SPECS.md

MSNA Signal Simulation - Technical Specifications

Overview

This document describes the technical implementation for simulating realistic integrated Muscle Sympathetic Nerve Activity (MSNA) obtained through microneurography recordings. The simulator generates physiologically accurate integrated MSNA signals with realistic noise profiles suitable for algorithm development, testing, and educational purposes.

Physiological Background

MSNA Characteristics

Muscle Sympathetic Nerve Activity (MSNA) is a direct measurement of the sympathetic nervous system activity to skeletal muscle vasculature. Key physiological characteristics include:

• Cardiac Phase Locking: MSNA bursts are phase-locked to the cardiac cycle, occurring during diastole (~1.3 seconds after the R-wave)
• Burst Incidence: Percentage of cardiac cycles containing sympathetic bursts (typically 30-80% in healthy adults)
• Respiratory Modulation: Sympathetic activity is modulated by respiration, with reduced activity during inspiration
• Burst Morphology: Individual bursts have symmetric, roughly Gaussian-shaped profiles after rectifying and integration.

Recording Methodology

MSNA is recorded using microneurography, where tungsten microelectrodes are inserted into peripheral nerves (commonly the peroneal nerve). The raw signal undergoes amplification, bandpass filtering, and integration to get the integrated MSNA signal which is typically used for analysis.

Signal Generation Methodology

Cardiac Timing Generation

The simulator generates realistic ECG R-wave timing with physiological heart rate variability (HRV). The approach models natural cardiac rhythm variations observed in healthy individuals through normally distributed RR intervals with appropriate variability.

$$\text{RR}_{\text{intervals}} \sim \mathcal{N}(\text{mean}_{\text{RR}}, \sigma_{\text{HRV}})$$

Where $\text{mean}{\text{RR}} = 60 / \text{heart rate}$ (seconds) and $\sigma{\text{HRV}} \approx 0.04$ seconds (40ms standard deviation). Physiological constraints ensure all intervals fall within realistic bounds (0.4s < RR < 1.5s). The implementation uses a cumulative summation of these normally distributed RR intervals with clipping to reasonable physiological limits, creating a realistic sequence of R-wave times that serves as the temporal foundation for the sympathetic burst occurrences.

Respiratory Modulation

Respiratory influence on sympathetic activity represents one of the most important physiological coupling mechanisms in autonomic control. The simulator models this through sinusoidal modulation with irregular breathing patterns, reflecting the central respiratory-cardiovascular coupling observed in humans.

$$\text{modulation}(t) = 0.6 + 0.4 \times \frac{1 + \cos(2\pi f_{\text{resp}} \times t + \phi(t))}{2}$$

Where $f_{\text{resp}} = \text{respiratory rate} / 60$ (Hz) and $\phi(t)$ represents breathing irregularity through a harmonic distortion. Inspiration corresponds to the negative phase of the cosine function, resulting in reduced sympathetic outflow during inspiratory phases. This coupling ensures that burst probability varies systematically with the respiratory cycle, mimicking the inhibitory effects of lung inflation on sympathetic nerve activity.

Burst Occurrence Determination

MSNA bursts cannot occur more frequently than once per cardiac cycle due to the refractory period of the sympathetic nervous system and its tight coupling to cardiac timing.

$$P_{\text{burst}} = \frac{\text{burst incidence}}{100} \times \text{respiratory modulation}(t_{\text{cycle}})$$

For each cardiac cycle, the simulator evaluates burst probability based on the target burst incidence modulated by current respiratory phase. This ensures that respiratory coupling affects not just burst amplitude but also burst occurrence probability. Within each cardiac cycle that receives a burst, timing follows a normal distribution centered at 1.3 seconds post-R-wave with 0.15 seconds standard deviation, constrained to fall within [0.8s, RR_interval - 0.2s].

Burst Morphology Generation

Through studying real MSNA signals, we find (to out surprise) that MSNA bursts exhibits a more symmetric and Gaussian-like profiles rather than the sharp rise and exponential decay. The simulator generates these realistic burst shapes through a combination of primary Gaussian components with subtle asymmetric features that reflect the complex neural population dynamics underlying each burst.

$$\text{burst}(t) = \exp\left(-\frac{t^2}{\sigma^2}\right) + \text{asymmetry component}(t)$$

The primary component uses a Gaussian with $\sigma \approx 0.8$, while the asymmetry component adds a secondary Gaussian offset in time to create the slight irregularities observed in real recordings. Burst duration follows $\mathcal{N}(0.5, 0.1)$ seconds, clipped to [0.3, 0.8]s. Amplitude varies exponentially with additional respiratory modulation, ensuring that bursts occurring during expiration tend to be larger than those during inspiration.

Noise Modeling

Multi-Frequency Noise Architecture

Real MSNA recordings contain many distinct distributions of noise, with complex nuances, and of multiple frequency ranges. The simulator tries to be as comprehensive as possible, and models noise that captures this complexity through frequency-specific components rather than simple white noise addition.

Pink Noise Component

Pink noise (1/f noise) represents the dominant component in most biological signals, arising from the intrinsic variability of biological systems across multiple time scales. This component provides the foundational noise floor that characterizes all neural recordings. The implementation uses exponential smoothing of white noise to create the characteristic 1/f power spectral density:

$$ \text{filtered noise}[i] = \alpha \times \text{white noise}[i] + (1-\alpha) \times \text{filtered noise}[i-1] $$

Where $\alpha = 0.05$ provides appropriate correlation structure. This component provides the pervasive background noise that gives MSNA recordings their characteristic "fuzzy" appearance. The pink noise ensures that low frequencies have higher power than high frequencies, matching the spectral characteristics observed in real neural recordings.

Band-Limited Noise Components

Different frequency bands in MSNA recordings correspond to distinct physiological and technical noise sources, each requiring specialized modeling approaches to capture their unique characteristics. We generate four frequency bands of noise, that are generated through bandpass filtering white noise.

• Low frequency noise (0.01-0.5 Hz)
• Mid frequency noise (0.5-10 Hz)
• High frequency noise (50-200 Hz)

Structured Artifacts

Beyond random noise components, MSNA recordings contain structured artifacts that arise from specific environmental and physiological sources. These artifacts have characteristic patterns that distinguish them from random noise.

Powerline interference represents one of the most common structured artifacts in biomedical recordings. The simulator includes 60 Hz fundamental frequency interference at 3% of noise floor, along with 120 Hz harmonic at 1.5% of noise floor. These sinusoidal components create a characteristic periodic interference pattern.

Breathing artifacts manifest as very low frequency modulation synchronized with respiratory cycles. Beyond the physiological respiratory modulation of sympathetic activity itself, mechanical effects of breathing create additional signal variations through electrode movement, tissue displacement, and changes in electrical impedance. This component operates at the respiratory frequency with 10% noise floor amplitude, creating slow oscillations.

Burst-like artifacts occur sporadically throughout recordings and represent transient events such as muscle twitches, electrode movement, or electrical transients. These artifacts have exponential decay profiles with sinusoidal modulation, making them superficially similar to actual MSNA bursts but lacking the precise cardiac timing relationship. Their occurrence follows Poisson statistics based on the noise floor parameter, with higher noise floors corresponding to more frequent artifacts.

Noise Floor Parameter Control

The noise floor parameter provides general control over signal quality, scaling all noise components proportionally. In general, values of 0.1 represent clean recordings with good electrode contact and minimal interference, while values around 0.3 represent typical clinical recordings with moderate noise. Value of 0.5 or higher represent poor quality recordings with significant interference, movement artifacts, or suboptimal electrode placement.