1. Overview: Electromyographic Biophysics & Motor Unit Recruitment
Electromyography (EMG) is an electrophysiological diagnostic and research methodology dedicated to recording, analyzing, and quantifying the electrical potential fields generated by skeletal muscle fibers during neuromuscular excitation. At the microscopic structural level, skeletal muscle contraction is orchestrated by functional entities termed Motor Units (MUs). A single motor unit comprises an anterior alpha motor neuron originating within the spinal cord ventral horn, its peripheral axon, and every individual multinucleated extrafusal muscle fiber innervated by its terminal axon collaterals.
When an action potential propagates down the motor axon, it triggers acetylcholine release across the neuromuscular junction, inducing membrane depolarization along the muscle fiber sarcolemma. This propagating wave of extracellular charge displacement constitutes a Single Fiber Action Potential (SFAP). The linear algebraic spatio-temporal summation of all active fiber potentials within an individual motor unit creates the Motor Unit Action Potential (MUAP):
$$MUAP(t) = \sum_{k=1}^{N_f} SFAP_k(t - \tau_k)$$
where $N_f$ designates the total number of muscle fibers comprising the active motor unit, and $\tau_k$ accounts for axonal conduction delays and synaptic propagation dispersion across the motor endplate. When surface electrodes (sEMG) are positioned over the muscle belly, they record the global interference pattern, $V_{\text{sEMG}}(t)$, representing the stochastic superimposition of thousands of asynchronous MUAP trains modulated by spatial volume conduction:
$$V_{\text{sEMG}}(t) = \sum_{j=1}^{M} \sum_{i=1}^{P_j} MUAP_{j}(t - t_{j,i}) * h(t) + \eta(t)$$
where $M$ denotes the number of recruited motor units, $t_{j,i}$ represents the firing instants of unit $j$, $h(t)$ denotes the non-homogeneous filtering transfer function of subcutaneous adipose and dermal tissue layers, and $\eta(t)$ embodies ambient biological, thermal, and instrumentation noise.
During progressive physical effort, force modulation obeys Henneman's Size Principle: smaller, slow-twitch (Type I, fatigue-resistant) motor units are recruited first at low thresholds, exhibiting smaller amplitude MUAPs. As force demands escalate toward Maximal Voluntary Contraction (MVC), larger fast-twitch (Type IIa/IIx, high-velocity) units are progressively activated alongside increased motor firing rates (rate coding), transitioning the visual trace from discrete baseline oscillations into a dense, high-frequency interference pattern.
2. Operational Guidelines & Interactive Telemetry
The MyoScope simulation interface provides an interactive, calibrated laboratory to study muscle electrophysiology, interference waveforms, and real-time DSP feature extraction. Follow these workflows to systematically explore recruitment dynamics:
- Isometric Contraction Simulation: Click and hold the cyan "PRESS & HOLD TO FLEX" button (or touch and hold on mobile displays). Notice the instantaneous transition from stochastic microvolt baseline noise into high-amplitude interference bursts. Releasing the button instantly ceases active recruitment, demonstrating post-contraction resting potential recovery.
- Automated Clinical Demonstration: Click the "Start Demo" button at the top of the sidebar. The system will systematically glide through baseline rest, moderate recruitment, muscle fatigue spectral shifts, and neuropathic tremor bursts with human-paced physiological transitions and visual parameter focus. Interact with any slider or canvas to immediately regain manual authority.
- Preset Selection: Expand the Neuromuscular Properties panel to alternate between experimental states:
- Standard Isometric Flex: Clean physiological interference pattern with balanced frequency distribution (10–500 Hz).
- Muscle Fatigue: Simulates metabolic lactic acid accumulation and intracellular $pH$ decline, resulting in slowed conduction velocities ($v \downarrow$) and low-frequency spectral compression ($P_{\text{mean}} \downarrow$).
- Neuropathic Tremor Fibrillation: Demonstrates pathological involuntary motor synchronization, manifesting as rhythmic 4–7 Hz burst packets.
- Maximal Voluntary Contraction (MVC): Full physiological recruitment demonstrating maximum spatial summation and signal clipping.
- Hardware Filtering Modes: Toggle between raw biopotentials, 50/60 Hz notch filtering, and real-time linear envelope extraction (half-wave rectification paired with a second-order Butterworth low-pass filter) to observe how myoelectric prosthetic control signals are derived.
- Oscilloscope Sweep & Display: Adjust the Time Base Window to scale between high-resolution individual spike morphologies (50 pts) and long-term recruitment trends (300 pts). Dynamic Voltage Auto-Scale continuously optimizes vertical gain to prevent clipping.
3. Mathematical Signal Processing & DSP Implementation
MyoScope computes synthetic bio-signal traces at 60 Hz utilizing discrete-time physiological stochastic differential generators. Real-time amplitude and energy metrics are calculated over a sliding circular sample window $\mathbf{x} = [x_1, x_2, \dots, x_N]$ containing $N$ active discrete data points.
Statistical Metric Computations
The Peak Absolute Voltage ($V_p$) captures maximum instantaneous fiber synchronization:
$$V_p = \max_{1 \le i \le N} |x_i|$$
The Root Mean Square ($V_{\text{rms}}$) reflects the true physiological power and effective metabolic energy of the active motor units, directly proportional to physiological muscle tension:
$$V_{\text{rms}} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} x_i^2}$$
The Mean Absolute Value ($V_{\text{mean}}$), also termed the Average Rectified Value (ARV), represents the standard baseline biomarker utilized in myoelectric prosthesis microcontrollers:
$$V_{\text{mean}} = \frac{1}{N} \sum_{i=1}^{N} |x_i|$$
Fatigue Modeling & Spectral Shift
Under sustained ischemic contraction, localized muscle fatigue alters the membrane depolarization conduction velocity ($v$), shifting the power spectral density (PSD) toward lower frequencies. The simulator models this by modulating the carrier frequency parameter $\omega_{\text{carrier}}$ and adding sub-harmonic decay:
$$S(t) = \sum_{m=1}^{K} A_m(t) \cdot \sin\left(\omega_m \cdot t + \phi_m\right) + \mathcal{N}(0, \sigma_{\text{baseline}}^2)$$
where $A_m(t)$ is driven by the dynamic flex envelope, and $\mathcal{N}(0, \sigma^2)$ injects Gaussian thermal noise mimicking skin-electrode impedance mismatches ($Z_{\text{skin}} \approx 10\text{--}50\text{ k}\Omega$).