computational-neuroscience-bci

Computational Neuroscience & Brain-Computer Interface

Otak adalah komputer biologis yang paling canggih — 86 miliar neuron, 100 triliun sinapsis, mengonsumsi 20W daya. Computational neuroscience mencoba memahami otak melalui model matematis dan simulasi. Brain-Computer Interface (BCI) mencoba membaca dan menulis informasi dari/ke otak. Catatan ini mencakup neural signal processing, brain imaging analysis, computational neuron models, BCI hardware stack, dan neuroprosthetics — dengan formula, algoritma, dan implementasi.

Daftar Isi

1. Neural Signal Processing — Spike Sorting, LFP, ECoG
2. Brain Imaging Analysis — fMRI, DTI, MEG
3. Computational Models of Neuron
4. BCI Hardware Stack — OpenBCI, Neuralink, Utah Array
5. Neurofeedback & Neuroprosthetics
6. Signal Decoding & Machine Learning
7. Ethics & Safety Considerations
8. References

1. Neural Signal Processing — Spike Sorting, LFP, ECoG

1.1 Signal Types & Frequency Bands

Signal	Frequency	Amplitude	Spatial Resolution	Invasive?
EEG	0.5-100 Hz	10-100 μV	~1-10 cm	No
ECoG	0.5-200 Hz	10-5000 μV	~1-5 mm	Semi
LFP	1-300 Hz	50-5000 μV	~50-350 μm	Yes
Spike	300-3000 Hz	50-500 μV	~10-50 μm	Yes
MEG	1-100 Hz	10-1000 fT	~5-10 mm	No

1.2 Spike Sorting

Waveform extraction:

1. Bandpass filter: 300-3000 Hz
2. Threshold detection: V > 4·σ_noise
3. Extract waveform window: ±1-2 ms around peak
4. Align to peak or principal component

Threshold formula:

σ_noise = median(|V|) / 0.6745  (robust estimator)

Threshold = 4·σ_noise ≈ 4·RMS_noise

P(false positive | 4σ) ≈ 0.003% (Gaussian assumption)

Clustering algorithms:

1. PCA dimensionality reduction:
   - Extract first 2-3 principal components
   - Variance explained: typically 70-90%

2. Clustering:
   - K-means (fast, but need k)
   - Gaussian Mixture Model (probabilistic)
   - Template matching (matched filter)
   - MountainSort / Kilosort (state-of-the-art)

Kilosort algorithm:

1. Whitening: decorrelate channels
2. Template learning: learn spike templates via gradient descent
3. Matching pursuit: assign spikes ke templates
4. Drift correction: track electrode movement over time

1.3 Local Field Potential (LFP)

Origin:

LFP = weighted sum of synaptic currents from local population
Spatial reach: ~250-500 μm (depends on tissue conductivity)

Frequency bands:

Delta: 0.5-4 Hz   (deep sleep, unconsciousness)
Theta: 4-8 Hz     (hippocampus, memory encoding)
Alpha: 8-13 Hz    (visual cortex, eyes closed)
Beta: 13-30 Hz    (motor cortex, active thinking)
Gamma: 30-100 Hz  (feature binding, attention)
High gamma: 80-150 Hz (multi-unit activity proxy)

Power spectral density:

PSD(f) = |FFT(signal)|² / (fs·N)

fs: sampling frequency
N: number of samples

1.4 ECoG (Electrocorticography)

Grid electrodes:

Standard grid: 8×8 electrodes, 1 cm spacing
High-density: 8×8 electrodes, 3 mm spacing

Advantage over EEG:
  - Higher spatial resolution (no skull/scalp attenuation)
  - Higher frequency content (up to 200 Hz, even 500 Hz gamma)
  - Higher SNR (10-100× better than EEG)

2. Brain Imaging Analysis — fMRI, DTI, MEG

2.1 fMRI — BOLD Signal

BOLD (Blood-Oxygen-Level-Dependent) contrast:

BOLD signal ∝ Δ[HbR] (deoxyhemoglobin concentration)

Neural activity → increased blood flow → increased oxyhemoglobin
→ decreased deoxyhemoglobin → increased T2* signal

Hemodynamic response function (HRF):
  h(t) = (t/τ1)^n1 · exp(-t/τ1) - A·(t/τ2)^n2 · exp(-t/τ2)

  τ1 ≈ 6s, τ2 ≈ 16s, n1 ≈ 6, n2 ≈ 1, A ≈ 0.35
  Peak: ~5-6s after neural activity
  Duration: ~12-15s

GLM (General Linear Model):

Y = X·β + ε

Y: voxel time series (T×1)
X: design matrix (T×N regressors)
  - Task regressors (convolved with HRF)
  - Nuisance regressors (motion, drift, physiological)
β: parameter estimates (N×1)
ε: residual noise

β = (X^T·X)^-1 · X^T · Y

t-statistic: t = β / SE(β)

Multiple comparisons:

Voxels: 64×64×30 = 122,880 (typical)
Family-wise error rate (FWER): P(at least 1 false positive)

Bonferroni: threshold = α / N = 0.05 / 122,880 ≈ 4×10^-7
FDR (False Discovery Rate): control expected proportion of false positives
Cluster correction: threshold clusters by size

2.2 DTI — Diffusion Tensor Imaging

Diffusion tensor:

D = [Dxx Dxy Dxz
     Dxy Dyy Dyz
     Dxz Dyz Dzz]

Eigenvalues: λ1 ≥ λ2 ≥ λ3
Eigenvectors: principal diffusion directions

Scalar metrics:

MD (Mean Diffusivity) = (λ1 + λ2 + λ3) / 3
FA (Fractional Anisotropy) = √(3/2) · √[(λ1-MD)²+(λ2-MD)²+(λ3-MD)²] / √(λ1²+λ2²+λ3²)

FA = 0: isotropic (CSF, gray matter)
FA ≈ 1: highly anisotropic (white matter tracts)

Tractography:

Deterministic:
  - Streamline propagation along principal eigenvector
  - Stop when FA < threshold (0.2) or angle > threshold (45°)

Probabilistic:
  - Sample diffusion direction dari tensor distribution
  - Repeat 1000× per seed
  - Build connectivity probability map

2.3 MEG — Magnetoencephalography

Principle:

Neural currents generate magnetic fields
SQUID (Superconducting Quantum Interference Device) detects fields

Signal: 10-1000 fT (femtotesla)
Earth magnetic field: 50,000 nT = 50,000,000,000 fT
→ Need shielded room (mu-metal)

Source localization:

Forward problem: given source J, calculate field B at sensors
  B = G · J
  G: lead field matrix (depends on head geometry)

Inverse problem: given B, estimate J
  J = G⁺ · B  (minimum norm estimate)

  G⁺: pseudoinverse or regularized inverse
  Regularization: Tikhonov (L2) atau L1 (sparse)

3. Computational Models of Neuron

3.1 Hodgkin-Huxley Model (1952)

Membrane current:

C_m · dV/dt = -g_Na·m³·h·(V-E_Na) - g_K·n⁴·(V-E_K) - g_L·(V-E_L) + I_ext

C_m: membrane capacitance (~1 μF/cm²)
g_Na, g_K, g_L: maximal conductances
E_Na, E_K, E_L: reversal potentials
m, h, n: gating variables (0-1)
I_ext: external current

Gating variables:

dx/dt = α_x(V)·(1-x) - β_x(V)·x

α_m(V) = 0.1·(V+40) / (1 - exp(-(V+40)/10))
β_m(V) = 4·exp(-(V+65)/18)

α_h(V) = 0.07·exp(-(V+65)/20)
β_h(V) = 1 / (1 + exp(-(V+35)/10))

α_n(V) = 0.01·(V+55) / (1 - exp(-(V+55)/10))
β_n(V) = 0.125·exp(-(V+65)/80)

Action potential threshold:

V_threshold ≈ -55 mV
Peak: +40 mV
Repolarization: -70 mV (resting)
Duration: ~1-2 ms

3.2 Izhikevich Model (2003)

Simplified 2D model:

dv/dt = 0.04·v² + 5·v + 140 - u + I
du/dt = a·(b·v - u)

if v ≥ 30 mV:
  v = c
  u = u + d

v: membrane potential
u: recovery variable
a, b, c, d: parameters (determine neuron type)

Parameter sets:

Regular spiking (RS):    a=0.02, b=0.2, c=-65, d=8
Intrinsically bursting (IB): a=0.02, b=0.2, c=-55, d=4
Chattering (CH):         a=0.02, b=0.2, c=-50, d=2
Fast spiking (FS):       a=0.1,  b=0.2, c=-65, d=2
Low-threshold spiking (LTS): a=0.02, b=0.25, c=-65, d=2
Thalamo-cortical (TC):   a=0.02, b=0.25, c=-65, d=0.05
Resonator (RZ):          a=0.1,  b=0.26, c=-65, d=2

Advantage:

Hodgkin-Huxley: 4 ODEs, computationally expensive
Izhikevich: 2 ODEs, 1000× faster
Can reproduce 20+ neuron firing patterns

3.3 Leaky Integrate-and-Fire (LIF)

Simplest model:

τ_m · dV/dt = -(V - V_rest) + R·I(t)

if V ≥ V_threshold:
  emit spike
  V = V_reset

τ_m = R·C_m: membrane time constant (~10-20 ms)

Firing rate (steady-state):

ν = [τ_m · ln((V_rest - V_reset + R·I)/(V_rest - V_threshold + R·I))]^-1

Untuk I > I_threshold:
  ν ≈ (R·I - ΔV) / (τ_m · ΔV)  (linear approximation)

4. BCI Hardware Stack — OpenBCI, Neuralink, Utah Array

4.1 Electrode Types

Type	Material	Impedance	Lifespan	Resolution
Surface EEG	Ag/AgCl	5-20 kΩ	Reusable	1-10 cm
ECoG grid	Platinum	1-5 kΩ	Permanent implant	1-5 mm
Utah array	Silicon	50-500 kΩ	1-5 years	~100 μm
Neuropixels	CMOS	<100 kΩ	Single use	~20 μm
Neuralink	Polymer	<50 kΩ	>10 years (target)	~12 μm

4.2 Utah Array

Specification:

10×10 electrode grid
Electrode length: 1.0-1.5 mm
Electrode spacing: 400 μm
Total: 96 electrodes (4 corner electrodes are reference)
Material: doped silicon, insulated with Parylene

Signal quality over time:

Month 0: SNR = 10-15 dB
Month 6: SNR = 5-10 dB
Month 12: SNR = 3-5 dB
Month 24+: SNR < 3 dB (many channels lost)

Degradation cause: glial scarring, electrode drift

4.3 Neuralink N1

Specification:

Threads: 64 threads
Electrodes per thread: 16
Total electrodes: 1024
Electrode size: 12 μm diameter
Thread thickness: 4-6 μm
Insertion: robotic sewing machine
Wireless: Bluetooth Low Energy
Battery: inductive charging

Bandwidth:

1024 channels × 20 kHz sampling × 10 bits = 204.8 Mbps raw
On-chip compression: 200× reduction
Wireless throughput: ~1-5 Mbps

4.4 OpenBCI

Cyton board:

Channels: 8 EEG
Sampling: 250 Hz
Resolution: 24-bit ADC
Wireless: RF dongle (2.4 GHz)
Cost: $500-1000

Ganglion board:
  Channels: 4 EEG
  Cost: $200

5. Neurofeedback & Neuroprosthetics

5.1 Neurofeedback

Protocol:

1. Record real-time EEG/ECoG
2. Extract feature (e.g., alpha power at C3/C4)
3. Compare to target (e.g., increase alpha by 20%)
4. Provide feedback (visual, auditory, haptic)
5. User learns to modulate brain state

Applications:

ADHD: increase SMR (12-15 Hz), decrease theta (4-8 Hz)
Anxiety: increase alpha, decrease high beta
Depression: asymmetry training (F3/F4 alpha)
Peak performance: increase gamma (40 Hz)

Efficacy:

Meta-analysis (Arns et al., 2014):
  ADHD: effect size d = 0.6 (medium-large)
  Anxiety: d = 0.5 (medium)
  Epilepsy: d = 0.8 (large)

5.2 Motor Neuroprosthetics

Brain-controlled cursor:

Training:
  1. User imagines moving hand left/right/up/down
  2. Record motor cortex ECoG/spikes
  3. Decode intended direction dari neural activity
  4. Cursor moves sesuai decoded direction

Decoder:
  - Kalman filter: x_t = A·x_{t-1} + K·(z_t - H·x_t)
  - x: cursor position/velocity
  - z: neural firing rates

Braingate clinical trial:

Participant: tetraplegic
Implant: 96-channel Utah array (M1)
Performance:
  - Typing: 90 chars/min (2021, decoded dari attempted handwriting)
  - Robot arm control: pick and place
  - Cursor control: 90% accuracy

5.3 Sensory Neuroprosthetics

Cochlear implant:

Microphone → Sound processor → Transmitter → Electrode array (cochlea)

Electrodes: 12-22 channels
Frequency mapping: basal = high freq, apical = low freq

Speech understanding:
  - Quiet: 70-90%
  - Noise: 40-60%

Retinal implant:

Argus II (Second Sight):
  - 60 electrodes (6×10 grid)
  - Implanted on retina
  - Glasses-mounted camera
  - Visual acuity: ~20/1260 (legal blindness = 20/200)

6. Signal Decoding & Machine Learning

6.1 Feature Extraction

Time-domain:

Mean, variance, skewness, kurtosis
Zero-crossing rate
Waveform length

Frequency-domain:

Power spectral density (Welch method)
Band power: delta, theta, alpha, beta, gamma
Spectral entropy

Time-frequency:

Short-time Fourier Transform (STFT)
Wavelet transform (Morlet wavelet)
Common Spatial Patterns (CSP) — for EEG

6.2 Common Spatial Patterns (CSP)

For 2-class motor imagery:

Goal: find spatial filters w that maximize variance for class 1
      and minimize variance for class 2

Optimization:
  maximize: w^T · Σ1 · w / w^T · Σ2 · w

  Σ1, Σ2: covariance matrices untuk class 1 dan 2

Solution: generalized eigenvalue problem
  Σ1 · w = λ · Σ2 · w

Performance:

CSP + LDA: 70-85% accuracy (2-class motor imagery, healthy subjects)
CSP + LDA: 50-70% accuracy (patients, limited training data)

6.3 Deep Learning for Decoding

CNN for EEG:

Input: (channels, time) = (64, 1000) untuk 4s @ 250Hz
Architecture:
  Conv2D(1, 64, kernel=(1, 50))  → temporal filtering
  Conv2D(64, 64, kernel=(64, 1)) → spatial filtering (CSP-like)
  BatchNorm + ReLU
  MaxPool(1, 3)
  Conv2D(64, 128, kernel=(1, 10))
  Global Average Pool
  FC(128, num_classes)
  Softmax

RNN/LSTM for sequential decoding:

Input: time series of neural features
LSTM layers: capture temporal dynamics
Output: sequence of decoded states

Advantage: model temporal dependencies
Disadvantage: need more data, slower training

Transfer learning:

Pre-train pada large dataset (e.g., BCI Competition IV)
Fine-tune pada subject-specific data

Improvement: +5-15% accuracy dengan limited subject data

7. Ethics & Safety Considerations

7.1 Safety Thresholds

Neural tissue heating:

FDA limit: <1°C temperature increase
Neuralink: <0.1°C (validated via simulation)

Power dissipation: P = I²·R
For 1024 channels @ 1 μA: P ≈ 1-10 μW (negligible)

Infection risk:

Utah array: 5-10% infection rate over 5 years
Neuralink: target <1% (hermetic packaging)

7.2 Privacy & Security

Neural data sensitivity:

EEG/ECoG bisa reveal:
  - Motor intent (before action)
  - Emotional state
  - Cognitive load
  - Attention focus
  - Potentially: thoughts, preferences

Encryption: AES-256 untuk wireless transmission
Access control: multi-factor authentication

8. References

Dayan, P., & Abbott, L. F. (2001). Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. MIT Press. — Foundational computational neuroscience.
Rieke, F., Warland, D., de Ruyter van Steveninck, R., & Bialek, W. (1997). Spikes: Exploring the Neural Code. MIT Press. — Neural coding theory.
Niedermeyer, E., & da Silva, F. L. (Eds.). (2005). Electroencephalography: Basic Principles, Clinical Applications, and Related Fields (5th ed.). Lippincott Williams & Wilkins. — EEG bible.
Wolpaw, J. R., & Wolpaw, E. W. (Eds.). (2012). Brain-Computer Interfaces: Principles and Practice. Oxford University Press. — BCI comprehensive text.
Hochberg, L. R., et al. (2012). “Reach and Grasp by People with Tetraplegia Using a Neurally Controlled Robotic Arm.” Nature, 485(7398), 372-375. — Braingate clinical results.
Izhikevich, E. M. (2003). “Simple Model of Spiking Neurons.” IEEE Transactions on Neural Networks, 14(6), 1569-1572. — Izhikevich model.
Jun, J. J., et al. (2017). “Fully Integrated Silicon Probes for High-Density Recording of Neural Activity.” Nature, 551(7679), 232-236. — Neuropixels.
Musk, E., & Neuralink. (2019). “An Integrated Brain-Machine Interface Platform with Thousands of Channels.” Journal of Medical Internet Research. — Neuralink N1.

Koneksi ke Vault

Catatan	Koneksi
advanced-ai-algorithms-breakthroughs	Neural decoding = deep learning application
hierarchy-ai-levels	BCI = human-AI symbiosis (Level 8-9)
math-and-algorithms	Signal processing, linear algebra, optimization
research-methodology	Clinical trials, experimental design
cryptography-biometrics	Neural/BCI authentication (EEG passthought)

Azhar's Notes

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computational-neuroscience-bci

Daftar Isi

1. Neural Signal Processing — Spike Sorting, LFP, ECoG

1.1 Signal Types & Frequency Bands

1.2 Spike Sorting

1.3 Local Field Potential (LFP)

1.4 ECoG (Electrocorticography)

2. Brain Imaging Analysis — fMRI, DTI, MEG

2.1 fMRI — BOLD Signal

2.2 DTI — Diffusion Tensor Imaging

2.3 MEG — Magnetoencephalography

3. Computational Models of Neuron

3.1 Hodgkin-Huxley Model (1952)

3.2 Izhikevich Model (2003)

3.3 Leaky Integrate-and-Fire (LIF)

4. BCI Hardware Stack — OpenBCI, Neuralink, Utah Array

4.1 Electrode Types

4.2 Utah Array

4.3 Neuralink N1

4.4 OpenBCI

5. Neurofeedback & Neuroprosthetics

5.1 Neurofeedback

5.2 Motor Neuroprosthetics

5.3 Sensory Neuroprosthetics

6. Signal Decoding & Machine Learning

6.1 Feature Extraction

6.2 Common Spatial Patterns (CSP)

6.3 Deep Learning for Decoding

7. Ethics & Safety Considerations

7.1 Safety Thresholds

7.2 Privacy & Security

8. References

Koneksi ke Vault

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