Prostate Phantom: Pneumatic Actuation & Sensing

• The paper presents two designs—active and sensorized phantoms—with pneumatically controlled chambers that either actuate shape changes or measure pressure responses to emulate BPH.
• MRI-derived anatomy combined with FEM inverse control enables precise, controllable deformations, achieving average errors of 3.47% and 1.41% in forward and inverse modeling respectively.
• A compliance-driven sensor placement strategy in the DRE posterior zone improved force observability by 22.5%, offering sparse yet effective instrumentation for clinical training.

Searching arXiv for the specified papers and closely related work on pneumatically actuated or sensorized prostate phantoms. A pneumatically actuated prostate phantom is a synthetic prostate model whose geometry changes through controlled pneumatic loading of internal chambers. In the arXiv literature, the term encompasses at least two closely related but technically distinct device classes: an active multi-chamber phantom in which three independently controlled internal pneumatic cavities produce volumetric and shape change to emulate benign prostatic hyperplasia (BPH) (Tian et al., 21 Aug 2025), and a sensorized prostate phantom in which three internal pneumatic chambers are present but function strictly as intrinsic pressure sensors rather than actuators (Tian et al., 5 Jun 2026). The active architecture is MRI-derived, FEM-modeled, and validated through 3D reconstruction, with average errors of 3.47% in forward modeling and 1.41% in inverse modeling across demonstrations spanning approximately normal to symptomatic BPH volumes (Tian et al., 21 Aug 2025). The sensorized architecture uses the pressure response of sealed chambers, combined with ten surface displacement markers, to optimize force observability in the clinically relevant posterior contact region for Digital Rectal Examination (DRE) training, reporting a 22.5% increase in the mean reconstructability score in the target region relative to a global QR-based placement strategy (Tian et al., 5 Jun 2026). A broader computational context is provided by a fully three-dimensional third-medium contact framework for hyperelastic solids with pneumatic loading, intended for hyperelastic contact, self-contact, and pneumatically actuated systems (Xu et al., 2 Dec 2025).

1. Terminological scope and conceptual distinctions

Within recent work, “pneumatically actuated prostate phantom” refers specifically to a prostate phantom that can change its shape and volume on demand using pneumatic actuation (Tian et al., 21 Aug 2025). The goals stated for this class of phantom are to replicate BPH in both symmetric and asymmetric forms, achieve realistic, anatomically grounded deformation, and provide a platform for validating robotic-assisted procedures and enhancing training (Tian et al., 21 Aug 2025). The defining structural feature is a multi-chamber design: three independently controlled internal pneumatic cavities paired with inverse FEM-based control to hit target volumes and shapes (Tian et al., 21 Aug 2025).

A distinct but related configuration is the pneumatically integrated sensorized prostate phantom used for DRE training, in which the internal chambers are not actuators. In that system, the phantom is not pneumatically actuated; the three internal pneumatic chambers function strictly as intrinsic pressure sensors, and no internal actuation is applied (Tian et al., 5 Jun 2026). External contact induces volumetric deformation of each sealed chamber and corresponding pressure changes, making the chambers a sensing modality complementary to local surface displacement measurements (Tian et al., 5 Jun 2026).

This distinction is technically consequential. In the active phantom, internal chamber pressure is the control input that drives deformation (Tian et al., 21 Aug 2025). In the sensorized phantom, chamber pressure is an output induced by external palpation and interpreted through a compliance model (Tian et al., 5 Jun 2026). A plausible implication is that the same geometric motif—embedded pneumatic chambers—supports two different system roles: actuation for shape generation and sensing for force observability.

2. MRI-derived geometry, chamber architecture, and fabrication

The active prostate phantom is designed from MRI-derived anatomy. Its source imaging pipeline uses the Cross-institution Male Pelvic Structures dataset, comprising 589 cases from seven institutions with labeled segmentations (Tian et al., 21 Aug 2025). A 3D convolutional Variational Autoencoder encodes voxelized prostates at $32 \times 32 \times 32$ resolution into a 64-D latent space using $3 \times 3 \times 3$ convolution filters, batch normalization, and LeakyReLU, with loss

$$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$

and training for 500 epochs with batch size 10 (Tian et al., 21 Aug 2025). A real patient-derived model was selected for the phantom; the VAE-generated “average prostate” of 27.3 ml was aligned to the patient-derived model of 26.3 ml using ICP, yielding mean closest-point distance 1.00 mm and latent-space distance 0.64 (Tian et al., 21 Aug 2025).

The final active geometry contains three internal pneumatic chambers integrated into a single prostate geometry: Chamber 0 at the base for uniform expansion, and Chambers 1 and 2 at left and right for lateral asymmetry (Tian et al., 21 Aug 2025). The chamber layout is explicitly linked to clinical deformation modes: Chamber 0 yields symmetric enlargement, while Chambers 1 and 2 enable asymmetric enlargement (Tian et al., 21 Aug 2025). Latent-space clustering identified primary shape variability along the anteroposterior and proximodistal axes, with larger variability at the base, which motivated the third chamber there (Tian et al., 21 Aug 2025).

Both the active and the sensorized phantom use lost-wax casting to realize embedded internal chambers in silicone (Tian et al., 21 Aug 2025, Tian et al., 5 Jun 2026). The sensorized phantom is molded from Ecoflex 00-10 silicone via a lost-wax process, producing a compliant prostate-shaped phantom appropriate for DRE (Tian et al., 5 Jun 2026). The active phantom uses Smooth-On EcoFlex silicone gel, with nominal Young’s modulus $E \approx 50$ kPa, and its fabricated device includes a visible ring artifact from mold seams that had negligible effect on bulk volume changes (Tian et al., 21 Aug 2025). In the active design, each chamber interfaces with microblower-driven pneumatic tubing and a pressure sensor (Tian et al., 21 Aug 2025).

The sensorized phantom defines the clinically relevant posterior contact region as a circular ROI on the posterior surface, 15 mm radius around the expected DRE contact center (Tian et al., 5 Jun 2026). Three internal chambers, annotated as Chamber 0, 1, and 2, are positioned to sense volumetric changes induced by external palpation, including in the posterior region where DRE contact occurs (Tian et al., 5 Jun 2026). Ten surface displacement markers are added, but placement inside the ROI is forbidden to avoid obstructing the examiner’s finger and to preserve natural contact mechanics (Tian et al., 5 Jun 2026).

3. Pneumatic actuation, sensing physics, and control formulations

In the active phantom, pneumatics were chosen because they deliver smooth volumetric changes, continuous deformation, compact actuation, and MRI compatibility (Tian et al., 21 Aug 2025). Hardware actuation is provided by three Murata microblowers (MZB3004T04), one for each chamber, and pressure sensing uses Freescale MPXV7025G sensors integrated per chamber for closed-loop regulation (Tian et al., 21 Aug 2025). The control stack couples SOFA simulation, including the SoftRobot and SoftRobot Inverse plugins, to Arduino-based hardware; a 3D scanner consisting of a webcam and motorized rig captures shapes for validation (Tian et al., 21 Aug 2025).

Forward tests included chamber pressures up to approximately 26.4 kPa, while inverse-control cases often required low-kPa actuation depending on target volume (Tian et al., 21 Aug 2025). Each chamber is actuated and sensed independently, although physical interactions among chambers can produce unintended pressure and shape variations (Tian et al., 21 Aug 2025). The authors note that direct forward pressure application may create chamber interactions and variations due to the microblowers’ unidirectional nature; inverse optimization mitigates this by distributing pressures across chambers (Tian et al., 21 Aug 2025).

The active inverse control uses SOFA’s SoftRobot Inverse plugin to solve a quadratic program that maps desired volume to required pressure. The volume error is defined as

$\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$

where $S_{\mathrm{free}}$ is the difference between target volume and free volume, $\mathbf{W}_{va}$ is the compliance matrix mapping actuation to volume change, and $\delta a$ represents actuation variables (Tian et al., 21 Aug 2025). The optimization is

$$\lambda^* = \arg\min_{\lambda} \tfrac{1}{2}\,\|\delta\|^2 \quad \text{s.t.}\quad \delta_{\min} \le \delta \le \delta_{\max},\;\lambda \ge 0,$$

which yields chamber pressures that minimize volume error while enforcing bounds (Tian et al., 21 Aug 2025).

In the sensorized phantom, the pneumatic chambers are sealed and serve as intrinsic pressure sensors rather than sources of actuation (Tian et al., 5 Jun 2026). Under the isothermal ideal gas law,

$PV = \text{const},$

a small volume change $3 \times 3 \times 3$0 leads to a measurable pressure change

$3 \times 3 \times 3$1

so chamber pressures provide global, volume-derived signals complementary to local surface displacements (Tian et al., 5 Jun 2026). This calibration model links deformation and force to pressure variation under small deformations (Tian et al., 5 Jun 2026).

A more general continuum-mechanical treatment of pneumatic loading is provided by the three-dimensional third-medium framework for hyperelastic contact and pneumatically actuated systems (Xu et al., 2 Dec 2025). There, pneumatic loading is introduced volumetrically in the third medium through

$3 \times 3 \times 3$2

which yields a hydrostatic Cauchy stress

$3 \times 3 \times 3$3

in the third medium (Xu et al., 2 Dec 2025). Inflation corresponds to negative $3 \times 3 \times 3$4, suction to positive $3 \times 3 \times 3$5, and internal inflation can induce folding and self-contact without explicit contact-interface discretization (Xu et al., 2 Dec 2025). This suggests a direct modeling route for prostate phantoms that combine internal chamber actuation with large deformation or chamber-wall interaction.

4. Finite-element modeling and compliance representations

The active phantom uses FEM both for forward prediction and inverse control. Its mechanical model is a linear elastic co-rotational FEM on a tetrahedral mesh, with quasi-static deformation, gravity included, and fixation constraints applied at tube junctions via penalty springs (Tian et al., 21 Aug 2025). Pressure is applied to internal chamber surfaces, and cavity surface meshes are barycentrically mapped to the 3D tetrahedral mesh to propagate forces bidirectionally (Tian et al., 21 Aug 2025). The constitutive relation is Hooke’s law,

$3 \times 3 \times 3$6

with co-rotation used to improve geometric accuracy under large rotations while retaining linear elastic stress-strain behavior (Tian et al., 21 Aug 2025). Although the nominal silicone modulus is about 50 kPa, the effective $3 \times 3 \times 3$7 in the simplified linear model was manually calibrated to 1.65 MPa to align forward simulation with measurements (Tian et al., 21 Aug 2025).

The governing equilibrium equation for the active model is stated as

$3 \times 3 \times 3$8

where $3 \times 3 \times 3$9 are nodal displacements, $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$0 internal elastic forces, $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$1 fixation forces, $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$2 gravity, and $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$3 pressure or constraint forces via Lagrange multipliers (Tian et al., 21 Aug 2025). Pressure loading on a cavity triangle $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$4 of area $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$5, normal $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$6, and chamber pressure $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$7 is

$$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$8

distributed equally to the triangle’s three nodes (Tian et al., 21 Aug 2025).

The sensorized phantom is modeled through a finite-element compliance dataset generated in SOFA by applying unit external forces in the three Cartesian directions at 1000 surface locations sampled via farthest-point sampling (Tian et al., 5 Jun 2026). At each sampled input, the simulation records both surface node displacements and chamber pressures; no internal actuation is applied, so the response captures passive compliance only (Tian et al., 5 Jun 2026). The full compliance matrix $$\mathcal{L} = \mathrm{BCE}(f, x) + \beta \,\mathrm{KLD}, \qquad \beta = 0.01,$$9 relates incremental inputs and outputs by

$E \approx 50$0

Its rows comprise 3 chamber pressure channels plus 3 displacement components per surface node, for $E \approx 50$1 surface nodes and thus $E \approx 50$2 channels; its columns correspond to unit-force inputs applied at 1000 locations in 3 directions, giving $E \approx 50$3 columns (Tian et al., 5 Jun 2026). To mitigate scale disparities between pressure in Pa and displacement in mm, each modality is normalized so that its maximum sensitivity in $E \approx 50$4 equals 1 (Tian et al., 5 Jun 2026).

From this full matrix, the reduced sensing representation is

$E \approx 50$5

with linear compliance relation

$E \approx 50$6

and modality-separated forms

$E \approx 50$7

$E \approx 50$8

(Tian et al., 5 Jun 2026). The reduced matrix $E \approx 50$9 is formed by indexing $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$0 to the final selected 13 channels, namely 3 pressures and 10 displacement markers (Tian et al., 5 Jun 2026).

The third-medium framework (Xu et al., 2 Dec 2025) provides a complementary FE formalism for cases involving hyperelasticity, self-contact, and pneumatic loading. Its total potential energy includes solid contributions, a third-medium base energy, a regularization term depending on $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$1, and pneumatic energy $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$2 (Xu et al., 2 Dec 2025). The framework is explicitly developed for complex contact interactions in hyperelastic solids and pneumatically actuated systems, and it uses second-order serendipity elements in 3D because the regularization term requires second derivatives of shape functions (Xu et al., 2 Dec 2025).

5. Region-aware sensing and force observability in the posterior DRE zone

The sensorized phantom is organized around the problem of force observability in the clinically relevant posterior contact region (Tian et al., 5 Jun 2026). For a candidate sensor set $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$3, the local sub-compliance at surface node $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$4 is

$\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$5

whose rows are the measurement channels in $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$6 and whose columns are the unit-force responses at node $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$7 in the $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$8, $\delta = S_{\mathrm{free} - \mathbf{W}_{va}\,\delta a,$9, and $S_{\mathrm{free}}$0 directions (Tian et al., 5 Jun 2026). The per-node reconstructability score is the minimum singular value,

$S_{\mathrm{free}}$1

so larger $S_{\mathrm{free}}$2 indicates that forces applied at node $S_{\mathrm{free}}$3 are more observable given the selected sensors (Tian et al., 5 Jun 2026).

The proposed sensor placement strategy is weighted greedy and region-aware. The posterior ROI receives weight $S_{\mathrm{free}}$4, while nodes outside the ROI have $S_{\mathrm{free}}$5 (Tian et al., 5 Jun 2026). Marker placement inside the ROI is forbidden, and a minimum-distance constraint $S_{\mathrm{free}}$6 enforces spatial diversity (Tian et al., 5 Jun 2026). Starting from the three chamber pressure sensors, the method iteratively adds surface markers to maximize the weighted mean reconstructability: $S_{\mathrm{free}}$7 where Cand is the set of unselected surface nodes outside the ROI (Tian et al., 5 Jun 2026). The process continues until $S_{\mathrm{free}}$8 markers are selected, yielding a 13-channel set together with the three pressure sensors (Tian et al., 5 Jun 2026).

For comparison, the study uses a global pivoted-QR strategy adapted from Manohar et al. (Tian et al., 5 Jun 2026). Initialized with the three pressure sensors, it selects the surface node whose compliance rows are most linearly independent of those already chosen, subject to the same distance constraint: $S_{\mathrm{free}}$9 where $\mathbf{W}_{va}$0 is the residual of node $\mathbf{W}_{va}$1’s compliance rows after orthogonal projection against the rows indexed by $\mathbf{W}_{va}$2 at iteration $\mathbf{W}_{va}$3, and $\mathbf{W}_{va}$4 is the Frobenius norm (Tian et al., 5 Jun 2026).

The reported result is a targeted regional gain rather than a uniform global improvement. The mean of $\mathbf{W}_{va}$5 over ROI nodes is 22.5% higher under weighted greedy than under global QR (Tian et al., 5 Jun 2026). The selected 10 markers ring the ROI boundary on the posterior side—pulled toward the ROI by the weighting but excluded from it by the constraint—while remaining markers on the anterior side provide off-ROI coverage (Tian et al., 5 Jun 2026). The paper interprets this as improved force observability in the posterior DRE zone under practical restrictions such as sparse instrumentation and unobstructed contact (Tian et al., 5 Jun 2026).

This sensing result is not itself an actuation result, but it is directly relevant to pneumatically actuated phantom development. The paper notes that, given related work on an active multi-chamber prostate phantom, integrating actuation and closed-loop control with the sensing framework is a natural extension (Tian et al., 5 Jun 2026). A plausible implication is that future active phantoms may combine chamber-wise actuation, chamber-wise pressure sensing, and externally tracked deformation in a unified estimation-control architecture.

6. Validation, performance envelope, and modeled behaviors

The active phantom was validated using a motorized scanner that acquires more than 100 images per state, with Meshroom used for 3D reconstruction and ICP alignment, mean closest-point distances, latent-space distances, and implicit distance heatmaps used for analysis (Tian et al., 21 Aug 2025). Quantitatively, average volume error was 3.47% in forward modeling and 1.41% in inverse modeling (Tian et al., 21 Aug 2025). One example forward case reports $\mathbf{W}_{va}$6 kPa, $\mathbf{W}_{va}$7 kPa, $\mathbf{W}_{va}$8 kPa, with 29.96 ml measured versus 30.00 ml simulated, corresponding to error $\mathbf{W}_{va}$9 ml (Tian et al., 21 Aug 2025).

The active device is intended to span clinically relevant volumetric states. Baseline volumes are reported as normal approximately 26.3 ml and symptomatic BPH $\delta a$0 ml, while demonstrations span approximately 26–45 ml (Tian et al., 21 Aug 2025). For symmetric targets, inverse-control pressures were typically uniform across chambers, for example around 2.73 kPa for higher volumes and around 0.99 kPa near 30 ml (Tian et al., 21 Aug 2025). Lateral chambers create asymmetric bulges, whereas the base chamber yields uniform expansion (Tian et al., 21 Aug 2025).

The system is modeled quasi-statically; microblowers provide fast actuation, but time constants, rise times, and control update rates are not reported (Tian et al., 21 Aug 2025). Repeatability was sufficient to achieve low volume errors, and stability is implied by the inverse solver results (Tian et al., 21 Aug 2025). At higher pressures, however, the physical phantom tends to round more than the simulation predicts, indicating some nonlinearity in material behavior and possible path-dependent effects (Tian et al., 21 Aug 2025).

The third-medium framework provides benchmark evidence for robust simulation of pneumatic loading and contact behaviors that are relevant to soft phantoms (Xu et al., 2 Dec 2025). In a pneumatically actuated cubic box, suction with $\delta a$1 produced inward collapse with self-contact, while pressure with $\delta a$2 produced outward expansion (Xu et al., 2 Dec 2025). In a multi-chamber pneumatic soft robot actuator, chamber pressure $\delta a$3 yielded strong inflation, chamber contact, and large global deformation (Xu et al., 2 Dec 2025). These are not prostate-specific experiments, but they demonstrate the class of nonlinear contact phenomena that may arise in highly compliant, internally pressurized structures.

7. Use cases, limitations, and trajectories of development

The active phantom is positioned as a platform for DRE training, particularly for symmetric and asymmetric enlargement cues, and for testing robotic-assisted biopsy or focal therapy systems where organ deformation matters (Tian et al., 21 Aug 2025). Its anatomy is MRI-derived, its deformation is controllable, and its pneumatic actuation is MRI-compatible (Tian et al., 21 Aug 2025). The phantom can be mounted or suspended for scanning and instrument access, and external tools such as ultrasound probes, needles, or robot tools can approach the organ externally (Tian et al., 21 Aug 2025).

The sensorized phantom is oriented toward DRE training feedback on where and how hard the trainee palpates, with emphasis on the posterior aspect of the prostate via the rectal wall, the zone clinically central for detecting nodules or stiffness changes (Tian et al., 5 Jun 2026). The rationale for prohibiting markers directly in the ROI is to preserve an unobstructed, anatomically realistic finger–tissue interface while reducing occlusion and fabrication complexity (Tian et al., 5 Jun 2026). Its hybrid sensing strategy—global chamber pressures plus targeted surface displacement markers—is presented as a sparse alternative to dense instrumentation that would stiffen the phantom or impede DRE (Tian et al., 5 Jun 2026).

Several limitations are explicit. For the active phantom, the linear elastic model and calibrated effective stiffness $\delta a$4 MPa diverge from the nominal silicone modulus and from real prostate viscoelasticity, contributing to larger errors at large deformation and to physical rounding not captured by the model (Tian et al., 21 Aug 2025). No embedded tactile or force sensing is yet included, no explicit urethral lumen or zonal differentiation is modeled, carcinoma-like stiffness heterogeneity is absent, and chamber interactions can produce non-ideal distributions under forward control (Tian et al., 21 Aug 2025). Future work includes integrating sensors for haptic feedback, exploring variable stiffness to simulate carcinoma, adopting hyperelastic or viscoelastic constitutive models, refining meshing and boundary conditions, adding more chambers, and developing automated imaging feedback for closed-loop shape control (Tian et al., 21 Aug 2025).

For the sensorized phantom, the FE evaluation is based on one anatomy and one ROI definition, namely a single posterior 15 mm radius region, and the constitutive model, boundary conditions, and exact material parameters used in simulation are not detailed (Tian et al., 5 Jun 2026). Hardware validation, noise robustness, and real-world force reconstruction and localization are planned (Tian et al., 5 Jun 2026). Future directions include validation on physical hardware, extension to multi-ROI and moving-ROI scenarios, and evaluation across diverse soft-body geometries (Tian et al., 5 Jun 2026).

The third-medium framework indicates another direction: robust treatment of hyperelastic contact and self-contact in pneumatically actuated systems without explicit contact searches or interface discretization (Xu et al., 2 Dec 2025). The authors explicitly adapt their formulation into a workflow for designing and simulating a pneumatically actuated prostate phantom, including geometry acquisition, third-medium embedding in pneumatic chambers and gap regions, pressure ramping, and calibration of material and third-medium parameters (Xu et al., 2 Dec 2025). This suggests that future prostate phantoms combining internal pneumatic actuation, large strain, external probing, and self-contact may move beyond simplified linear elastic models toward more comprehensive nonlinear formulations.

Taken together, the recent literature delineates three converging lines of development: MRI-derived active multi-chamber phantoms for controllable BPH replication (Tian et al., 21 Aug 2025), sensorized phantoms with compliance-optimized sparse sensing for posterior DRE force observability (Tian et al., 5 Jun 2026), and general hyperelastic pneumatic-contact formulations capable of handling large deformation and self-contact (Xu et al., 2 Dec 2025). Their intersection defines the current technical landscape of the pneumatically actuated prostate phantom as an emerging research platform for DRE training, robotic validation, and soft-robotic medical simulation.