Scientific methods / biohybrid-hh-cable/1.0.0

Biohybrid Neural Interface Laboratory
Methods & Validation

← Open the laboratory · Numerical evidence · Reference register · 34 crucial questions & answers · Stage 02 controls

This laboratory calculates an electrically stimulated engineered neuron, propagation through its axon tract, conductance-based transmission to receiving cells, and ideal extracellular recordings. Every membrane color and trace comes from the compartment solution. The geometry includes synthetic branching, a hydrogel scaffold, explicit synaptic landing branches, a stimulating source/return pair and three recording contacts.

The initial release is a canonical Hodgkin–Huxley active-cable benchmark at 6.3 °C. It is not fitted to human cortical neurons, cultured graft neurons, stem-cell preparations, or a particular commercial implant. Numerical agreement with NEURON verifies the specified equations and implementation; it does not establish biological prediction. The synthetic cells are representative geometric constructions, not reconstructed specimen morphologies.

1. Evidence and architecture

Adewole et al. demonstrate optically controlled living electrodes with engineered neuronal aggregates and long axon tracts, including in-vitro stimulation/readout and rat implantation proof of concept. Struzyna et al. support micro-TENN architecture and anatomical host integration. These studies motivate the living bridge but do not measure the parameters of this electrical relay. The model makes an explicit exploratory substitution: electrical volume-conductor stimulation and ideal electrical recording around a defined active-cable network.

Brown et al.’s Science Corporation preprint concerns a mouse cortical-surface optical microwell graft and behavioral reporting. The separate company architecture description proposes broader electronics and scaling. The laboratory treats the microwell result as a named preclinical experiment, and future bandwidth, channel count and chronic performance as prospective claims. Passive cell wells are not electrical recording channels.

2. Active membrane and axial current

For compartment i, Vᵢ is intracellular minus extracellular potential. Current is positive outward across the membrane. The cable balance is:

Cᵢ dVᵢ/dt = −Iᵢ,ion − Iᵢ,syn + Iᵢ,injected
              + Σⱼ gᵢⱼ [(Vⱼ + φₑ,ⱼ) − (Vᵢ + φₑ,ᵢ)]
Iᵢ,ion = ḡNa,ᵢ mᵢ³ hᵢ (Vᵢ − ENa)
          + ḡK,ᵢ nᵢ⁴ (Vᵢ − EK) + gL,ᵢ (Vᵢ − EL)
dx/dt = αx(V)(1 − x) − βx(V)x

The rate functions follow the original HH model in NEURON’s absolute-voltage convention. Removable singularities at the activation-rate limits use analytic limiting values. The temperature factor is 3^((T − 6.3)/10), used as a benchmark convention; changing T does not produce a validated mammalian membrane model. All visible membrane-bearing compartments carry the stated capacitance and active channel densities. Ends are sealed. There is no myelin, ion depletion, adaptation current, plasticity, inhibitory cell type, or spontaneous input in this release.

Membrane areas are calculated from the actual equivalent cylinder lengths and diameters. With area in µm², capacitance in nF is area × 10⁻⁵ at 1 µF/cm², and a density in S/cm² becomes total conductance in µS by multiplying area × 0.01. Axial resistance uses cylinder cross-sectional areas and the two adjacent half-segments. Branch endpoints have explicit massless junctions, so a shared parent resistance is not independently duplicated for each child.

The soma is an equivalent electrical cylinder. Its displayed ellipsoid is a schematic surface; neurite diameters are enlarged ×2 for readability while centerlines and electrode positions retain their physical coordinate system. The 2D fallback also uses minimum pixel widths and marker sizes for legibility. The 3D scale bar gives length at the camera focus plane; perspective changes apparent scale with depth. No electrical parameter is calculated from a display enlargement.

Time integration

The solver performs a backward-Euler tree voltage solve with channel gates held fixed, followed by a Rush–Larsen update at the new voltage:

x(t + Δt) = x∞(V) + [x(t) − x∞(V)] exp[−Δt / τx(V)]

The Hines elimination solves the branched voltage system without dense inversion. This is a first-order split method, not an exact nonlinear solution. Initial gates are at the scalar equilibrium of the stated ionic model, giving a default rest of -64.9741 mV. Invalid settings, singular contact positions and unsupported voltage excursions cause a visible calculation error. The code does not silently clip voltages to hide instability.

A Web Worker calculates each complete experiment. Replay subsequently reads the saved voltage frames and measurements. Display slowdown does not alter biological time or numerical state. Default runs save 801 frames at 0.05 ms intervals; spike times use interpolated crossings of the fine integration steps. The reduced mobile population has one graft and two host cells, with the same default time and spatial resolution.

3. Host–graft synapses and interpretation

Each anatomically assigned presynaptic branch has its own spike detector at 0 mV. An upward crossing schedules an event after the specified delay. The conductance kernel has a peak-normalizing factor A:

g(t) = gpeak A [exp(−(t − tevent)/τdecay)
                  − exp(−(t − tevent)/τrise)]  for t ≥ tevent
I_syn = g(t) (V − E_syn),   E_syn = 0 mV

The event is applied at the first solver step on or after its scheduled time, introducing at most one step of timing quantization. The postsynaptic voltage is still solved from its membrane and axial currents; a synaptic event does not force a host spike. Multiple inputs add conductance. Changing the number of functional targets or setting conductance to zero preserves the constructed axon geometry and its axial connections.

“Relay-consistent recruitment” means a host crossed threshold after an event at that same host. This temporal condition alone cannot exclude direct field activation at arbitrary settings. The laboratory separately counts early host spikes. The default disconnected counterfactual produces four graft soma spikes and zero host soma spikes; that paired calculation supports synaptic dependence for the default experiment. A nonzero recording in the disconnected experiment can still be volume-conducted activity from the graft.

For export compatibility, the legacy metric successfulTransmission remains true when at least one host meets that temporal condition; relayConsistentHosts counts those cells. Neither field alone establishes synaptic dependence. The matched causal audit supplies the intervention needed for that narrower interpretation.

The timing summaries are signed differences between first upward 0 mV crossings: the first graft's monitored trunk tip minus its soma, and the earliest host soma minus that graft soma. They are not matched-event propagation measurements for every possible electrode position. A negative value means the tip or a host fired before the monitored graft soma; direct field activation or reverse propagation can change that order. The mixed-activation example gives approximately −0.982 ms for tip minus soma and −0.714 ms for earliest host minus graft soma. These values do not mean a negative physical conduction time. Velocity is reported only when the monitored tip follows the soma, and even then an event-order difference alone cannot prove that the same action potential traveled between them. Use the spatial voltage replay, individual spike times and matched synapses-off controls to interpret the mechanism.

4. Electrode coupling and extracellular recordings

Stimulation uses an explicit source and equal opposite return in an infinite, real, homogeneous, isotropic conductor. Each current disk is sampled at 48 equal-area quadrature sites: four radial annuli and twelve angles. The extracellular potential enters differences between connected cable nodes; electrode current is not substituted for soma current injection. Rectangular pulse edges use their exact overlap with each numerical step, preserving the two-phase charge balance.

Point source: φₑ(r) = I / (4π σ |r − rsource|)
Line source:  φₑ(r) = I / (4π σ L) ∫segment ds / |r − r(s)|
Finite recording contact: Vcontact = (1/A) ∫disk φₑ(r) dA

Recorded sources are the total outward transmembrane currents: capacitive, ionic and synaptic. Somata use the point-source approximation; neurites use the analytic line-source kernel shared with the Cortex Laboratory. Passive recording disks average those potentials with the same deterministic quadrature. Junctions have no membrane and contribute no source current. The reference is at infinity. The neural component, imposed-field artifact and their sum are separate quantities in the interface and CSV exports.

Finite-disk averaging is an approximate contact correction. It does not solve the conductive metal, an insulating substrate, electrode polarization, double-layer impedance, amplifier loading, filtering, noise or stimulus saturation. The displayed scaffold is not a separately solved conductivity region. There is no finite-element or electrodiffusion claim and no ephaptic feedback from the calculated neural field.

Contacts must stay at least 3 µm from the modeled membrane and from each other. A complete-disk geometric clearance calculation checks the membrane between quadrature samples. This exclusion prevents singular unsupported placements; it does not validate near-membrane physics. A point source obeys inverse-distance scaling, while a complete neuron’s multipolar signal can change non-monotonically with position. Inverse-conductivity validation holds the source currents fixed, because changing conductivity during stimulation can also alter firing.

5. Parameter register

The default conductance, morphology, sparse network and contact configuration are chosen to make an inspectable numerical experiment. They are not measured thresholds, an implant specification or a therapeutic recommendation. Every JSON export carries the normalized settings, model version, units, metrics and limitations of the completed run. Modified controls do not relabel previously calculated results.

6. Numerical verification and retained discrepancies

Acceptance thresholds were documented before the final studies. Numerical tests cover equilibrium, zero input, spike initiation and propagation, length/diameter effects, synaptic transmission, disconnected behavior, amplitude/polarity, finite contacts, distance, conductivity with fixed sources, local current balance, deterministic replay, time and space refinement, parameter rejection and exported data integrity.

The temporal study uses the predeclared 0.005, 0.0025 and 0.00125 ms levels. Both adjacent comparisons use the same saved sample grid and matching per-neuron threshold-event counts. All seven monitored RMS differences decrease at the second halving; the coarse-to-half versus half-to-quarter difference ratios range from 1.65 to 2.10. This measures difference scaling for these discrete solutions, not error against an exact solution or proof of asymptotic convergence order. Nonlinear spike timing and delayed-event quantization contribute to the differences. Further spatial refinement to 6.25 µm also continues the trend. These are bounded comparisons at declared settings, not guarantees throughout every extreme parameter combination. Recorded runtime in the validation environment was approximately 0.949 s for the default 40 ms calculation, excluding page and rendering startup. Browser hardware affects this measurement.

Preserved failed spatial test

The initial spatial test failed. Recording 1 changed approximately 17.6% relative to the coarse result, or 21.3% relative to the refined result, exceeding the 10% gate. Selecting a synaptic target by its nearest discretized compartment could move it onto another anatomical branch during refinement.

The correction uses a fixed 6 µm dendritic landing branch, so the physical target stays fixed as segment size changes. The original failure, cause and correction remain in docs/biohybrid/VALIDATION_HISTORY.md and the numerical JSON report. The acceptance tolerance was not relaxed.

Independent native NEURON comparison

The reference uses NEURON 9.0.1 with native HH channels, its cable solver, Exp2Syn, NetCon and membrane-current bookkeeping. Python independently rebuilds axial resistances and disk/line forward fields from the shared geometry and settings. The prescribed extracellular field is represented by mathematically equivalent nodal current sources, including the massless branch endpoints. This compares the defined discretized cable; it is not an independent tissue conductivity boundary solve.

No time shift, baseline correction or amplitude rescaling is applied before comparison. Frozen acceptance criteria are membrane RMS ≤1 mV, spike timing ≤0.1 ms, identical spike counts, and maximum extracellular error ≤0.001 µV. The stricter pointwise membrane criterion of ≤0.5 mV is a preserved additional diagnostic in the native report, reported separately from its acceptance flag. Its threshold has not been changed.

The full membrane comparison includes Float32 replay quantization. Double-precision monitor traces and spike times agree more closely. Very close agreement between solvers at the same step does not remove the time-refinement error shown above; both implement the same stated finite-step convention.

7. Controlled experiments and source attribution — Stage 02

The next stage addresses a causal question: does host recruitment depend on the assigned host–graft synapses under the exact settings being tested? It also distinguishes that question from the origin of an extracellular waveform. Read the 34-question scientific decision register, then use the controlled-experiment workbench.

Matched controls and per-cell interpretation

The causal audit recalculates three independent runs: the assigned junctions, the identical network with every host–graft peak conductance set to zero, and the assigned network with stimulus amplitude set to zero. Morphology, membrane and axial parameters, temperature, initial condition, electrode placement, resolution and observation window remain matched. The deliberately removed synaptic conductance changes postsynaptic loading. Removing conductance is a mathematical intervention; it does not model a drug, surgical transection, cell death or tissue injury.

A host that fires in the assigned run and loses every somatic spike in the blocked run is labeled “lost with block.” A host that fires in both is “persists with block”; it cannot establish exclusive synaptic mediation. A host that starts firing after conductance removal is “appears with block.” Cells that never fire in either run are “silent in both.” Counts, first-spike times and all host spike times remain in the protocol record. Temporal order alone is still only relay-consistent evidence. These labels apply to the finite observation window and this mathematical network.

The blocked recording remains nonzero while host recruitment is zero. Its small host-source component reflects subthreshold membrane currents. A separate mixed-activation positive control uses a 300 µm tract, stimulation x = 300 µm, −30 µA first phase, one pulse and a 25 ms observation window: all three hosts fire with assigned junctions; host 2 still fires without them, while hosts 1 and 3 lose their spikes. A one-graft/one-host direct-activation control at −40 µA also persists with zero coupling. These are synthetic benchmark counterexamples, not measured graft behavior.

Known-source decomposition

V_neural,k(t) = Σ_i L_ki I_membrane,i(t)
V_graft,k(t)  = Σ_(i in graft) L_ki I_membrane,i(t)
V_host,k(t)   = Σ_(i in host)  L_ki I_membrane,i(t)
V_neural,k(t) = V_graft,k(t) + V_host,k(t)

The original Float64 membrane currents and the same finite-contact transfer coefficients produce both components. The underlying membrane equations and original combined recording are unchanged. This is a partition of known simulated sources, not an inverse reconstruction or experimental spike-sorting method. The instantaneous waveforms add; separate peak-to-peak values generally do not, because their extrema occur at different times. A host-source field does not establish a host spike or a functional synapse.

The default sample-wise partition residual is 1.33227e-14 µV across 2,403 contact samples, against a predeclared 1e-10 µV acceptance. Independent native NEURON membrane currents are also partitioned and projected through independently implemented Python transfer coefficients. Maximum graft-source disagreement is 1.52007e-11 µV; maximum host-source disagreement is 1.26836e-11 µV, each against an unchanged 0.001 µV electrical criterion.

Finite parameter studies, dose and reproducibility

Five study axes vary one setting at a time: signed first-phase current, each synaptic peak conductance, recording height, the shared graft/host axon-diameter parameter or conductivity. Two to seven finite, unique, ordered values are allowed. Paired synapses-off controls are optional for each sample. The workbench reports recruited-cell counts in the listed sample order; these are not population activation probabilities. Adjacent valid samples can bracket a response change. No interpolation, monotonic threshold search, Lapicque fit or untested extrapolation is performed. Failures retain their actual settings and error message and break response intervals.

Moving a passive recording disk leaves membrane dynamics unchanged. Changing conductivity alters both stimulation and recording, so those response studies are not isolated inverse-conductivity tests. The diameter parameter applies to the engineered tract and host axons; graft terminal branches use 0.8 times that diameter. Changing it alters axial conductance and membrane area together in both populations, so downstream changes cannot be attributed solely to the engineered tract. Each case starts from the same equilibrium and explicit base settings; it is not a continuation from the previous case.

A separate refinement check recalculates the observed current-response bracket endpoints at 0.005 and 0.0025 ms with all other settings fixed. At −12 µA, both steps recruit zero hosts; at −18 µA, both recruit three hosts, with one somatic spike per host. The largest event-index-matched host spike-time change is 0.0197458 ms. The frozen acceptance checks recruitment and per-host spike counts; timing changes are reported without a new timing tolerance. This supports these two sampled endpoints, not an exact threshold or uniform convergence of every value between them.

Q_first [nC] = I_first [µA] × phase duration [ms]
Q_absolute,phase = |Q_first|
A_disk [µm²] = π r²
D_geometric [µC/cm²] = Q_absolute,phase [nC] × 10⁵ / A_disk [µm²]

Equal opposite phases give zero prescribed net charge, but charge balance does not establish electrochemical or tissue safety. Nominal density uses the geometric disk area; electrode material, impedance, polarization, reaction kinetics and damage are not solved. The default numerical example is 9.60000 nC per phase and 1358.12 µC/cm² per phase. It is not a device operating recommendation.

Protocol workers run at most 14 solves, 120 million node-steps and eight million saved voltage values per solve. Excessive requests are rejected before calculation; the solver resolution is never reduced silently. Cancellation terminates the worker. A new run cannot overwrite a later request, and retained results keep their completed settings when controls change. Protocol JSON contains each normalized setting, intervention, host event, source amplitude, unit and failure. CSV contains a row per requested condition; failed measurements remain blank. “Inspect run” recalculates its exact settings for the main anatomical replay.

Verification and a retained storage-precision failure

10 of 10 quantified Stage 02 acceptance studies pass, including causal loss, zero-input monitored events, mixed and direct activation, source identity, all five default study grids, explicit placement-error retention and the analytical storage-precision check. Dedicated automated tests additionally exercise deterministic repeatability, control matching, malformed protocols, work budgets, cancellation message contracts and export corruption.

Retained failed supplemental diagnostic: reconstructing source currents from the saved Float32 voltage movie misses a provisional fixed 0.001 µV absolute criterion for the host source: maximum error 0.00127357 µV. The graft error is 0.0000963900 µV. This failure remains in the report. The exported quantitative source waveforms use their original Float64 calculations.

A separate independent calculation propagates each stored voltage’s Float32 half-ULP through the axial-current matrix and recording transfer matrix. All 4,806 population/contact samples lie within that analytical quantization bound, with maximum error-to-bound ratio 0.606757. Passing this different, physically justified storage-precision check does not turn the failed absolute diagnostic into a pass. The native-source comparison above checks the original quantitative waveforms separately.

Retained cross-runtime exact-literal failure

Two original exact-literal regression comparisons failed in GitHub CI. Peak-to-peak values saved under Node 24.19.0 were not bit-identical under Node 22.23.3: R2 was 9.745329941385737 versus 9.745329941385254 µV, a difference of approximately 4.83 × 10⁻¹³ µV. The raw values and failed job remain in the release verification record. This was a failed cross-runtime bit-equality assumption; it was not a failed native-reference or convergence criterion.

The replacement regression compares every original voltage, trace, recording and event exactly against the frozen released solver in the same runtime, with pinned source provenance and dependencies. The worker transport test likewise requires exact equality to a direct calculation in that runtime. Neither check adds an error allowance, and the independent native-reference and physical convergence tolerances remain unchanged. ECMAScript permits implementation-approximated transcendental functions; cross-runtime bit identity is not assumed. These measurements do not isolate a particular built-in operation as the cause of the observed difference.

The source-hashed report and reproduction script are retained as docs/biohybrid/stage2-validation.json and scripts/validate-biohybrid-stage2.mjs. Initial Node measurements were approximately 4.31 seconds for the three-run default audit; browser, device, population and resolution determine actual elapsed time.

8. Growth on a separate timescale

The growth module is a seeded geometric model over days. It combines persistent direction, a target-directed cue, stochastic steering, branching, cylinder-wall reflections, target-sphere encounters, a formation trial and a maturation delay. It does not run on the electrical replay clock and does not reproduce the concentration-based model of Marinov et al.

Branching uses p = 1 − exp(−λ Δt), with λ in day⁻¹. This preserves the constant-hazard survival probability across step subdivisions; the full branching process is still an approximation because at most one child is created per path per step, at the step endpoint. Segment/sphere intersection checks an entire extension, avoiding missed targets between endpoints. Each distinct path–target encounter gets one formation trial. An accepted encounter becomes a candidate only after an assumed maturation interval; every candidate remains explicitly unvalidated for function. Seeded steering, branching and formation streams are separate, so changing formation probability does not move the existing trajectories.

The default elongation rate of 180 µm/day, cue strength, branching hazard, formation probability and maturation interval are exploratory estimates. Published micro-TENN growth rates depend strongly on preparation and culture stage. The laboratory does not turn a culture observation into an in-vivo integration forecast. The default realization can encounter targets without forming any candidate synapses.

Only an explicit button transfers the number of candidate host targets to pending electrical settings. This transfers a count, not the identity, trajectory or individual weight of each candidate connection. The user then runs a separate electrical calculation with the assigned synaptic conductance. The grown geometry is not substituted for the electrical cable mesh. A path cap suppresses additional branches and reports that limitation; a vertex cap stops the calculation at the last completed step and reports the truncated horizon. Growth tests establish deterministic and geometric consistency, not experimental calibration.

9. Reproduction and release limits

node scripts/validate-biohybrid-stage2.mjs
node --test tests/biohybrid-engine.mjs tests/biohybrid-export.mjs \
  tests/biohybrid-growth.mjs tests/biohybrid-reference.mjs \
  tests/biohybrid-protocols.mjs tests/biohybrid-sources.mjs \
  tests/biohybrid-protocol-export.mjs tests/biohybrid-workers.mjs \
  tests/biohybrid-response-boundary.mjs
node scripts/validate-biohybrid.mjs
node scripts/biohybrid/reference-input.mjs /tmp/biohybrid-input.json.gz
python scripts/biohybrid/neuron-reference.py \
  /tmp/biohybrid-input.json.gz docs/biohybrid/neuron-validation.json
npm run build

The independent reference dependency is pinned to NEURON 9.0.1. The repository retains the scientific architecture, numerical report, native comparison, growth methods and validation history. The WebGL scene uses calculated compartment voltage, while the 2D fallback uses the same data and color map. The verification browser had WebGL disabled: the fallback, computation and interaction path were visually checked; a GPU-enabled browser remains necessary for a direct visual check of the 3D view.

Remaining scientific work includes measured graft-cell morphologies and channel fits; temperature/preparation-specific calibration; experimental stimulus and recording comparisons; heterogeneous scaffold/tissue conductivities; electrode impedance and noise; inhibition, adaptation, plasticity and synaptic variability; validated growth-to-connectivity mapping; and empirically calibrated long-term changes. The degradation preset is a sensitivity study, not a prediction of implantation lifetime.

10. Component-level reference register

Each entry states which component it supports and what it does not establish. Experimental, mathematical, estimated and hypothetical claims remain separate.