Model accuracy

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

1. The catheter calculator (referred to below as the analytic model, or simply the calculator): VirtuCath's composite-mechanics chain. Predicts static section stiffnesses (EA, EI, GJ), their compliance counterparts (L/EA, L/GJ), and derived failure-mode KPIs (burst pressure, external crush pressure, tensile and torque failure loads) from material and geometry inputs, from first principles: classical laminate theory and established composite micromechanics, combined through beam and section mechanics.
2. The simulations built on top of it. Three simulations start from what the calculator resolves:
   • The steering simulator (the simulator) predicts steering behavior under actuation (pull-wire deflection, gravity loading, multi-body equilibrium) with VirtuCath's own quasi-static multi-body solver: a chain of rigid segments joined by bending, twist and axial springs set from the calculator's section stiffnesses, solved to a converged static equilibrium at every frame.
   • The Kink Radius simulation, a 2D finite-element model of one cross-section, finds the bend limits: kink, collapse, and permanent set (its own section below).
   • The Pushability simulation, a 2D finite-element push test of the shaft's free length, finds the buckling behavior (its own section below).

The layers feed each other: the simulations consume the section properties and layup the calculator resolves. Each model is still characterized independently, against benchmarks appropriate to its job. This page documents all of them.

Two words recur below, and they are not interchangeable. Verification asks whether the software solves its equations correctly; it is checked against established analytical and numerical references. Validation asks whether the predictions match physical reality; it is checked against bench measurement. VirtuCath publishes both kinds of evidence, and each claim on this page is labeled as one or the other.

Evidence at a glance

Prediction	Benchmark	Headline result	Full document
Bending stiffness (EI) (the calculator)	In-house three-point-bend testing of manufactured shafts, plus published bench data for a 7 Fr braided shaft in three braid patterns (validation)	Median absolute error 11%; bias conservative (−12%, under-predicts); worst case contained at one describable edge of the envelope	Stiffness Validation Report VR-VC-003 v1.0: 📄 PDF
Kink and collapse bend radii (the Kink Radius simulation)	Analytic Brazier limit point for a thin tube (verification)	Limit-point curvature within +2–6% of theory, linear EI within 0.06%. Radii are screening values: rank designs in the app, confirm the finished design on the bench	Bend limits on this page
Buckling under push (the Pushability simulation)	Classical Euler critical loads for the four ideal end conditions, plus the elastica post-buckling solution (verification)	Buckling knee within 8% of the Euler load; post-buckling plateau just above it, as elastica theory requires; the ideal-column reference itself within 0.2% of textbook	Buckling on this page
Deflected shape, small deflection (the simulator)	Analytical cantilever-beam solution, 400 randomized configurations (verification)	Verified: negligible mean bias, small residuals across the parameter space	Small Deflection Verification Report VR-VC-002 v1.0: 📄 PDF
Deflected shape, pullwire actuation (the simulator)	Cosserat Rod continuum-robot reference (Rao et al., 2021), 280 randomized runs (verification)	Verified: strong agreement on tendon force and tip deflection angle	Verification Report VR-VC-001 v4.0: 📄 PDF

Every quantitative claim on this page traces to one of these documents. The sections below give the context each number needs: what was tested, where the model is strong, and where you should reach for bench testing instead.

Quick reference: when to trust the predictions

• ✅ 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)
• ✅ Push and buckling behavior under the ideal restraints (verified against Euler; see Buckling); absolute push forces inherit the stiffness accuracy above
• ⚠️ Bend limits (kink / collapse): the failure mechanism is the most stable output; treat radii as screening values and confirm the finished design by bench test (see Bend limits)
• ⚠️ 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

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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. This section gives the bench evidence first, then the regime map.

Bench validation of predicted EI

Reference document: VirtuCath™ Stiffness Validation Report (VR-VC-003 v1.0). This is the validation leg of the evidence table above: the calculator's predicted bending stiffness (EI) compared against physical measurement. (The two simulator reports, covered in Dynamic simulator accuracy, are the verification leg.)

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):

Metric	Value
Median absolute error	11%
Mean absolute error	16%
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 (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.

Strength-limit 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.

Bend limits are not in this panel: they come from the Kink Radius simulation, covered next.

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Bend limits: the Kink Radius simulation

The app's bend limits are measured, not estimated: the Kink Radius simulation bends each section's real cross-section step by step (the actual layup, the pull-wire lumens, the bend direction) and reports the events it observes: the moment peak that leads to collapse, 50% lumen loss (the ISO 25539-2 / EN 13868 kink definition), and each layer's first crease. Because the events are observed on your geometry rather than predicted by a formula, the simulation sees what no closed form can: which layer gives first, how the answer moves with bend direction, and what failing actually looks like for this design.

The section mechanics are verified against classical theory. Against the analytic Brazier limit point for a thin isotropic tube, where the closed form is exact and there is no material uncertainty to hide in, the solver lands:

quantity	agreement with theory
limit-point curvature	+2% to +6%
limit-point moment	−2.3% to +0.4%
linear EI	within 0.06%

Measured across wall slendernesses of r/t = 20, 40 and 50. The small drift with r/t is in the expected direction, not error: the finite-element section carries finite ovality where Brazier assumes it is small.

The failure mechanism is the output the tool leads with, because it is the most stable. Across a sweep of solver settings, how a section ends (collapse, lumen closure, self-intersection) agreed in 29 of 30 runs. That stability is numerical, not bench validation: it says the mechanism belongs to the design rather than to the solver settings. The tool reports it first and lists the radii beneath it as the evidence.

Radii are shown at the precision the physics supports. Displayed radii are rounded to the nearest millimetre (0.05 in): a bend radius is a size, and the display is honest about that. Where a section ends by snapping rather than by a smooth moment peak, the snap radius is reported as an endpoint (the section snaps near here) rather than dressed up as a converged number. Exports carry full precision.

Material limits are anchored on measured kinks. The crease strain that marks each polymer's permanent-set limit is anchored on observed kink events on production catheter constructions, and is consistent with the structural strain limits the flexible-pipe industry codifies for the same polymer classes (API 17J). The behaviour this produces (reinforced constructions limited by strain, unreinforced tubes by collapse) matches the pattern across several hundred published minimum-bend-radius specifications mined from manufacturer catalogs: Freelin-Wade, Parker Parflex, NewAge Industries and Zeus for plastic tubing; Alfagomma/Kuriyama, Parker, Aflex and Festo for hydraulic hose, alongside the SAE 100R-series tables; and Performance Pipe and DuraLine field-bending guidance for PE pipe.

Bench validation of the measured radii is an early, growing program. The measured-kink dataset today is a handful of production constructions: not yet enough to state accuracy statistics that would mean anything, and this page does not publish statistics it cannot stand behind. What the data so far supports is the trust ordering below, and it is why the tool's own guidance is to rank in the app and confirm on the bench.

The tool does not report what it cannot measure. A solid multi-lumen core has no open bore to ovalise into a limit point, so for cored sections the tool reports material strain and the geometric endpoints and states that collapse does not apply, rather than printing a number that is not a measurement. The same rule runs through the results: an event the ramp did not reach says not reached, and a quantity that was not computed is left blank rather than shown as zero.

How far to trust a given prediction

The simulation solves the cross-section mechanics (ovalization, collapse, lumen loss) from the actual layup, so the tiers below are not about the geometry: they are about the material strain limits the solved strains are judged against.

• Most reliable: sections whose polymers sit close to one of the calibrated families, where the crease limit is anchored on observed kink events.
• Reasonable: jackets between or beyond the calibrated families. The crease limit is interpolated, so treat the crease radius as a good estimate rather than a number to design a margin against. Collapse and lumen-loss radii do not depend on the crease limit and are unaffected.
• Indicative: thick-walled sections (wall approaching a third of the section radius). Creasing there is governed by plasticity the elastic material model does not carry, and the tool flags it on the run. Rank designs here; confirm the winner on the bench.

Predictions assume a single monotonic bend at room temperature; cyclic kink limits run roughly 2× tighter. Where a specific assumption is strained on a specific section, the app says so in that value's tooltip rather than leaving you to work it out.

The intended workflow is the one that works everywhere in this tool: use the simulation to explore, rank and narrow the design space (it will tell you which construction is better, which bend direction is weaker, and why), then confirm the finished design's bend limit on the bench.

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Buckling: the Pushability simulation

The Pushability simulation solves a 2D quasi-static push of the shaft's free distal length and reports the full force/stroke curve. The solver is verified against classical column mechanics:

• The four textbook Euler loads (free, pinned, guided, and clamped end conditions) are reproduced by the stepped-column reference to within 0.2%.
• The full push simulation finds its buckling knee within 8% of the Euler load under the ideal restraints, and the post-buckling plateau sits just above that load, as elastica theory requires. The knee moves by less than 2% as solver resolution changes.
• A square frictionless wall reproduces the free-tip case, so the wall-contact mode collapses to the textbook condition it should.

As everywhere in this tool, relative comparisons between designs and scenarios are the reliable output; absolute push forces inherit the accuracy of the section stiffnesses they are computed from (see the bench validation above).

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Steering simulator accuracy

The steering simulator powers the runtime physics on the Steering Simulation tab: 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 verification studies below were re-run on this solver when it replaced the previous multi-body engine; every reported number reproduces to seven decimal places, so the published reports stand as they are.

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 (it treats the catheter backbone as a continuous elastic rod with six degrees of freedom at every point and makes 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 what it 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.

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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.

Related pages

• Kink Radius: the simulation behind the bend limits covered above.
• Pushability: the simulation behind the buckling results covered above.
• Catheter Analysis: where the predicted stiffnesses are shown.
• Simulation Readouts: runtime simulator metrics that depend on the calculator outputs covered above.
• Materials Library: the polymer and metal property defaults referenced above.