Neural interface laboratories / Design & testing

Regenerative Peripheral Nerve Interfaces

Design the muscle graft. Route the nerve. Position the contacts. Test the signals your assumptions produce.

Mechanistic design model

A muscle-graft RPNI forward model with calculated electrical pickup and an independent transport diagnostic. Synthetic motor units; uncalibrated tissue parameters. No clinical outcome, graft-survival or prosthesis-performance prediction.

Choose a starting design

01 / Design specification

A pair of independent muscle-graft interfaces.

Graft geometry

Each module is a separate free muscle graft. Dimensions describe an idealized rectangular tissue volume; grafts share the selected geometry.

Separate muscle graftsEach rectangular graft receives one terminal nerve and one differential recording channel.Graft lengthmm30 × 15 × 5 mm is a harvested human graft example in Vu et al. 2020. Dimensions here are editable and are not an optimized implant prescription.Graft widthmmA rectangular placement envelope, with x-aligned representative muscle fibers. Real implanted graft geometry is not reconstructed.Graft thicknessmmControls geometry and the separate steady slab transport diagnostic. Does not automatically determine survival.Gap between graft edgesmmActual edge-to-edge spacing in y. The same coordinates drive the electrical calculation and anatomy view.

Recording contacts

One differential channel per graft. Move its two finite disk contacts along the fibers, across the graft, or into its depth.

Bipolar center spacingmmPositive and negative contacts differ along x; zero spacing is the exact common-mode cancellation control.Pair midpoint along fibersmmMidpoint x relative to each graft center. Geometry normalization keeps contact disks within the rectangular planform.Pair lateral offsetmmMidpoint y relative to each graft center; both contacts lie in the x-y plane.Contact depth below topmm0 is the top graft face. This controls physical position; it does not specify an insertion procedure.Contact disk radiusmmArea-averaged extracellular potential over a disk. Electrode-tissue impedance and contact polarization are not modeled.

Nerve routing & motor units

Physical graft identity and source command identity remain separate. Routing is a seeded assignment assumption, not a prediction of fascicle identification.

Nerve diametermmAn illustrative terminal nerve envelope. Diameter does not set an anatomical motor-axon count or source amplitude.Nerve insertion depthmmThe terminal nerve tip is the origin of the assumed intragraft regrowth path; there is no distal nerve stump.Equivalent units per graftunitsA representative equivalent-source cohort, not measured motor-unit number. Changing it changes total source power.Same-pool allocationfractionProbability that a physical graft source retains its correspondingly labeled command pool. Off-label allocations are synthetic; no fascicle identification or surgical efficacy is predicted.Equivalent territory radiusmmThree weighted representative fibers span each territory. This is a reduced spatial quadrature, not a histologic fiber census.

Regeneration & maturation

Arrival uses distance and a prescribed axon speed. Subsequent source maturation is an adjustable exponential. These clocks are not fitted to longitudinal RPNI measurements.

Regrowth onset lagdaysAn assumed postconstruction delay before growth from the terminal nerve tip.Assumed intragraft regrowthmm/dayArrival is lag + straight branch length / speed. No mechanistic axon guidance or biological calibration is implied.Source maturation constantdaysAfter assumed arrival, equivalent source amplitude rises exponentially. This is not a validated NMJ formation or force-recovery law.Available source-amplitude fractionfractionAn independently imposed amplitude multiplier. It is not an oxygen-derived viability, surviving-cell fraction, or clinical success probability.Recording daydaysSource maturation is evaluated on this day for the finite stochastic recording.Biological observation horizondaysTime since construction; independent of the millisecond recording window.

Electrical source & tissue

Balanced traveling source tripoles in an infinite, homogeneous anisotropic conductor. Source current is an explicit equivalent-source assumption.

Equivalent tripole currentµANominal current scale of one unit; each traveling tripole receives half this scale, distributed across three weighted fibers. Absolute amplitudes require calibration.Prescribed muscle wave speedm/sSpeed of the equivalent traveling muscle source; distinct from axonal regrowth in mm/day. No membrane dynamics are solved.Tripole pole spacingmmPrescribed +1, −2, +1 source separation. Current balance holds through onset and endpoint tapers.Source regularization radiusmmSmooth ellipsoidal source core in conductivity-transformed coordinates. Explicitly limits point-source singularities; not an anatomical fiber radius.Longitudinal conductivityS/mConstant conductivity along x throughout the infinite domain. An exploratory value, not a measured graft property.Transverse conductivityS/mConstant conductivity along y and z throughout the domain. No muscle-host discontinuity is resolved.

Drive & acquisition

Independent seeded spike trains drive the source pools. Noise is additive, white and Gaussian; there is no fitted amplifier, impedance or movement artifact model.

Target command poolZero-based source-pool label used for target versus other decomposition, not an anatomical motor-function identity.Target pool drivefractionDrives synthetic threshold recruitment and independent Poisson event trains; no descending neural control model is included.Other pools drivefractionThe same drive is applied to every non-target labeled source pool. Zero provides a target-only experiment.Rate at recruitmentHzPoisson event-rate assumption, not a measurement of reinnervated motor neurons. No refractory period, fatigue or synchronization is modeled.Rate at full driveHzSynthetic recruitment thresholds range from 0 to 0.8, with linear rate increase above threshold.Independent channel noise RMSµVUser-imposed white Gaussian noise, independent between channels. Not an empirical implant noise floor or impedance prediction.Recording windowmsA finite realization of prescribed equivalent sources; mean is removed separately from each command-pool trace.Recording sample rateHzFinite trace sampling rate. Source kernels are independently oversampled and interpolated at fractional event times; no antialias filter is imposed.

Transport diagnostic

Steady, one-dimensional diffusion with first-order consumption and equal supply at both faces. Independent of the electrical source model; it does not predict viability.

Slab diffusivitymm²/sExploratory transport coefficient in D c″ − k c = 0; fixed bath concentrations on the two thickness faces.First-order consumptions⁻¹Consumption is k × concentration. This exact steady 1D diagnostic omits capillaries, convection, zero-order metabolism and survival thresholds.

Numerics & reproducibility

Contact quadrature controls spatial averaging. A common seed helps compare designs without redrawing the synthetic cohort.

Contact quadrature orderGauss integration in squared radius with 4 × order angular samples; refine to assess spatial averaging error.Source waveform oversamplingfactorSource kernels use this many steps per recording sample. Expected variance integrates the piecewise-linear kernel exactly; refine independently to assess waveform error.Random seedReproducible territories, routing, source strengths, Poisson events and channel noise. Seeds index synthetic realizations, not patients.

Preparing the reference design…

02 / Geometry review

Nerve-to-muscle recording interface

Two independent grafts

Preparing anatomical view…

Anatomy layers & display

Nerve routing Motor-unit territories Contacts Labels Transport overlay

Coordinates and ruler in millimeters. Tissue and motor-unit anatomy are procedural.

Select a recording contact to inspect its geometry.

Biological age / assumed remodeling

Day 120

Electrical replay / recorded at day 120

0 msReplay ×0.1

The biological and electrical clocks are separate. Signal replay returns the anatomical view to the recording day.

Volume per graft—mm³ / specified geometry

Territories reached—Synthetic axon arrival / shown day

Mean source amplitude gain—Continuous gain / shown day

Trace RMS at recording day—µV / signal + noise

03 / Calculated electrical recording

What the contacts pick up

Channel

Synthetic signal + noiseTarget source contributionOther source contribution

Each channel sums the geometry-dependent motor-unit waveforms and specified noise. These are synthetic extracellular signals, not measured or fitted human EMG.

04 / Source separation

From command pool to channel

Rows are bipolar channels; columns are source command pools. Values express geometry-dependent pickup under the stated source model.

Channel similarity

Expected clean-channel correlation from shared modeled sources. This is neither finite-trace correlation nor decoder accuracy.

05 / Independent transport test

Thickness and supply distance

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Fixed concentration at both faces; first-order consumption. This mathematical slab test does not include a developing vascular network or predict graft survival.

06 / Assumed biological sequence

Arrival precedes source maturation

Arrival fractionMean source amplitude gainDashed: pinned design

A prescribed nerve-growth delay and speed determine arrival at each synthetic territory. A separate exponential controls subsequent source strength. Oxygen is not used as a hidden viability gate.

07 / Controlled design study

Change one design variable

VariableFromTo

Readout

The same seed, drive and recording horizon are used at each point. Results describe sensitivity to the selected variable within this model.

Sweep values & effective geometry

Run a study to inspect exact values.

08 / Seed variability

Repeat the synthetic population

Run independent seeds at fixed design parameters to see how source placement, current-strength multipliers and command routing change expected signal power.

Seed variation excludes uncertain biological parameters, patient differences and measurement uncertainty. Its range is not a clinical confidence interval.

09 / Design comparison

Keep a reference design

Pin a result, edit the design and run again. The table will keep the changed assumptions alongside the computed differences.

Exact values at the displayed biological age

Readout	Value	Meaning

Reproducible design record

Model 1.0.0 · seed 2048 · local computation

Restore a saved design

Paste an exported experiment or choose its JSON file. Parameters require an exact model-version match; saved numerical results are recomputed.

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The interface represented here

A nerve-to-muscle recording interface

A muscle-graft RPNI supplies a denervated muscle target to a terminal nerve or separated fascicle. Reinnervated muscle can amplify motor commands into recordable electrical activity. This laboratory represents that architecture with separate graft modules, synthetic motor units and physical electrode coordinates.

A nerve bridge, regenerative sieve, dermal sensory interface and engineered neural graft involve different anatomy and boundary conditions. Use the nerve-regeneration laboratory to explore repair across a peripheral nerve gap.

Evidence & verification

Inspect every assumption

Human and animal studies motivate the design questions. The numerical tests check the equations and limiting cases. The model does not infer patient outcomes, functional muscle force, sensory perception, stimulation thresholds or device safety.

Read the equations, parameter provenance and primary studies →