Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometry

Madina Kojanazarova; Sidaty El Hadramy; Philippe C. Cattin

cs.AIAug 21, 2026

Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometry

Authors: Madina Kojanazarova, Sidaty El Hadramy, Philippe C. Cattin

Organizations: University of Basel, Department of Biomedical Engineering, Allschwil, Switzerland

Abstract

Accurate soft tissue simulation is essential for surgical training, pre-operative planning, and haptic feedback systems. While learning-based surrogate models trained on data using the finite element method (FEM) offer a promising path to real-time inference, their reliability depends on well-calibrated constitutive models. Existing approaches neither provide systematic guidance on model selection across stiffness levels, nor generalize across different tissue stiffnesses or geometries. We perform a comprehensive calibration of hyperelastic constitutive models in the SOFA Framework using gravity-loaded silicone beams with different stiffnesses. Using calibrated simulations as training data, we use a softness conditioned equivariant graph neural network, enabling deformation and force prediction across multiple tissue types and unseen geometries. Our model achieves sub-millimeter mean deformation accuracy at 0.010s inference time, while showing that force prediction quality is directly tied to upstream calibration consistency.

Figures & tables

Figure 1: Overview of the proposed pipeline for experimental material calibration, synthetic data generation, and surrogate learning.

Figure 2: Silicone beams at different lengths for the softener ratio $S0.5$ .

Figure 3: Optimization results for the Ogden model for softness $S0.5$ .

Model	Softness	Surface dist $\downarrow$ [mm]	HD95 $\downarrow$ [mm]	Dice $\uparrow$	Vol. diff. $\downarrow$ [%]	Time $\downarrow$ [s]
Arruda- Boyce	$S0$	$1.697$	$4.333$	$0.955$	$0.732$	$125.70$
	$S0.5$	$1.765$	$4.521$	$0.936$	$2.606$	$83.04$
	$S1$	$10.281$	$22.661$	$0.571$	$2.802$	$92.30$
	Average	$4.581$	$10.505$	$0.821$	$2.047$	$100.35$
Mooney- Rivlin	$S0$	$1.706$	$4.352$	$0.953$	$0.731$	$66.09$
	$S0.5$	$1.753$	$4.502$	$0.943$	$2.605$	$42.18$

Table 1: Hyperelastic constitutive model calibration results across three softness levels (

S0

S0.5

S1

), optimized by maximizing volumetric overlap (Dice) between simulated and ground-truth beam deformations. For each softness level, metrics are averaged over the three tested beam lengths (

50\text{\,}\mathrm{mm}

100\text{\,}\mathrm{mm}

, and

150\text{\,}\mathrm{mm}

). Surface distance, 95th percentile Hausdorff distance (HD95), Dice score, volume difference, and simulation time are reported per softness level and as an average.

Figure 4: Examples of generated binary shapes of soft tissues with rigid inclusions.

Model	Softness	$Sim_{max}$ [mm]	$F_{max}$ [N]	$Tip_{mean}$ [mm]	$F_{mean}$ [N]
Mooney- Rivlin	$S0$	$13.92\pm 3.88$	$12.92\pm 5.32$	$7.91\pm 4.82$	$4.80\pm 4.59$
	$S0.5$	$13.78\pm 4.14$	$6.19\pm 2.69$	$7.94\pm 4.89$	$2.33\pm 2.30$
	$S1$	$13.46\pm 4.24$	$3.87\pm 2.43$	$7.82\pm 4.87$	$1.42\pm 1.54$
Ogden	$S0$	$16.32\pm 6.53$	$29.71\pm 25.31$	$9.88\pm 6.54$	$6.94\pm 11.44$
	$S0.5$	$16.40\pm 6.41$	$18.35\pm 18.67$	$9.89\pm 6.54$	$3.94\pm 7.47$
	$S1$	$11.20\pm 4.82$	$2.34\pm 1.98$	$7.04\pm 4.87$	$1.01\pm 1.19$

Table 2: Features of the simulated dataset.

Sim_{max}

and

F_{max}

indicate the average maximum depth and force reached per poke.

Tip_{mean}

and

F_{mean}

indicates the average depth and force in each snapshot.

Dataset	Softness	Force Absolute Error [N]	Mean Euclidean Distance [mm]	Max Euclidean Distance [mm]	Mean Relative Tip Error [%]
Mooney- Rivlin	$S0$	$0.537\pm 1.001$	$0.097\pm 0.152$	$1.205\pm 0.854$	$2.3\pm 2.5$
	$S0.5$	$0.310\pm 0.540$	$0.097\pm 0.155$	$1.228\pm 0.924$	$2.1\pm 2.3$
	$S1$	$0.258\pm 0.650$	$0.092\pm 0.157$	$1.268\pm 0.944$	$2.2\pm 2.6$
	Average	$0.337\pm 0.708$	$0.095\pm 0.155$	$1.239\pm 0.918$	$2.2\pm 2.4$
Ogden	$S0$	$2.269\pm 6.358$	$0.127\pm 0.209$	$1.496\pm 1.084$	$2.5\pm 2.6$
	$S0.5$	$1.407\pm 5.155$	$0.132\pm 0.219$	$1.517\pm 1.104$	$2.4\pm 2.5$

Table 3: GNN prediction results for the different datasets and softness levels.

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Accurate modelling of soft tactile sensors remains difficult because finite element methods (FEM) are computa- tionally expensive, while real-time simulators often lack fidelity for hyperelastic deformation. Large physical datasets are also impractical to collect because repeated testing can damage fragile sensors. We present a data-efficient framework that combines limited real-world validation, high-fidelity FEM, and graph neural networks (GNNs) for accurate real-time prediction of two-dimensional tactile deformation in a planar soft tactile structure. The key idea is to decouple validation from training: 82 camera-tracked contact configurations are used only to tune and validate an ANSYS FEM model, which then generates 768 synthetic contact scenarios for GNN training. We evaluate both forward prediction from marker deformation to contact localisation and inverse inference from contact configuration to marker deformation. The validated FEM achieves sub-0.5 mm error in more than 90% of validation cases, while the learned GNN surrogate reaches a mean absolute error of 0.32 mm with millisecond-scale inference, compared with minute-scale FEM simulation. Models trained entirely on synthetic FEM data retain sub-millimetre accuracy on real measurements from the 2D tactile structure, demonstrating strong sim-to-real transfer within the tested planar setting. We further integrate the learned model into a real-time visualisation pipeline, enabling rapid deformation prediction for virtual prototyping and simulator-based design exploration without extensive physical testing.

Abstract

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