1. Biophysical Architecture & Cortical Tonotopy
The human auditory sensory pathway represents one of the most sophisticated biological signal decomposition systems in nature. Acoustic pressure waves collected by the outer pinna travel through the external auditory canal, impinging on the tympanic membrane. Mechanical vibrations propagate across the ossicular chain (malleus, incus, stapes) to the oval window of the fluid-filled cochlea. Inside the cochlea, hydrodynamic basilar membrane displacement follows Greenwood’s frequency-position coordinate function:
$$f(x) = A \left(10^{a x} - k\right)$$
Where $x$ is normalized distance along the cochlear coil, $A$ is the basilar lower cutoff frequency, $a$ governs spatial logarithmic progression, and $k$ is an anatomical correction offset. Mechanical shearing forces deflect stereocilia bundles atop inner hair cells, triggering inward potassium ion influx ($K^+$) through mechanically gated channels ($TMC1/TMC2$). The resultant receptor potentials open voltage-gated calcium channels ($Ca_V1.3$), driving exocytosis of glutamate neurotransmitters onto spiral ganglion dendrites.
Action potentials race through the acoustic nerve (Cranial Nerve VIII) into the ipsilateral cochlear nucleus, bilateral superior olivary complexes, lateral lemniscus, and inferior colliculus. From there, auditory information synaptically transfers through the medial geniculate body ($MGB$) of the dorsal thalamus, delivering tonotopically ordered inputs to the transverse temporal gyri of Heschl (Brodmann Areas 41 and 42) inside the Sylvian fissure.
MicBrain visualizes this functional mapping directly onto the 150 real-world meshes of the Destrieux anatomical cortical atlas ($75$ parcels per hemisphere). The system separates incoming acoustic frequencies into $15$ discrete sub-bands, projecting these components across primary auditory, secondary association, fronto-parietal, motor, and limbic cortical structures.
2. Signal Processing Pipeline & Adaptive Mathematical Formulation
Digital acoustic frames are captured at $44.1\,\text{kHz}$ or $48.0\,\text{kHz}$ via the browser Web Audio API. Incoming audio streams are fed through a $2048$-point complex Fast Fourier Transform ($FFT$) window:
$$X[k] = \sum_{n=0}^{N-1} x[n] \cdot e^{-j 2\pi k n / N}, \quad k \in [0, N/2 - 1]$$
The frequency resolution per bin is $\Delta f = f_s / N \approx 21.5\,\text{Hz}$ at $44.1\,\text{kHz}$. Frequency bins are gathered into 15 functionally distributed cortical bands $I_b = [k_{\min, b}, k_{\max, b}]$. The raw power spectral density within band $b$ is computed as:
$$P_b(t) = \frac{1}{|I_b|} \sum_{k \in I_b} |X[k, t]|^2$$
Because ambient room acoustics and biological vocal energy decay sharply with increasing frequency (approximate $1/f$ spectral tilt), raw spectral bands would overwhelmingly favor low frequencies. To compensate, MicBrain implements an Adaptive Spectral Whitening (AGC) algorithm. Each band dynamically updates a rolling peak $P_{\text{peak}, b}(t)$ and noise baseline $P_{\text{floor}, b}(t)$:
$$P_{\text{peak}, b}(t) = \max\left(P_{\text{peak}, b}(t - \Delta t) \cdot \lambda_{\text{decay}},\, P_b(t) \cdot G\right)$$
$$P_{\text{floor}, b}(t) = P_{\text{floor}, b}(t - \Delta t) \cdot (1 - \gamma) + P_b(t) \cdot \gamma$$
Where $\lambda_{\text{decay}} = 0.996$, $\gamma = 0.002$, and $G$ represents the user-selected input gain. The whitened energy output $Y_b(t)$ is computed using normalized scaling:
$$Y_b(t) = \frac{P_b(t) \cdot G - P_{\text{floor}, b}(t)}{P_{\text{peak}, b}(t) - P_{\text{floor}, b}(t) + \epsilon}$$
The signal is subsequently subjected to a non-linear noise gate threshold $\theta_{\text{gate}}$ and integrated using an exponential smoothing filter with smoothing coefficient $\alpha = 0.08$:
$$E_b(t) = (1 - \alpha) \cdot E_b(t - \Delta t) + \alpha \cdot \max\left(0, \frac{Y_b(t) - \theta_{\text{gate}}}{1 - \theta_{\text{gate}}}\right)$$
To simulate physiological micro-voltage fluctuations, each individual Destrieux cortical region $R_j$ ($j \in [1, 150]$) computes an instantaneous cortical activation potential $S_j(t)$:
$$S_j(t) = E_{B(R_j)}(t) \cdot \left[1.0 + M_{\text{DMN}} \cdot \sin(\omega_j t + \phi_j)\right]$$
Where $M_{\text{DMN}}$ is the Default Mode Network slow-wave modulation depth ($0.05 - 0.2\,\text{Hz}$ resting-state metabolic drift), and $\omega_j, \phi_j$ are spatial phase constants assigned to each anatomical parcellation.
3. Destrieux Cortical Parcellation Mapping Table
The 15 acoustic-to-cortical bands are systematically allocated across the human Destrieux atlas. Low frequencies activate deep limbic and motor planning regions, mid-range vocal formants target transverse temporal and insular areas, and high frequencies illuminate dorsal parietal and occipital structures:
- Band 0 (0–60 Hz): Subcallosal gyrus, pericallosal sulcus, suborbital sulcus (Infralimbic & Autonomic Integration).
- Band 1 (60–120 Hz): Anterior cingulate gyrus & sulcus (Salience & Motor Vigilance).
- Band 2 (120–180 Hz): Middle cingulate cortex (Somatic Action Selection).
- Band 3 (180–250 Hz): Posterior cingulate & retrosplenial cortex (DMN Hub & Episodic Retrieval).
- Band 4 (250–350 Hz): Inferior frontal gyrus, pars opercularis & orbitalis (Broca’s Motor Speech Area).
- Band 5 (350–500 Hz): Middle frontal gyrus (Dorsolateral Prefrontal Working Memory).
- Band 6 (500–750 Hz): Superior frontal gyrus & frontomarginal sulcus (Executive Control).
- Band 7 (750–1000 Hz): Precentral gyrus (Primary Motor Cortex $M1$, Vocal Tract/Laryngeal Homunculus).
- Band 8 (1000–1500 Hz): Central sulcus & postcentral gyrus (Primary Somatosensory Cortex $S1$).
- Band 9 (1500–2000 Hz): Transverse temporal gyrus of Heschl & planum temporale (Primary Auditory Cortex $A1$).
- Band 10 (2000–3000 Hz): Middle temporal gyrus & insular circular sulci (Secondary Auditory & Interoception).
- Band 11 (3000–4000 Hz): Inferior temporal gyrus & lateral occipitotemporal sulcus (Auditory-Visual Association).
- Band 12 (4000–5000 Hz): Supramarginal gyrus & angular gyrus (Wernicke’s Area / Phonological Loop).
- Band 13 (5000–6500 Hz): Superior parietal lobule & precuneus (Visuospatial Spatial Attention).
- Band 14 (6500–8000 Hz): Calcarine sulcus, cuneus, & occipital pole (Primary Visual Cortex $V1$ / Synesthetic Cross-Modal).
4. Explore Related Biomedical Simulations
⚖️ Legal Notices, Nominative Fair Use & Professional Disclaimers
• Editorial Independence & Non-Affiliation: This software laboratory is an independent educational and biophysical simulation developed by BioniChaos. It is not affiliated with, maintained by, sponsored by, or endorsed by the FreeSurfer Development Team, Massachusetts General Hospital, Harvard University, or any commercial medical imaging entity.
• Trademark & Atlas Attribution: "Destrieux Cortical Atlas", "FreeSurfer", and associated anatomical designations are scholarly terms and trademarks owned by their respective research institutions. All anatomical names and nomenclature are referenced strictly for nominative identification, neuro-anatomical education, and academic commentary under applicable international copyright and fair use provisions.
• Not Medical or Diagnostic Advice: All algorithms, Fourier transforms, spectral whitening routines, and 3D cortical field potential renderings in this tool are mathematical approximations intended strictly for educational visualization, training, and conceptual demonstration. This application does not provide clinical neuro-diagnostic, audiometric, electroencephalographic, or surgical guidance and must never be utilized for patient diagnosis or clinical decision-making.
• Acoustic Calibration Disclaimer: Transduction amplitude depends on user hardware, uncalibrated microphone transducers, room reverberation, and browser operating system limits. Telemetry output does not represent calibrated clinical Sound Pressure Level (SPL) or certified quantitative EEG voltages.
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.