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Model accuracy

VirtuCath™ uses two distinct model layers, each characterized separately:

  1. The catheter calculator — VirtuCath's composite-mechanics chain. Predicts static section stiffnesses (EA, EI, GJ) and derived failure-mode KPIs (Elastic Instability Radius, Max Moment) from material and geometry inputs, from first principles — classical laminate theory and established composite micromechanics, combined through beam and section mechanics. Referred to below as the analytic model.
  2. The dynamic simulator — predicts catheter behavior under actuation (pullwire-driven deflection, gravity loading, multi-body equilibrium) using a multi-body physics engine.

The two layers feed each other — the dynamic simulator uses the section stiffnesses produced by the calculator — but their accuracy is characterized independently against different benchmarks. This page documents both.

Terminology used on this page:

  • The analytic model (or the calculator) — VirtuCath's composite-mechanics chain, item 1 above.
Quick reference — when to trust predicted stiffness
  • ✅ Polymer-only segments
  • ✅ Sparse-reinforcement layers
  • ✅ Coil-reinforced sections
  • ✅ Moderate-density ribbon braids at typical angles
  • ✅ Comparing two similar configurations (relative accuracy is preserved — see A note on relative accuracy)
  • ✅ Pullwire-driven deflection within the published parameter space (both small- and large-deflection cases are verified — see Dynamic simulator accuracy)
  • ⚠️ Densely-packed braids — verify with physical testing
  • ⚠️ Braids at extreme angles — verify with physical testing
  • ⚠️ Materials that differ from datasheet values — characterize and override the Materials Library entry

Catheter calculator accuracy (EA / EI / GJ)​

The calculator predicts stiffness from first principles: layer stiffnesses are built from constituent material properties and geometry using classical laminate theory and composite micromechanics, then combined through beam and section mechanics — not by empirical curve-fit to any dataset. Because predictions follow from mechanics, the model responds predictably as construction inputs change. Accuracy is still not uniform across the design space — it depends on the regime your design falls into.

Bench validation of predicted EI​

Reference document: VirtuCath™ Stiffness Validation Report (VR-VC-003 v1.0). Where the two simulator verification reports further down this page confirm the mathematical accuracy of the physics engine against analytical and continuum-robot references, this report validates the calculator's predicted bending stiffness (EI) against physical measurement.

Two independent sources of measured EI were used:

  • In-house bench testing. Manufactured catheter shafts from multiple manufacturers and constructions, tested in three-point bend across multiple support spans with replicates. A gauge-length-independent "true" EI was recovered by a Timoshenko shear-separation fit, which removes short-span shear and test-fixture artifacts. Each specimen was modeled in VirtuCath from its nominal engineering drawing with datasheet material properties.
  • Independent literature. Published bench-measured stiffness for a 7 Fr thin-wall braided shaft in three distinct braid patterns, reproduced by VirtuCath to within approximately 10% — including the correct relative softening of the diamond pattern.

Across the eight qualifying constructions (five bench specimens + three literature patterns):

MetricValue
Median absolute error11%
Mean absolute error16%
Mean bias−12% (conservative — under-predicts)
Within ±15%6 of 8 constructions
Ratio range (predicted / measured)0.55× – 1.10×

Three findings from the report matter most for day-to-day use:

  1. The error is systematic, not random. Its direction is consistent (under-prediction on six of eight constructions) and its magnitude correlates with construction type. Constructions of similar type carry a similar bias — which is why relative comparison between similar designs is preserved with substantially higher fidelity than the absolute error implies (see A note on relative accuracy).
  2. Worst-case behavior is contained and conservative. The largest deviations (25–45% under-prediction) occur at one describable edge of the envelope: the stiffest, highest-braid-angle steel-braided constructions. See Where the model is less accurate.
  3. Input material properties are the dominant user-controlled uncertainty. EI scales approximately linearly with constituent modulus, and as-extruded polymer modulus typically differs from datasheet values by ~±15%. Supplying as-tested material properties in place of datasheet values narrows the prediction directly (see Material properties matter).

Scope: bending stiffness (EI) in the linear-elastic regime, room temperature and dry, for the common catheter envelope (~2–8 Fr braided multi-layer shafts). GJ and EA come from the same first-principles laminate and section mechanics but await comparable bench data; their quantitative validation is deferred.

What's in this report: validation methodology (multi-span three-point bend with Timoshenko shear separation, specimen inclusion criteria), the per-construction predicted-vs-measured table, a log–log parity plot, accuracy statistics with a robustness check including the excluded specimens, the systematic-error analysis, and the validity-domain limitations.

📄 Download full report (PDF)

Where the model is most accurate​

Sections where one mechanism dominates the response:

  • Polymer-only segments
  • Sparse reinforcement layers
  • Single-direction coil-reinforced sections
  • Moderate-density ribbon braids at typical angles

In these regimes, predicted stiffnesses are typically within ~10–15% of physical bench testing — consistent with the bench validation result (median error 11% across the qualifying set).

Where the model is less accurate​

Densely-packed braids, particularly at extreme braid angles. In this regime the wires are forced into close contact under bending, and the response depends on wire-to-wire interactions that a simplified composite-mechanics model captures less faithfully than the simpler fiber-in-matrix case. Predictions here can deviate by up to ~50% from physical measurement; treat them as design-screening estimates and validate against bench testing before locking in a final design.

The bench validation characterized this corner directly: on the two stiffest, highest-braid-angle steel-braided specimens, the model under-predicted EI by 25–45% — conservative and consistent in direction on both, so it behaves as a characterizable offset in that region rather than random scatter. Relative comparison between similar constructions remains valid there (see below).

A note on relative accuracy​

Even in regimes where absolute predicted stiffness has elevated uncertainty, the model's error is systematic rather than random. Two similar catheter configurations evaluated in VirtuCath tend to be biased in the same direction by similar amounts. This is now demonstrated on the bench: across the validation set, the error direction was consistent and its magnitude correlated with construction type rather than scattering from one specimen to the next (VR-VC-003, §6.1).

This makes the tool well-suited for A/B-style design comparisons — e.g., evaluating two candidate braid pitches, two matrix materials, or two pattern variants — and for iterative design workflows where the question is "which configuration is stiffer, and by how much?" rather than "what is the exact stiffness in absolute terms?" Use VirtuCath to identify the best candidate design quickly, then anchor the absolute stiffness with physical testing of the leading candidate.

Other KPIs in the Failure Mode panel​

The remaining Failure Mode Analysis values — Tensile Failure Load (First Yield), Torque Failure, Burst Pressure, and External Crush Pressure — are governed by material strength limits, wall geometry, and the wire contribution rather than the composite stiffness chain. They inherit the usual datasheet-strength uncertainty (~10–20%) plus the residual gap from the underlying composite-mechanics step.

Tensile Failure Load (First Yield) and Torque Failure estimate the load at which the first material in the section reaches its strength limit — a conservative first-yield onset rather than ultimate rupture. For tension in particular, real rupture is higher, since ductile wires keep carrying load past first yield. These are typically accurate within a factor of two and usually conservative. Tensile predictions can be optimistic for sections with thin liners, where stress concentrations cause real failure to occur sooner than an analytical model predicts.

Burst Pressure uses Barlow's law with a rule-of-mixtures hoop strength estimate. The result tends to over-predict the true wall-failure threshold by 2–3×, because real failure initiates in the reinforcement wire layer rather than uniformly across the wall. Treat it as a screening upper bound and apply a safety factor for design margin.

The Elastic Instability Radius and its associated Max Moment are covered in their own section below.

Elastic Instability Radius — what it predicts, what it doesn't​

This is the bend radius at which the cross-section first starts behaving in a way the linear-elastic model can no longer reliably predict. Bend a catheter past this radius and you've left the regime where this tool is accurate.

This is not the same as the visible "kink" radius you'd measure by physically wrapping the catheter around a mandrel. Real catheters often survive past the predicted instability point — they enter a regime (cross-section flattening, wrinkling, partial collapse) that the linear-elastic model can't trace. In those cases the visible kink usually happens at a tighter bend than predicted, and the Elastic Instability Radius works as a conservative early warning.

For some designs, however, the actual visible failure can happen at a looser bend than predicted. The analytical model captures one specific instability mechanism well, but other mechanisms can win for certain combinations of wall thickness, matrix stiffness, and reinforcement. For those designs the prediction is less conservative than you'd want, and physical bench testing remains the only reliable check.

Treat the Elastic Instability Radius as the point where the model becomes unreliable, and as a useful relative indicator for comparing similar designs. Don't treat it as a definitive answer to "where will this catheter kink?" — that question is harder than any analytical model can answer.

Coil-reinforced sections — what's different​

For sections reinforced with a coil, the Elastic Instability Radius is computed as the more conservative of two predicted failure events: the elastic ovalization limit, and the polymer matrix yield. Whichever happens at a looser bend is the value displayed.

This combined treatment reflects that coil sections have polymer exposed between hoops, unlike braid sections where the reinforcement forms a continuous laminate. For coil designs with stiff polymer matrices, the polymer between hoops can permanently deform before any elastic mechanism triggers; in those cases matrix yield is the binding constraint. Reporting the more conservative of the two keeps the value usable as a lower bound for design margins regardless of which mechanism governs.

The same combined approach extends to External Crush Pressure for coil sections: the displayed value is the more conservative of polymer ring collapse and polymer yield in hoop compression.

What the 70% display behavior means​

In the Simulation Analysis tab, the OD/ID ovalization display gives a visual cue when the operating bend gets close to the instability point:

  • Below 70% of the instability curvature, live numbers in black — predictions are trustworthy.
  • At 70% and beyond, the numbers freeze at the 70%-threshold values and switch to a directional format (>X.XX / <Y.YY). Past 70% the cross-section is changing faster than linear theory predicts, so the display stops pretending to give you a precise number and tells you the direction it's moving instead. As you back off the bend, the live display returns.

Dynamic simulator accuracy​

The dynamic simulator powers the runtime physics in the Simulation Control and Simulation Analysis tabs — it solves the catheter's multi-body equilibrium under pullwire actuation. Unlike the calculator (which predicts section properties), the simulator's job is to predict the full-length deflected shape given those section properties as inputs.

The simulator is verified against two independent benchmarks: a small-deflection analytical cantilever-beam reference, and a large-deflection state-of-the-art continuum-robot reference (Cosserat Rod). Both verification reports are published in full alongside this documentation.

Small deflection — cantilever beam benchmark​

Reference document: VirtuCath Software Small Deflection Verification Report (VR-VC-002 v1.0). Verified against the analytical equations for a uniform cantilever beam under a transverse distributed load (gravity), restricted to the linear-elastic regime (tip deflection < 5% of body length).

The benchmark covered 400 randomized single-segment configurations spanning a wide range of lengths, stiffnesses, and linear densities. Both tip deflection and tip angle agreed closely with the analytical predictions, with negligible mean bias and small absolute residuals across the parameter space. The cantilever case is considered VERIFIED — the engine correctly reproduces continuum bending mechanics across the linear-elastic range.

What's in this report: Per-run parity plots and residual histograms for the 400-run cantilever sweep, parameter ranges, discretization-effect analysis, and pass/fail criteria.

📄 Download full report (PDF)

Large deflection — Cosserat Rod benchmark​

Reference document: VirtuCath Software Verification Report (VR-VC-001 v4.0). Verified against the Cosserat Rod model — the highest-fidelity approach for continuum robots, treating the catheter backbone as a continuous elastic rod with six degrees of freedom at every point and making no geometric assumptions about the final shape — as published by Rao et al. (2021) in Frontiers in Robotics and AI.

The benchmark covered 280 randomized simulations across 1-segment and 3-segment pullwire-actuated catheters, spanning a wide range of segment lengths, tendon offsets, pullwire displacements, and stiffnesses. The simulator was compared against Cosserat-Rod reference values for both required tendon force and final tip deflection angle, and agreement was strong across the tested parameter space. The pullwire-actuated case is considered VERIFIED.

What's in this report: Parameter ranges and parity plots for the 280-run pullwire-actuated sweep, the Cosserat-Rod reference implementation, and worst-case behavior at the boundaries of the tested envelope.

📄 Download full report (PDF)

What the simulator verification covers — and doesn't​

These studies verify the mathematical accuracy of the core elastic-rod solver against established analytical and continuum-robot benchmarks. They do not yet include direct validation of the deflected shape against physical catheter prototypes; that work is a separate, more extensive program. (The static section stiffnesses the simulator consumes as inputs are separately validated against physical bench measurement — see Bench validation above.) For pullwire-actuated behavior, the Cosserat-Rod reference is the appropriate state-of-the-art benchmark, and the simulator agrees with it across the tested envelope.

Material properties matter​

Both the calculator and the simulator rely on the polymer and metal properties from the Materials Library matching your production materials. Library values are sourced from manufacturer datasheets, but real-world material behavior varies — lot-to-lot variation, processing history, moisture content, aging, and strain-rate sensitivity can shift modulus by 5–15% from datasheet values, especially for polymers.

If your production materials deviate from the library defaults, predicted stiffnesses (and therefore the simulated dynamic response that depends on them) will shift accordingly. For tighter agreement with your build, characterize your specific materials and override the library entries with measured values. The bench validation quantified this as the dominant user-controlled uncertainty: because EI scales approximately linearly with constituent modulus, the ~±15% difference between datasheet and as-tested polymer modulus propagates almost directly into predicted EI — material characterization is the single most effective lever you have to tighten agreement.