >= 750) & (time < 1250)] = 25
gDyn[(time >= 1250) & (time < 1750)] = 50
gDyn[(time >= 1750) & (time < 2250)] = 75
gDyn[(time >= 2250) & (time < 2500)] = 100
# Phase 2: Reset and repeat pattern
gDyn[(time >= 3250) & (time < 3750)] = 25
gDyn[(time >= 3750) & (time < 4250)] = 50
gDyn[(time >= 4250) & (time < 4750)] = 75
gDyn[(time >= 4750) & (time <= 5000)] = 100
# Static gamma follows same pattern
gStat = gDyn.copy()
# Add small physiological variability
gDyn = gDyn + np.random.normal(0, 1, len(time))
gStat = gStat + np.random.normal(0, 1, len(time))
# Ensure non-negative
gDyn = np.maximum(gDyn, 0)
gStat = np.maximum(gStat, 0)
# Package fusimotor drives for the simulation
gMN = {
"name": "gMN",
"gDyn": gDyn, # Dynamic fusimotor drive array
"gStat": gStat, # Static fusimotor drive array
}
print("Fusimotor drive parameters:")
print("\t- Stepwise increases: 0 → 25 → 50 → 75 → 100 pps")
print("\t- Starting at 0.75s, stepping every 0.5s")
print("\t- Resets at 2.5s and repeats pattern")
Fusimotor drive parameters:
- Stepwise increases: 0 → 25 → 50 → 75 → 100 pps
- Starting at 0.75s, stepping every 0.5s
- Resets at 2.5s and repeats pattern
Initialize Joint Dynamics#
The joint model provides realistic biomechanical constraints and creates the closed-loop system where muscle forces influence joint motion, which in turn affects proprioceptive feedback.
joint_dynamics = JointDynamics(
inertia__kg_m2=0.001, # Realistic joint inertia
damping__Nm_s_per_rad=0.002, # Light damping for stability
)
# Initialize joint angle array for closed-loop integration
artAng = np.zeros_like(time)
artAng[0] = 0.0 # Initial joint angle
print("Joint dynamics parameters:")
print(f"\t- Inertia: {joint_dynamics.inertia__kg_m2} kg⋅m²")
print(f"\t- Damping: {joint_dynamics.damping__Nm_s_per_rad} N⋅m⋅s/rad")
print(f"\t- Initial angle: {artAng[0]}°")
Joint dynamics parameters:
- Inertia: 0.001 kg⋅m²
- Damping: 0.002 N⋅m⋅s/rad
- Initial angle: 0.0°
Create Neural Populations#
Instantiate all neural population objects with physiologically appropriate parameters. Each population type has specialized properties reflecting their biological counterparts.
# Create motor neuron pool
# Motor neuron pool (default spike_threshold__mV=50.0 for proper spike detection)
aMN = AlphaMN__Pool(recruitment_thresholds__array=recruitment_thresholds) # α-motoneurons
# Create descending drive population
DD = DescendingDrive__Pool(n=nDD, poisson_batch_size=DDorder, timestep__ms=dt)
# Create afferent populations
Ia = AffIa__Pool(n=nIa, timestep__ms=dt) # Primary spindle afferents
II = AffII__Pool(n=nII, timestep__ms=dt) # Lower thresholds for Group II
Ib = AffIb__Pool(n=nIb, timestep__ms=dt) # Golgi tendon organ afferents
# Create interneuron populations for reflex modulation
gII = GII__Pool(n=ngII) # Group II interneurons
gIb = GIb__Pool(n=ngIb) # Group Ib interneurons
print(f"(OK) Created {len([aMN, DD, Ia, II, Ib, gII, gIb])} neural populations")
(OK) Created 7 neural populations
Create Proprioceptive Models#
Initialize the sensory models that convert mechanical variables (muscle length, velocity, force) into neural signals that drive the afferent populations.
# Golgi Tendon Organ - monitors muscle force/tension
gto = GolgiTendonOrganModel(
simulation_time__ms=tstop * pq.ms,
time_step__ms=dt,
gto_parameters=GolgiTendonOrganModel.create_default_gto_parameters(),
)
# Muscle Spindle - monitors muscle length and velocity
spin = SpindleModel(
simulation_time__ms=tstop * pq.ms,
time_step__ms=dt,
spindle_parameters=SpindleModel.create_default_spindle_parameters(),
)
print("(OK) Initialized proprioceptive models (spindle, GTO)")
(OK) Initialized proprioceptive models (spindle, GTO)
Create Muscle Model#
Initialize Hill-type muscle model. This model converts motor neuron activation into realistic force generation with appropriate biomechanical properties.
# Muscle model
hill_muscle = HillModel(
simulation_time__ms=tstop * pq.ms,
time_step__ms=dt,
muscle_parameters=HillModel.create_default_muscle_parameters(),
n_motor_units_type1=nType1,
n_motor_units_type2=nType2,
initial_joint_angle__deg=artAng[0],
muscle_role="flexor",
)
print("(OK) Created muscle model")
print(f"\t- Motor units: {nType1 + nType2}")
print(f"\t- Force capacity: ~{hill_muscle.F0:.1f} N")
(OK) Created muscle model
- Motor units: 120
- Force capacity: ~33.8 N
Create Arrays for Real-Unit Forces#
Store musculotendon force in real units [N] for analysis
# Musculotendon force array [N]
musculotendon_force__N = np.zeros_like(time)
print("(OK) Initialized force tracking arrays")
(OK) Initialized force tracking arrays
Define Callback Functions#
These functions handle the integration of different system components during the simulation, including spike events and step-wise updates.
def spkEvent(i, muscle, delay):
muscle.add_spike(i, delay)
def eachStep(
muscle,
spin,
golgi,
popD,
ncD,
gMN,
joint_dyn,
step_counter,
tendon_tap_schedule, # List of (time_ms, magnitude_percent) tuples
tendon_tap_duration=100, # ms
):
"""
Step-wise integration function called at each simulation timestep.
This function orchestrates the complex interactions between:
- Muscle mechanics and force generation
- Proprioceptive feedback from spindles and GTOs
- Joint dynamics and closed-loop control
- Neural population dynamics and spike generation
- Multiple tendon tap perturbations with varying amplitudes
Parameters
----------
muscle : HillModel
Muscle model
spin : SpindleModel
Muscle spindle model
golgi : GolgiTendonOrganModel
Golgi tendon organ model
popD : dict
Dictionary of neural populations
ncD : dict
Dictionary of network connections
gMN : dict
Fusimotor drive parameters
joint_dyn : JointDynamics
Joint biomechanics model
step_counter : iterator
Simulation step counter
tendon_tap_schedule : list of tuples
List of (time_ms, magnitude_percent) defining tap timing and amplitudes
tendon_tap_duration : float
Duration (ms) of each tendon tap stretch
"""
i = next(step_counter)
current_angle = artAng[i]
# MUSCLE MECHANICS: Integrate muscle with current joint angle
L, V, A = muscle.integrate(current_angle)
# TENDON TAP PERTURBATION: Triangular pulse (ramp up, then down)
current_time = h.t
for tap_time, tap_magnitude in tendon_tap_schedule:
tap_end_time = tap_time + tendon_tap_duration
tap_midpoint = tap_time + (tendon_tap_duration / 2.0)
if tap_time <= current_time < tap_end_time:
# Triangular pulse: ramp up to peak at midpoint, then ramp down
max_perturbation = L * (tap_magnitude / 100.0)
if current_time < tap_midpoint:
# Rising edge: 0 → peak (first half)
progress = (current_time - tap_time) / (tendon_tap_duration / 2.0)
length_perturbation = max_perturbation * progress
else:
# Falling edge: peak → 0 (second half)
progress = (tap_end_time - current_time) / (tendon_tap_duration / 2.0)
length_perturbation = max_perturbation * progress
L_perturbed = L + length_perturbation
# Velocity reflects the triangle slope
if current_time < tap_midpoint:
# Rising: positive velocity
V_perturbed = V + (max_perturbation / (tendon_tap_duration / 2000.0))
else:
# Falling: negative velocity
V_perturbed = V - (max_perturbation / (tendon_tap_duration / 2000.0))
# Acceleration spikes at tap onset and reverses at midpoint
if abs(current_time - tap_time) < dt.magnitude:
A_perturbed = A + (max_perturbation / ((tendon_tap_duration / 2000.0) ** 2))
print(
f"\t>> TENDON TAP (triangular) at t={current_time:.1f} ms: "
f"{tap_magnitude}% peak stretch ({max_perturbation:.4f} L0), "
f"duration={tendon_tap_duration} ms"
)
print(f"\t Baseline length: {L:.4f} L0 → Peak: {L + max_perturbation:.4f} L0")
elif abs(current_time - tap_midpoint) < dt.magnitude:
A_perturbed = A - 2 * (max_perturbation / ((tendon_tap_duration / 2000.0) ** 2))
else:
A_perturbed = A
# Use perturbed values for spindle feedback
L, V, A = L_perturbed, V_perturbed, A_perturbed
break # Only one tap active at a time
# PROPRIOCEPTIVE FEEDBACK: Use muscle kinematics for spindle feedback
Iay, IIy = spin.integrate(L, V, A, gMN["gDyn"][i], gMN["gStat"][i])
# FORCE FEEDBACK: Muscle force for GTO
f = muscle.F0 * muscle.muscle_force[i] # Musculotendon force [N]
musculotendon_force__N[i] = f # Store in real units
Iby = golgi.integrate(f)
# CLOSED-LOOP DYNAMICS: Update joint angle based on muscle torque
new_angle, _ = joint_dyn.integrate(
torque__Nm=muscle.signed_muscle_torque[i],
dt__s=float(dt.rescale(pq.s).magnitude),
)
# Update joint angle array for next timestep
if i < len(artAng) - 1:
artAng[i + 1] = new_angle
# DESCENDING DRIVE PROCESSING: Convert cortical signals to spikes
for DDcell in popD["DD"]:
if DDcell.integrate(DDdrive[i]):
spike_time = h.t + 1
if spike_time < tstop:
ncD["cmd->DD"][DDcell.pool__ID].event(spike_time)
# AFFERENT PROCESSING: Convert sensory signals to neural spikes
for Ia in popD["Ia"]:
if Iay >= Ia.RT:
if Ia.integrate(Iay):
# Ensure h.t is converted to a quantities object with units of ms
spike_time = h.t + float(Ia.axon_delay__ms)
if spike_time < tstop:
ncD["Spindle->Ia"][Ia.pool__ID].event(spike_time)
ii_spikes = 0
for II in popD["II"]:
if IIy >= II.RT:
if II.integrate(IIy):
spike_time = h.t + float(II.axon_delay__ms)
if spike_time < tstop:
ncD["Spindle->II"][II.pool__ID].event(spike_time)
ii_spikes += 1
ib_spikes = 0
for Ib in popD["Ib"]:
if Iby >= Ib.RT:
if Ib.integrate(Iby):
spike_time = h.t + float(Ib.axon_delay__ms)
if spike_time < tstop:
ncD["GTO->Ib"][Ib.pool__ID].event(spike_time)
ib_spikes += 1
Create Neural Network#
Assemble all neural populations into a connected network that implements the spinal reflex circuitry for single muscle control.
network = Network(
{
"DD": DD, # Descending drive
"aMN": aMN, # α-motoneurons
"Ia": Ia, # Group Ia afferents
"II": II, # Group II afferents
"Ib": Ib, # Group Ib afferents
"gII": gII, # Group II interneurons
"gIb": gIb, # Group Ib interneurons
"gMN": gMN, # Fusimotor parameters
}
)
print(f"(OK) Created network with {len(network.populations)} populations")
(OK) Created network with 8 populations
Configure Neural Connections#
Establish synaptic connections that implement physiologically realistic spinal reflex pathways, including both excitatory and inhibitory connections.
Neural Circuit Diagram:#
- Spindle (length/velocity) GTO (force) Cortex
v v v v
- Ia II Ib DD
- +———-+——–(+)————+———-(+)—–+
v
- α-MN —–> Muscle
v
- Joint Motion
v v
Spindle GTO
(feedback) (feedback)
Legend: (+) = excitatory, (-) = inhibitory
Key pathways: 1. Ia → MN: Monosynaptic stretch reflex (EXCITATORY, fast) 2. II → gII → MN: Polysynaptic length pathway (INHIBITORY, moderate speed) 3. Ib → gIb → MN: Autogenic inhibition (INHIBITORY, slower - force-dependent) 4. DD → MN: Descending cortical drive (EXCITATORY, voluntary control)
# DESCENDING CONTROL: Direct cortical drive to motor neurons (EXCITATORY)
network.connect("DD", "aMN", probability=0.3, weight__uS=0.05 * pq.uS)
# MONOSYNAPTIC STRETCH REFLEX: Ia afferents excite motor neurons (EXCITATORY)
# High connection probability (80%) reflects homogeneous excitatory distribution
network.connect("Ia", "aMN", probability=0.8, weight__uS=0.05 * pq.uS)
# POLYSYNAPTIC PATHWAYS: Group II pathway (afferents → interneurons → motor neurons)
# Lower connection probability (30%) captures predominantly indirect, disynaptic influence
network.connect(
"II", "gII", probability=0.3, weight__uS=0.025 * pq.uS
) # Afferent → Interneuron (EXCITATORY)
network.connect(
"gII", "aMN", probability=0.3, weight__uS=0.05 * pq.uS, inhibitory=True
) # Interneuron → MN (INHIBITORY, weak modulatory effect)
# INHIBITORY REFLEXES: Force feedback through Ib interneurons (autogenic inhibition)
# Lower connection probability (30%) captures predominantly indirect, disynaptic influence
network.connect(
"Ib", "gIb", probability=0.3, weight__uS=0.025 * pq.uS
) # Afferent → Interneuron (EXCITATORY)
network.connect(
"gIb", "aMN", probability=0.3, weight__uS=0.05 * pq.uS, inhibitory=True
) # Interneuron → MN (INHIBITORY, weak modulatory effect)
print("(OK) Configured synaptic connections")
print("\t- Excitatory pathways:")
print("\t\t• DD→MN (descending drive)")
print("\t\t• Ia→MN (monosynaptic stretch reflex)")
print("\t\t• Afferents→Interneurons: II→gII, Ib→gIb")
print("\t- Inhibitory pathways:")
print("\t\t• gII→MN (Group II interneuron inhibition)")
print("\t\t• gIb→MN (autogenic inhibition from force feedback)")
(OK) Configured synaptic connections
- Excitatory pathways:
• DD→MN (descending drive)
• Ia→MN (monosynaptic stretch reflex)
• Afferents→Interneurons: II→gII, Ib→gIb
- Inhibitory pathways:
• gII→MN (Group II interneuron inhibition)
• gIb→MN (autogenic inhibition from force feedback)
Connect Motors to Muscle#
Establish the neuromuscular junctions that convert motor neuron spikes into muscle fiber activation.
# Connect motor neurons to muscle (spike threshold automatically uses population default of 50.0 mV)
network.connect_to_muscle(
"aMN", muscle=hill_muscle, activation_callback=spkEvent, weight__uS=1.0 * pq.uS
)
print("(OK) Connected motor neurons to muscle")
(OK) Connected motor neurons to muscle
Configure External Inputs#
Setup external input pathways for sensory feedback and descending commands.
network.connect_from_external("cmd", "DD", weight__uS=1.0 * pq.uS)
network.connect_from_external("spindle", "Ia", weight__uS=1.0 * pq.uS)
network.connect_from_external("spindle", "II", weight__uS=1.0 * pq.uS)
network.connect_from_external("gto", "Ib", weight__uS=1.0 * pq.uS)
# Get NetCons for manual triggering during simulation
ncD = {
"cmd->DD": network.get_netcons("cmd", "DD"),
"Spindle->Ia": network.get_netcons("spindle", "Ia"),
"Spindle->II": network.get_netcons("spindle", "II"),
"GTO->Ib": network.get_netcons("gto", "Ib"),
}
print("(OK) Configured external input pathways")
(OK) Configured external input pathways
Prepare Simulation Models#
# Package all models for the simulation runner
models = {
"hill_muscle": hill_muscle,
"spin": spin,
"gto": gto,
"joint": joint_dynamics,
}
# Tendon tap parameters - multiple taps with increasing amplitudes
# Pattern: Taps every 0.5s with increasing amplitude, reset at 2.5s
# High amplitudes to elicit strong reflex responses
# Phase 1 (0-2.5s): 50%, 60%, 70%, 80%
# Phase 2 (2.5-5s): 50%, 60%, 70%, 80%
TENDON_TAP_DURATION = 100 # ms - duration of each stretch
TENDON_TAP_SCHEDULE = [
# Phase 1: Ascending amplitudes without cortical drive
(500, 50.0), # 0.5s: 50%
(1000, 60.0), # 1.0s: 60%
(1500, 70.0), # 1.5s: 70%
(2000, 80.0), # 2.0s: 80%
# Phase 2: Repeat pattern with cortical drive
(3000, 50.0), # 3.0s: 50%
(3500, 60.0), # 3.5s: 60%
(4000, 70.0), # 4.0s: 70%
(4500, 80.0), # 4.5s: 80%
]
print("\nTendon tap schedule:")
print(f"\t- Duration per tap: {TENDON_TAP_DURATION} ms")
print(f"\t- Phase 1 (0-2.5s): {len([t for t, m in TENDON_TAP_SCHEDULE if t < 2500])} taps")
print(f"\t- Phase 2 (2.5-5s): {len([t for t, m in TENDON_TAP_SCHEDULE if t >= 2500])} taps")
print(f"\t- Amplitudes: {sorted(set([m for t, m in TENDON_TAP_SCHEDULE]))}%")
# Create step callback function with access to step counter
def step_callback(step_counter):
return eachStep(
muscle=hill_muscle,
spin=spin,
golgi=gto,
popD=network.populations,
ncD=ncD,
gMN=gMN,
joint_dyn=joint_dynamics,
step_counter=step_counter,
tendon_tap_schedule=TENDON_TAP_SCHEDULE,
tendon_tap_duration=TENDON_TAP_DURATION,
)
Tendon tap schedule:
- Duration per tap: 100 ms
- Phase 1 (0-2.5s): 4 taps
- Phase 2 (2.5-5s): 4 taps
- Amplitudes: [50.0, 60.0, 70.0, 80.0]%
Run Spinal Network Simulation#
Execute the complete simulation with all integrated components.
print("\nStarting spinal network simulation...")
print(f"\tDuration: {tstop} ms")
print(f"\tTimestep: {dt} ms")
print(f"\tPopulations: {len(network.populations)}")
runner = SimulationRunner(
network=network,
models=models,
step_callback=step_callback,
)
# Motor neuron spike recording thresholds are now fixed in the Network class
results = runner.run(
duration__ms=tstop * pq.ms,
timestep__ms=dt,
membrane_recording={
"aMN": [0, 5, 10, 15, 20, 30, 40, 50, 60, 70],
},
)
print("Simulation completed successfully!")
# Save simulation results
joblib.dump(results, save_path / "spinal_network_results.pkl")
joblib.dump(artAng, save_path / "joint_angles.pkl")
joblib.dump(musculotendon_force__N, save_path / "musculotendon_force__N.pkl")
# Save drive signals for analysis and plotting
drive_signals = {
"time": time,
"descending_drive": DDdrive,
"gamma_dynamic": gDyn,
"gamma_static": gStat,
"tendon_tap_schedule": TENDON_TAP_SCHEDULE,
"tendon_tap_duration": TENDON_TAP_DURATION,
}
joblib.dump(drive_signals, save_path / "drive_signals.pkl")
# Save event timeline for plot annotations
events = {
# Tendon tap events: (peak_time_ms, amplitude_%, duration_ms)
# Note: peak_time is at the midpoint of the triangular pulse
"tendon_taps": [
(t + TENDON_TAP_DURATION / 2.0, m, TENDON_TAP_DURATION) for t, m in TENDON_TAP_SCHEDULE
],
# Gamma drive transitions: (time_ms, level_pps)
"gamma_transitions": list(zip(gamma_times, gamma_values)),
# Gamma drive periods: (start_time_ms, end_time_ms, level_pps)
"gamma_periods": [
(gamma_times[i], gamma_times[i + 1], gamma_values[i]) for i in range(len(gamma_times) - 1)
],
# Phase markers
"phase_boundary": 2500, # ms - transition from phase 1 to phase 2
"cortical_drive_onset": cortical_start_time, # ms - when sinusoidal drive starts
# Experimental phases with descriptions
"phases": [
{"start": 0, "end": 2500, "name": "Phase 1", "description": "Reflex gain modulation"},
{
"start": 2500,
"end": 5000,
"name": "Phase 2",
"description": "Reflex-voluntary interaction",
},
],
}
joblib.dump(events, save_path / "event_timeline.pkl")
print(f"Results saved to {save_path}")
print("\t- spinal_network_results.pkl (neural activity, muscle, spindle, GTO)")
print("\t- joint_angles.pkl (joint kinematics)")
print("\t- musculotendon_force__N.pkl (real-unit musculotendon force [N])")
print("\t- drive_signals.pkl (cortical drive, gamma drive, tap schedule)")
print("\t- event_timeline.pkl (event markers for plot annotations)")
print("\nNote: Intrafusal fiber tensions [FU] are in spinal_network_results.pkl")
print("\tAccess via: results.segments[0].analogsignals (look for 'intrafusal_tensions')")
print("\tConvert to real units: T[N] ≈ T[FU] * scaling_factor (no standard conversion)")
print(f"\tMusculotendon force capacity: {hill_muscle.F0:.1f} N")
Starting spinal network simulation...
Duration: 5000.0 ms
Timestep: 0.005 ms ms
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Baseline length: 0.9917 L0 → Peak: 1.4875 L0
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Baseline length: 0.9885 L0 → Peak: 1.6805 L0
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Baseline length: 0.9852 L0 → Peak: 1.7734 L0
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Simulation completed
Simulation completed successfully!
Results saved to results
- spinal_network_results.pkl (neural activity, muscle, spindle, GTO)
- joint_angles.pkl (joint kinematics)
- musculotendon_force__N.pkl (real-unit musculotendon force [N])
- drive_signals.pkl (cortical drive, gamma drive, tap schedule)
- event_timeline.pkl (event markers for plot annotations)
Note: Intrafusal fiber tensions [FU] are in spinal_network_results.pkl
Access via: results.segments[0].analogsignals (look for 'intrafusal_tensions')
Convert to real units: T[N] ≈ T[FU] * scaling_factor (no standard conversion)
Musculotendon force capacity: 33.8 N
Comprehensive Results Visualization#
Create a series of plots that tell the complete story of spinal network function, from neural activity to mechanical output.
print("\nGenerating comprehensive visualizations...")
# 1. NEURAL ACTIVITY: Raster plot showing all population spike patterns
populations_list = [
"aMN", # Motor output
"Ia",
"II",
"Ib", # Sensory input
"gII",
"gIb", # Interneurons
"DD", # Descending drive
]
fig1, axes1 = plt.subplots(len(populations_list), 1, figsize=(15, 12))
plot_raster_spikes(
results,
axes1,
populations=populations_list,
time_range=(0, tstop),
title="Spinal Network Activity (Single Muscle)",
)
plt.tight_layout()
plt.savefig(save_path / "neural_raster_plot.png", dpi=150, bbox_inches="tight")
plt.show()
# 2. MOTOR NEURON DYNAMICS: Membrane potentials showing integration
fig2, ax2 = plt.subplots(1, 1, figsize=(15, 6))
plot_membrane_potentials(
results,
[ax2],
populations=["aMN"],
cell_indices=[0, 10, 20, 30, 40],
time_range=(0, tstop),
title="Motor Neuron Membrane Potentials",
)
plt.tight_layout()
plt.show()
# 3. MUSCLE MECHANICS: Muscle dynamics
fig3, axes3 = plt.subplots(5, 1, figsize=(15, 20))
plot_muscle_dynamics(
results,
artAng,
time,
axes3,
muscle_name="hill_muscle",
include_signals=["artAng", "L", "force", "torque"],
include_activations=["TypeI", "TypeII"],
normalize=True,
time_range=(0, tstop),
title="Muscle Dynamics - Length, Force, and Activation",
)
plt.tight_layout()
plt.savefig(save_path / "muscle_dynamics.png", dpi=150, bbox_inches="tight")
plt.show()
# 4. PROPRIOCEPTIVE FEEDBACK: Spindle dynamics and sensory encoding
fig4, axes4 = plt.subplots(4, 1, figsize=(15, 16))
plot_spindle_dynamics(
results,
axes4,
muscle_name="hill_muscle",
include_signals=["L"],
include_activations=["Bag1", "Bag2", "Chain"],
include_tensions=["Bag1", "Bag2", "Chain"],
include_afferents=["Ia", "II"],
time_range=(0, tstop),
title="Muscle Spindle Dynamics - Proprioceptive Feedback System",
)
plt.tight_layout()
plt.savefig(save_path / "spindle_dynamics.png", dpi=150, bbox_inches="tight")
plt.show()
# 5. FORCE FEEDBACK: GTO dynamics and protective reflexes
fig5, axes5 = plt.subplots(2, 1, figsize=(15, 8))
plot_gto_dynamics(
results,
axes5,
muscle_name="hill_muscle",
include_signals=["force", "Ib"],
time_range=(0, tstop),
title="Golgi Tendon Organ Dynamics - Force Feedback System",
)
plt.tight_layout()
plt.savefig(save_path / "gto_dynamics.png", dpi=150, bbox_inches="tight")
plt.show()
Generating comprehensive visualizations...
Total running time of the script: (11 minutes 49.477 seconds)