1. Biophysical Foundation & Experimental Psychophysiology
Human psychophysiology investigates the continuous, bidirectional information exchange linking cognitive processes within the central nervous system (CNS) to peripheral somatic and autonomic nervous system (ANS) targets. This simulation provides an anatomically grounded computational environment replicating the multimodal empirical dynamics reported in the benchmark PhysioNet Multimodal N-Back Music dataset. In cognitive psychophysiology, the working memory load imposed by continuous visual $N$-back tasks triggers localized metabolic escalation in the dorsolateral prefrontal cortex (dlPFC) and anterior cingulate cortex (ACC). Concurrently, sensory auditory processing of emotionally evocative musical tracks stimulates amygdaloid and limbic networks, driving divergent sympathetic and parasympathetic (vagal) efferent projections.
By coupling real-time mathematical differential equations of cardiac pacemaking, sudomotor sweat gland kinetics, and pneumographic airflow mechanics, this application serves as an interactive laboratory for cognitive ergonomics, neuroscience pedagogy, and biofeedback engineering.
2. Mathematical & Electrophysiological Formulations
2.1 Electrocardiogram (ECG) & Sympathovagal Modulations
The cardiac conduction cycle is modeled as an electrical vector loop $\vec{D}(t)$ projecting onto Einthoven Lead II coordinates:
$$V_{ECG}(\theta) = \sum_{k \in \{P, Q, R, S, T\}} a_k \exp\left(-\frac{(\theta - \mu_k)^2}{2 b_k^2}\right) + \eta(t)$$
where $\theta(t) \in [0, 2\pi)$ represents cardiac phase, $a_k$ wave amplitudes, $\mu_k$ angular phase centerlines, $b_k$ Gaussian dispersion parameters, and $\eta(t)$ represents wideband biopotential baseline drift. The instantaneous cardiac period $RR(t) = \frac{60}{HR(t)}$ in seconds is modulated continuously by sympathovagal balance:
$$HR(t) = HR_0 + \Delta HR_{cog}(N) + \Delta HR_{mus}(\sigma_{mus}) + \Delta HR_{RSA}(t) - \delta_{adapt}(t)$$
where $HR_0$ is resting intrinsic heart rate ($\sim 65\,\text{BPM}$), $\Delta HR_{cog}(N) = 15 \cdot \frac{N-1}{2}$ denotes prefrontal cognitive engagement, and $\Delta HR_{mus}$ encapsulates acoustic-emotional valence and tempo arousal.
2.2 Respiratory Sinus Arrhythmia (RSA)
Respiratory sinus arrhythmia represents the rhythmic modulation of cardiac vagal efferent activity coupled with pulmonary cycle mechanics. During inspiration, intrathoracic negative pressure increases venous return, while central respiratory drive transiently suppresses the nucleus ambiguus vagal brake, eliciting cardioacceleration. During expiration, parasympathetic tone surges, prolonging the $RR$ interval. This phase coupling is formulated as:
$$\Delta HR_{RSA}(t) = \alpha_{RSA} \cdot K_{RSA} \cdot \left[ \sin\left(\int_0^t \omega_{resp}(\tau)\,d\tau - \phi_{RSA}\right) \right]$$
where $\alpha_{RSA}$ denotes vagal gain, $\omega_{resp} = 2\pi \frac{f_{resp}}{60}$ is the instantaneous respiratory angular frequency, and $\phi_{RSA} \approx 0.45\,\text{rad}$ captures baroreceptor transmission latency.
2.3 Electrodermal Activity (EDA) & Sudomotor Nerve Kinetics
Electrodermal activity ($g_{EDA}$, measured in microSiemens, $\mu\text{S}$) reflects postganglionic sympathetic sudomotor nerve firings innervating palmar and plantar eccrine sweat glands. In accordance with the dual-component Bateman model, $g_{EDA}(t)$ is decomposed into a slowly varying tonic Skin Conductance Level ($SCL$) and rapid phasic Skin Conductance Responses ($SCR$):
$$g_{EDA}(t) = SCL(t) + \sum_{j} SCR_j(t - t_j)$$
Each discrete discrete sensory stimulus or performance error event occurring at $t_j$ initiates an impulse response delayed by an autonomic postganglionic conduction latency $t_{lat} \approx 1.2\text{--}1.8\,\text{s}$:
$$SCR(t') = w_j \left(1 - \exp\left(-\frac{t'}{\tau_r}\right)\right) \exp\left(-\frac{t'}{\tau_d}\right) \cdot \mathcal{U}(t')$$
where $t' = t - t_j - t_{lat}$, $\tau_r \approx 0.8\,\text{s}$ is the steep sudomotor filling rise time constant, $\tau_d \approx 2.5\,\text{s}$ is the reabsorption decay constant, $\mathcal{U}(\cdot)$ is the Heaviside step function, and $w_j$ scales with cognitive conflict, stimulus novelty, or internal error-monitoring distress.
3. Operational & Interactive Exploration Guide
- Condition Grid Selection: Toggle between the four quadrant conditions derived from the PhysioNet dataset: Calm Music / 1-Back (low cognitive load, low arousal baseline), Calm Music / 3-Back (high cognitive load, low arousal), Exciting Music / 1-Back (low cognitive load, high acoustic arousal), and Exciting Music / 3-Back (maximal dual-task autonomic stress).
- Interactive Canvas Calipers & Event Markers: Tap or click anywhere along the live signal traces to drop vertical measurement caliper flags. The application calculates the exact instantaneous heart rate ($HR$), skin conductance amplitude ($EDA$), and respiratory cycle phase at that temporal milestone. Click "CLEAR CALIPERS" to reset markers.
- Continuous Parameter Sliders: Fine-tune prefrontal cognitive demand from $N=1$ to $N=3$, musical arousal gain ($\sigma_{mus}$), target breathing frequency ($8\text{--}28\,\text{RPM}$), and vagal RSA coupling gain ($\alpha_{RSA}$). Observe how diminishing $\alpha_{RSA}$ reproduces clinical autonomic rigidity and vagal withdrawal.
- $N$-Back Response Console: Letters flash in the stimulus banner every 2 seconds. When the current letter matches the one presented exactly $N$ steps prior, click "MATCH [Y]" or press the 'Y' key on your keyboard. For non-targets, click "NO MATCH [N]" or press 'N'. Incorrect inputs trigger immediate error-related negativity ($ERN$) signatures, producing acute phasic EDA surges.
- Timeline Demo Mode & Audio Guide: Click "▶ START DEMO" to embark on a narrated, synchronized guided tour. The timeline dynamically spotlights UI control groups with glowing yellow accents, ducks background acoustic heartbeats, and steps through clinical scenarios.
4. Related Biomedical & Biophysical Simulators
Open Access License: This interactive educational module is released under
CC BY-NC 4.0 (Attribution-NonCommercial)
for non-commercial research, academic study, and clinical education.
Commercial & Enterprise Licensing: For white-labeling, proprietary LMS/course embedding, hardware dashboard telemetry integration, or custom feature engineering, secure a commercial license at
BioniCloud.com or contact
Dr. Yuri Beno.