Optical Neuroimaging & fNIRS

λ < 650 nm Electronic Absorption

Visible light is heavily absorbed by hemoglobin, melanin, and cytochromes. Penetration depth is limited to < 1 mm (skin surface only).

650–900 nm Diagnostic Window

Absorption drops by orders of magnitude ($\mu_a \sim 0.01 - 0.1\,\text{mm}^{-1}$). Scattering dominates, allowing photons to diffuse several centimeters into tissue.

λ > 950 nm Water Absorption

Vibrational overtones of water ($H_2O$) and lipids cause strong infrared absorption, closing the deep penetration window.

🍌 Banana-Shaped Adjoint Profile

Photons entering at the source diffuse outwards and upwards to the detector, forming a curved banana-shaped sensitivity kernel.

Mean Penetration Depth: $\bar{z}_{\text{max}} \approx \frac{1}{2} d_{\text{SD}}$ (at $d_{\text{SD}} = 30\,\text{mm}$, depth $\approx 15\,\text{mm}$).

📏 Scattering Anisotropy ($g \approx 0.9$)

Mitochondria and cell membranes cause forward-peaked Mie scattering. Reduced scattering coefficient:

$$\mu_s' = \mu_s (1 - g) \approx 1.0\,\text{mm}^{-1}$$

Spectroscopic Inversion Matrix

Evaluating at $\lambda_1 = 760\,\text{nm}$ and $\lambda_2 = 850\,\text{nm}$ allows exact linear separation:

$$\begin{bmatrix} \Delta[\text{HbO}] \\ \Delta[\text{HbR}] \end{bmatrix} = \frac{1}{d_{\text{SD}}} \mathbf{E}^{-1} \begin{bmatrix} \Delta\text{OD}_{760} / \text{DPF}_{760} \\ \Delta\text{OD}_{850} / \text{DPF}_{850} \end{bmatrix}$$

Total Hemoglobin & Blood Volume

Summing both chromophores gives total hemoglobin change:

$$\Delta[\text{HbT}] = \Delta[\text{HbO}] + \Delta[\text{HbR}] \propto \Delta\text{CBV}$$

Serves as direct surrogate for regional cerebral blood volume changes.

CW Continuous-Wave

Mechanism: Steady-state DC light injection.

Measures: Relative concentration changes ($\Delta\text{HbO}, \Delta\text{HbR}$).

Pros/Cons: Extremely low cost, lightweight portable caps, robust. Cannot measure absolute absorption ($\mu_a$).

FD Frequency-Domain

Mechanism: Intensity-modulated RF lasers ($50 - 200\,\text{MHz}$).

Measures: Amplitude attenuation $A$ and phase shift $\theta$.

Pros/Cons: Uncouples $\mu_a$ and $\mu_s'$ directly. Yields absolute baseline $\text{StO}_2$. Moderate hardware cost.

TD Time-Domain (TCSPC)

Mechanism: Picosecond laser pulses + SPAD detectors.

Measures: Photon time-of-flight distribution (TPSF).

Pros/Cons: Gold-standard depth discrimination via late photon time-gating. Bulky and expensive.

👶 Hypoxic-Ischemic Encephalopathy

1–3 per 1,000 live births. Standard care: 72 hours of whole-body Therapeutic Hypothermia ($33.5^\circ\text{C}$).

Continuous bedside fNIRS assesses cerebral metabolic extraction and autoregulation without MRI transport risks.

🩸 FTOE Biomarker

Fractional Tissue Oxygen Extraction:

$$\text{FTOE} = \frac{\text{SpO}_2 - \text{rSO}_2}{\text{SpO}_2}$$

Elevated FTOE (> 0.38) flags severe ischemia/hypoperfusion; collapsed FTOE (< 0.15) signals mitochondrial cell death.

⚡ Autoregulation Index (COx)

Pearson correlation between Mean Arterial Pressure (MAP) and cerebral $\text{rSO}_2$.

$\text{COx} \approx 0 \implies$ Intact autoregulation.
$\text{COx} > 0.3 \implies$ Pressure-passive circulation (high risk of IVH).

👶 Neonatal Head Characteristics

Scalp + Skull Thickness: $1.5 - 2.5\,\text{mm}$ (vs adult $8 - 14\,\text{mm}$).

Reduced Extracerebral Shunting: Minimal scalp muscle/bone allows photons to enter cortex almost directly.

Optode Separation: $d_{\text{SD}} = 15 - 20\,\text{mm}$ gives deep cortical sensitivity.

DPF: $\approx 4.4 - 4.8$ (calibrated for thin unmyelinated head).

⚠️ NICU Physical Constraints

Skin Fragility: Stratum corneum is immature; interface pressure must remain < 20 mmHg to prevent necrosis.

Phototherapy Interference: High-power blue phototherapy lamps (450 nm) for hyperbilirubinemia require > 60 dB optical filtering.

Incubator Heating: Optode surface must not exceed 41°C (IEC 60601-1 standard).

🌊 Motion Artifact Correction

Head movement causes shear displacement and optode decoupling.

Wavelet Filtering: Strips high-kurtosis detail coefficients.
Spline Interpolation: Reconstructs baseline offsets seamlessly.

📏 Short-Separation Regression

Short channels ($d_{\text{short}} \approx 8\,\text{mm}$) sample scalp/skin exclusively.

Adaptive GLM subtraction eliminates systemic extracerebral cardiac and vasomotor Mayer waves ($0.1\,\text{Hz}$).

Bandpass Filtering

Passband: $0.01 - 0.2\,\text{Hz}$

• Rejects cardiac pulsation ($1 - 2\,\text{Hz}$ neonate)
• Rejects respiratory rhythm ($0.3 - 0.7\,\text{Hz}$)
• Preserves slow neurovascular BOLD coupling

🔬 Real-Time Synthetic Pipeline

1. Simulate Raw Photons: Dual-wavelength attenuation curves at $760\,\text{nm}$ and $850\,\text{nm}$.

2. MBLL Transformation: Solve the $2\times 2$ extinction matrix for $\Delta[\text{HbO}]$ and $\Delta[\text{HbR}]$.

3. Calculate Bedside Biomarkers: Compute regional saturation $\text{rSO}_2$ and extraction $\text{FTOE}$.

🎯 Student Objectives

• Evaluate HIE clinical scenarios (therapeutic hypothermia vs rewarming).

• Assess how fontanelle proximity alters required optical source-detector spacing.

• Prepare system block diagrams for next week's Mid-Semester Design Review.