A preliminary comparison of prosthetic socket liner strain determined using digital image correlation and finite element analysis

Mohammadreza Freidouny; Michael L Madigan; Carson Squibb; Masaki Hada; Abbie Bailey; Trevor Johnson; Brian Kaluf; Michael K Philen

doi:10.1371/journal.pone.0353881

. 2026 Jul 14;21(7):e0353881. doi: 10.1371/journal.pone.0353881

A preliminary comparison of prosthetic socket liner strain determined using digital image correlation and finite element analysis

Mohammadreza Freidouny ¹, Michael L Madigan ¹, Carson Squibb ², Masaki Hada ², Abbie Bailey ², Trevor Johnson ³, Brian Kaluf ⁴, Michael K Philen ^2,^*

Editor: Alessandra Aldieri⁵

PMCID: PMC13367698 PMID: 42447121

Abstract

Improving prosthetic socket fit remains an important issue among prosthesis users. Understanding strains at limb-socket interface may help prosthetists improve socket fit. Previous studies have used finite element analysis (FEA) to predict stresses and strains at limb-socket interface. However, the selection of FEA model material properties as well as the validation of FEA strain results remain challenging. Digital image correlation (DIC) is a well-accepted optical technique that is widely used in experimental mechanics to noninvasively measure strains and can be used to validate FEA predictions. The goal of this feasibility study was to demonstrate the use of DIC to measure prosthesis liner strains of a unilateral transtibial prosthesis user and conduct a preliminary comparison of these strains with those estimated from an FEA model. One participant with a transtibial residual limb was recruited. Liner strains of the residual limb during two stepping tasks were measured with DIC. An FEA model of the residual limb was also developed, and its estimates of liner strains were compared with DIC measurements. Results showed that mean and probability distributions of principal strain values measured by DIC were in moderate to good agreement with FEA estimations. For example, DIC measured mean maximum and minimum principal strains of 0.041 and 0.021 in the anterior aspect of the residual limb when it was being vertically loaded, and FEA estimated mean maximum and minimum principal strains of 0.051 and 0.027 in the same region. The Bhattacharyya coefficient (a measure of overlap between two probability distributions, with values approaching 1 indicating high similarity) exceeded 0.90 for principal strain distributions between DIC and FEA on the anterior aspect of the residual limb during both tasks. These findings demonstrate that DIC can be used to refine FEA model material properties and results. As such, this methodology may help to advance the design of prosthetic sockets; however, as this study involved a single participant, findings are preliminary and intended to demonstrate methodological feasibility rather than generalize across the broader population of prosthesis users.

Introduction

Prosthesis users indicate the most important issue with their prosthesis is socket fit [1]. Poor socket fit can result from high stresses and strains at the limb-socket interface [2,3]. The challenge of measuring these stresses and strains has limited our understanding of factors associated with socket fit [4]. With this in mind, in-vivo methods that involve discrete transducers and sensors have been used to measure stresses at the limb-socket interface [5–9]. However, these methods have several technical challenges such as being expensive, bulky, non-linear, temperature sensitive, and having limited spatial resolution [4,8].

Finite element analysis (FEA) is a powerful tool for predicting stresses and strains [10]. Dickinson et al. [11] identified up to 45 studies from 2000 to 2016 that developed FEA models of lower residual limbs to estimate stresses and strains at the limb-socket interface or within the soft tissues. However, the challenge of experimentally measuring these stresses and strains has made the important step of validating FEA results difficult [12]. As a result, FEA model predictions of stresses and strains on the residual limb of lower limb amputees vary across different studies. For example, Lee and Ming [13] estimated peak normal stress of 230 kPa at the patellar tendon region of a transtibial residual limb during single-leg standing while Plesec and Harih [14] estimated peak normal stress of 106 kPa at the same region during the same task when using a higher body weight. Furthermore, FEA predictions of interface stresses have shown average errors of up to 12 kPa from experimental measurements [15,16], while skin shear stresses ranging from 4 to 23 kPa under cyclic loadings have been associated with skin damage risk [17], underscoring the importance of accurate FEA predictions for safe socket design. The use of experimental methods to directly measure stresses and strains with high spatial resolution and accuracy would enable the validation of FEA predictions.

Digital image correlation (DIC) is a well-accepted optical technique that is widely used in experimental mechanics to measure full-field surface displacements and strains [18,19]. DIC involves applying a speckled pattern on the surface of interest, capturing changes in this pattern over time using high-resolution digital cameras as loads are applied, and processing these changes in pattern using computational algorithms to determine strains. DIC has the potential to validate and improve FEA models of prosthetic sockets and residual limbs, yet only a limited number of studies have attempted to use it in prosthesis-related applications. For example, Moerman et al. [20] used DIC to estimate the mechanical properties of a silicone-gel material during indentation tests, representing human soft tissue, and then used these data to improve the corresponding FEA predictions. Saey et al. [21] used DIC to measure strain on the outer surface of a transtibial prosthetic socket under cyclic load simulating gait, with the goal of assessing socket mechanical properties in the design process. Solav et al. [22] used DIC to measure skin strain on a bare transtibial residual limb, without donning a liner or socket, during controlled seated tasks including knee flexion/extension and other muscle contractions. We are not aware of any studies that attempted to measure skin strain while an individual used their prosthesis during a load-bearing activity such as standing or walking.

The goals of this single-participant, feasibility study were to first demonstrate the use of DIC to measure the prosthesis liner strain of a unilateral transtibial prosthesis user during two stepping tasks, and then to conduct a preliminary comparison of these strains with those predicted from an FEA model. The results of this study will help establish a DIC methodology for studying lower limb prostheses that can inform the selection of FEA model material properties as well as validating FEA results. Thus, DIC has the potential to improve FEA models as well as the understanding of factors associated with prosthetic socket fit and comfort.

Methods

Human subject testing

One male participant (46 years old, 86 kg body mass) with a unilateral transtibial amputation as a result of trauma seven years prior was recruited. The participant was selected based on: a) having a below knee amputation at least one year prior; b) having a well-fitting prosthesis that was used daily; and c) schedule availability. The participant was recruited on December 1, 2023, and data collection was completed on the same day. The participant provided written informed consent prior to participation, and the study was approved by Virginia Tech Institutional Review Board (IRB 21–764).

Upon arrival, the participant removed his personal prosthesis and sat in a chair for 20 minutes to allow his residual limb volume to equilibrate. During this time, a custom-fabricated total surface bearing clear diagnostic socket was attached to his personal daily-use pylon and prosthetic foot by a certified prosthetist. Approximate lengths of the tibia and fibula were also palpated and obtained using a tape measure for later use with the FEA model. After 20 minutes, the bare residual limb was scanned using a Peel 3D scanner (Creaform, Lévis, Canada). The participant then donned a liner (6Y512 Uneo, Otto Bock, Duderstadt, Germany) and the diagnostic socket (Fig 1) and walked for approximately three minutes to acclimate to the socket. Prior to the experimental session, the exterior of the liner had been speckled using a 3D-printed stamp with 1.5 mm diameter speckles that were pseudo-randomly distributed spatially. The speckles were created using a fabric dye mixed with paint thickener.

The participant then completed two stepping tasks for analysis including a vertical loading task and a half-step loading task. During the vertical loading task, the participant initially stood on his unaffected leg with his prosthetic foot hovering just above a forceplate (FP4550−08, Bertec Corp., Columbus, OH, USA). When indicated by the researcher, the participant slowly lowered his prosthetic foot onto the forceplate, gradually applied more of his body weight onto his prosthetic foot until his full body weight was supported, then reversed the loading until the prosthetic foot was off the forceplate. The goal of this task was to apply primarily vertical loading to the prosthetic foot (Fig 2) with minimal transverse loading or changes in foot position and kinematics. During the half-step task, the participant stood in a tandem stance with the unaffected foot in front of the prosthetic foot and within a single-step distance from the forceplate. When indicated by the researcher, the participant initiated a step onto the forceplate by his prosthetic foot, similar to heel contact during gait, and gradually shifted full-body weight onto the prosthetic foot (Fig 3), then slowly pushed off to move backward and return to the starting position. The goal of this task was to apply both vertical and anteroposterior loading to the foot (Fig 2), but in a more controlled manner than normal gait. Because only two DIC cameras were available (see details below), two trials of each task were completed with both cameras used to capture video on the anterior aspect of the limb during the first trials and both cameras used to capture video on the lateral aspect of the limb during the second trials. This approach could introduce potential inconsistencies between trials due to possible changes in loading conditions or prosthetic foot positioning. To minimize inconsistencies between trials, participants were provided with verbal instructions and visual markers on the forceplate. Moreover, future studies should investigate intra-trial variability of strain measurements.

Fig 2 — The vertical dashed line indicates the time point at which the strain data was compared between DIC and FEA. A negative value in the anteroposterior force indicates the ground reaction force was directed posteriorly.

Digital image correlation

Two DIC cameras (Imager M-lite 5M, LaVision, Göttingen, Germany), each equipped with a lens (Color Skopar 28 mm f/2.8, Voigtländer, Braunschweig, Germany) to provide appropriate focal distance and field of view, were mounted at an approximate height of 20 cm above the forceplate and at a distance of 160 cm from the forceplate. The cameras had a focal length of 29 mm and a pixel size of 0.00345 mm. Camera calibration was performed using a pinhole fit model with a fit error of 0.0538 pixels. One pair of light projectors was used as the only light in the room and were adjusted in their position and orientation to minimize light reflection on the socket surface. Liner surface strains were calculated from the DIC recordings using DaVis 10 software (LaVision, Göttingen, Germany) with a subset size of 49 pixels and a step size of 16 pixels. DIC image processing included intensity normalization to have a uniform image contrast and a moving average filter with a length of 5 pixels to reduce noise. The height of the measurable strain region was approximately 7 cm and just distal to the fibular head (Fig 4). This height was limited due to the distal fiberglass wrap applied to maintain structural integrity and the proximal sealing sleeve used to maintain suspension of the prosthesis. The width of the measurable strain region in the circumferential direction was approximately 8 cm and limited due to our use of only two DIC cameras.

Finite element analysis

The point cloud data of the residual limb from Peel 3D scanner was imported into MeshLab [23], and the three-dimensional geometry of the limb was generated. The three-dimensional geometry of the prosthetic socket was provided to the investigators by the socket fabricator as a computer file. The liner was modeled as a 5.5 mm-thickness shell added to the outer surface of the residual limb. The use of computed tomography or magnetic resonance imaging to obtain tibia and fibula bone geometry was not feasible for this study. Alternatively, we incorporated bone structures from an open-access model [24] and modified their size and position to align with our initial tape measurements. All 3D geometries were then assembled, and a nonlinear quasi-static FEA model of the residual limb with liner and prosthetic socket (Fig 5) was generated with ABAQUS (Dassault Systèmes, RI, USA) to determine the maximum and minimum principal strains on the liner surface at two time points of interest (Fig 3), for comparison with the strains determined from DIC.

Soft tissues, including the skin, muscles, ligaments, fat, and tendons, were all modeled as linear elastic (Table 1). Three values of Young’s modulus (0.1, 0.2, and 0.3 MPa) with a Poisson’s ratio of 0.49 used by previous studies [11,25] were evaluated for all soft tissues to identify the best match with DIC measurements. A Young’s modulus of 0.3 MPa provided the closest liner strain match with DIC measurements and was selected for the final model. The bones, liner, and socket were also modeled as linear elastic materials as in prior studies (Table 1). A frictionless surface-to-surface contact was applied at the liner-socket interface. Liner-skin and bone-soft tissue interactions were defined to be tied. Using the available element libraries in ABAQUS, a free meshing technique using four-node tetrahedral elements (C3D4) was implemented for the soft tissue. The liner was meshed with four-node shell elements (S4). The socket and bones were meshed with 3-node shell (S3) and four-node tetrahedral (C3D4) elements, respectively.

Table 1. Material properties and elements used for modelling FEA components.

FEA Model Component	Material Properties	Elements
FEA Model Component	E (MPa), ν	Elements
Soft tissue	0.3, 0.49	C3D4
Liner	0.17, 0.49 [26]	S4
Bones	3000, 0.30 [27]	C3D4
Socket	2100, 0.33 [28]	S3

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After manually positioning the socket and residual limb to be longitudinally aligned and have minimal overlap, ABAQUS solver adjusted the shape of the residual limb and liner to eliminate any initial overlap with the socket surface. Once the overlap was removed, a vertical displacement boundary condition was applied to the socket to fully don the residual limb within the socket (Fig 6). After the donning process, vertical and anteroposterior forces and the resultant sagittal plane moment over time, calculated from ground reaction forces, were applied to a reference node at the tibia head. To simplify the loading conditions, moments in the frontal and transverse planes were neglected [29,30] and the location of the center of pressure of the ground reaction forces was assumed to be aligned with the tibial axis. Knee angle was determined using sagittal plane captured videos during both tasks.

Fig 6 — The sequence shows (from left to right): initial assembly of the residual limb and socket before FEA solving, adjusted alignment to eliminate overlap, and final placement of the residual limb within the socket.

DIC and FEA comparison

Due to differences in spatial resolution and mesh discretization, point-wise comparison of DIC and FEA strain fields was not feasible. Gomez et al. [31] faced a similar challenge when comparing FEA strain fields with medical image measurements; they addressed this by comparing strain histograms rather than point-wise values. To compare our DIC measurements with FEA model results, we compared strain mean, standard deviation (SD), and strain distributions within the measurable strain region. To compare strain distributions, probability distribution histograms of DIC and FEA strains were generated and compared using the Bhattacharyya coefficient (BC), a measure of the overlap between two probability distributions, where a value of 1 indicates complete overlap and 0 indicates no overlap [32].

Results

Maximum and minimum principal strains during the vertical loading task were compared between DIC (Fig 7) and FEA (Fig 8). Maximum and minimum principal strains represent tension and compression on the liner surface, respectively. At the time point of interest, the vertical ground reaction force was 0.96 times body weight and the anteroposterior ground reaction force was 0.06 times body weight (directed posteriorly). Within the anterior aspect of the measurable strain region, mean (SD) maximum principal strain was 0.041 (0.018) and 0.051 (0.030) for DIC and FEA, respectively, and mean (SD) minimum principal strain was 0.021 (0.016) and 0.027 (0.022) for DIC and FEA, respectively. The BC was 0.91 and 0.94 for maximum and minimum principal strain, respectively, indicating excellent DIC-FEA agreement (Fig 9). Within the lateral aspect of the measurable strain region, mean (SD) maximum principal strain was 0.030 (0.020) and 0.061 (0.041) for DIC and FEA, respectively, and mean (SD) minimum principal strain was 0.010 (0.016) and 0.045 (0.039) for DIC and FEA, respectively. The BC was 0.81 and 0.73 for maximum and minimum principal strain, respectively, indicating moderate to good DIC-FEA agreement, lower than that observed in the anterior aspect (Fig 9).

Maximum and minimum principal strains during the half-step loading task were compared between DIC (Fig 10) and FEA (Fig 11). At the time point of interest, the vertical ground reaction force was 0.92 times body weight, the anteroposterior ground reaction force was 0.15 times body weight (directed posteriorly), and the knee was fully extended. Within the anterior aspect of the measurable strain region, mean (SD) maximum principal strain was 0.013 (0.013) and 0.017 (0.015) for DIC and FEA, respectively, and mean (SD) minimum principal strain was 0.009 (0.010) and 0.018 (0.010) for DIC and FEA, respectively. The BC was 0.96 and 0.83 for maximum and minimum principal strain, respectively, indicating good to excellent DIC-FEA agreement (Fig 12). Within the lateral aspect of the measurable strain region, mean (SD) maximum principal strain was 0.009 (0.012) and 0.028 (0.016) for DIC and FEA, respectively, and mean (SD) minimum principal strain was 0.007 (0.004) and 0.044 (0.037) for DIC and FEA, respectively. The BC was 0.71 and 0.46 for maximum and minimum principal strain, respectively, indicating poor to moderate DIC-FEA agreement, lower than that observed in the anterior aspect (Fig 12).

Discussion

The goals of this single-participant, feasibility study were to demonstrate the use of DIC to measure prosthesis liner strains of a unilateral transtibial prosthesis user during two stepping tasks and conduct a preliminary comparison of these strains with those predicted from an FEA model. This is the first study that we are aware of that attempted to evaluate strains on a residual limb within a prosthetic socket during ecologically valid loading conditions. DIC-based measurements of liner strain were on the order of 0.0–0.1 when the limb was exposed to ground reaction forces near body weight during two stepping tasks. Strains were also shown to be sensitive to loading conditions between the two tasks and likely to the bony anatomy, as discussed below. A challenge with developing FEA models of a human limb for prosthesis-related applications is determining the mechanical properties of the tissues. Indeed, this has resulted in researchers using a range of values [11,25]. As shown here, the direct measurement of strains using DIC can assist with this process and can provide a level of face validity not typically achieved by FEA alone.

While we are not aware of any studies reporting DIC liner strain data obtained under similar conditions for comparison, Solav et al. [22] used DIC to determine skin strains of the residual limb of an individual with a unilateral transtibial amputation. While sitting with the residual limb bare and unsupported, peak strains were ~0.45 in compression and ~0.1 in tension during knee flexion and extension. While this task differs significantly from that investigated here, the order of magnitude of these strains is the same as the liner strains measured here. Differences of strain magnitude measured by Solav et al. [22] and our study could stem from several factors including the different measurement surfaces (bare skin vs. liner exterior), constraining effects of the socket, different loading conditions, and participant differences considering that both studies included only a single participant. Previous FEA studies of transtibial residual limbs have mainly reported internal soft tissue strains which differ based on loading tasks and modelling assumptions. For example, Portnoy et al. [33] reported peak compressive strains of ~0.85 and shear strains of ~1.06 in the internal soft tissues at the distal tibia during a single-leg quiet standing task. However, Mbithi et al. [29] reported peak compressive strains of ~0.41–0.81 and shear strains of ~0.06–0.15 in the same region during walking. Compressive strains in the internal soft tissue at distal tibia have also been shown to depend on modelling parameters, especially soft tissue stiffness, and could vary from ~0.2 to ~0.8 [34]. Such variabilities in strain values underscore the importance of experimental measurements for validating model predictions.

DIC showed higher localized maximum principal liner strains on the anterior aspect of the limb that may be associated with the tibial tuberosity and on the lateral aspect of the limb that may be associated with the fibular head. This may indicate higher contact pressure and shear stresses on the skin at these regions. Previous FEA studies have shown that peak pressure, contact pressure, and shear stress on the residual limb skin were observed at proximal tibia [14,30,35]. The direct measurement of liner strains using DIC provides a level of face validity not achieved by FEA alone.

A significant difference in liner strain pattern was identified between the two tasks. Compared to the vertical loading task (top left in Figs 7 and 8), both DIC (top left in Fig 10) and FEA (top left in Fig 11) showed liner strains on the anterior aspect of the tibia to be lower proximally and higher distally during the half-step task. This may be attributed to the anteroposterior component of the ground reaction force during the half-step task that would tend to rotate the prosthesis/socket relative to the residual limb. That both DIC and FEA exhibited these differences provides additional face validity and agreement of these two methods.

FEA liner strain fields (Figs 8 and 11) exhibited better general agreement with DIC (Figs 7 and 10) in maximum principal strain compared to minimum principal strain. This may be related to modelling soft tissues as linear elastic rather than hyperelastic. Hyperelastic models can better reproduce the compressive behavior of soft tissues [36]. Hyperelastic models were initially evaluated in our FEA model, but they either caused convergence instability in the solver, a limitation also reported by Cagle et al. [37] in their comparable transtibial FEA model, or caused larger disagreement with DIC measurements as compared to the linear elastic properties. FEA also showed better agreement with DIC in the anterior aspect compared to the lateral aspect of the residual limb. The lateral discrepancy was more pronounced during the half-step loading task, likely due to the omission of frontal and transverse plane moments in the FEA model; these moments are present during this task and could influence lateral strain distribution.

This study had multiple limitations and opportunities for improvement that are worth noting. Despite these, we believe the preliminary work reported here will be beneficial to the research community and contribute to future efforts with similar goals. First, this study was conducted on a single participant, which limits the generalizability of the findings. The results should be interpreted as preliminary and indicative of feasibility. Second, we acknowledge that our methodology first selected FEA model soft tissue material properties that minimized the differences in strains between DIC and FEA and then compared these same strains to assess the face validity of FEA predictions, which is best interpreted as a calibration rather than an independent validation. However, disassociating material property selection from FEA model assessment may provide a more rigorous validation process. Third, the soft tissue mechanical properties used within the FEA model were determined using a crude trial-and-error process and likely would benefit from a more rigorous mathematical [20] or sophisticated optimization process that was beyond the scope of this preliminary study. Fourth, the region over which DIC was able to determine strain was limited in size, representing approximately 10% of the total liner surface area. The boundaries of our DIC region were limited distally by the wrapping used to maintain the structural integrity of the socket-pylon connection, proximally by a sealing sleeve needed for prosthesis suspension, and circumferentially by only having access to two DIC cameras. FEA strain results were extracted exclusively from the region corresponding to the DIC field of view rather than from the full liner surface. Additionally, the inability to precisely locate the DIC region on the FEA model introduces uncertainty in region correspondence between the two methods. DIC-FEA comparisons and claims of agreement were therefore limited to the measured region, and regions of high strain outside of the measured region may have been missed. Future studies with a larger DIC region and more precise spatial registration between DIC and FEA will facilitate comparisons. Fifth, bone anatomy in the FEA model was based on a standardized open-access model and tape measurements on the residual limb. This may have resulted in discrepancies in bony anatomy geometry and liner strain differences between DIC and FEA. Sixth, the application of optical-based DIC limited our analysis to the liner and not the skin or other tissues of the limb that are accessible using FEA and likely more closely related to socket comfort. Seventh, the diagnostic socket used here was a total surface bearing socket that has material properties different from those of commercial sockets. Results may therefore differ with sockets using a different fitting strategy or with commercial sockets. Eighth, frontal and transverse plane moments were neglected, and the external loading applied to the limb was determined assuming static equilibrium. Inertial effects were also neglected, which is justified by the quasi-static nature of the tasks. Additionally, the center of pressure was assumed to be aligned with the tibial axis. Neglecting frontal and transverse plane moments may introduce bias in lateral strain estimates, while the assumed center of pressure alignment may introduce asymmetric bias in anterior–posterior strain distributions across the liner surface. Future work incorporating full six-degree-of-freedom loading would enable simulation of more ecologically valid conditions. Ninth, to minimize friction between the paint used to apply the speckled pattern on the liner and the interior of the socket, a water-based lubricant was applied to the interior of the socket prior to donning. This lubricant is not typically used by prosthesis users in practice and caused a frictionless liner-socket contact. Tenth, real prosthetic liners vary locally in thickness and stiffness; however, for simplicity, the liner was modeled as a uniform shell with constant thickness and stiffness. Eleventh, glare from our light sources reflecting off the clear diagnostic liner was a challenge which we attempted to minimize by using soft light sources and proper positioning of these relative to the testing area, but could not be entirely eliminated due to the movements of the socket during testing. Lastly, glare issues were more manageable under controlled, quasi-static loading conditions rather than dynamic gait. Therefore, as a preliminary study, simple controlled tasks were intentionally selected before progressing towards more ecologically valid loading conditions in the future.

In conclusion, this is the first study that we are aware of that attempted to evaluate strains on a residual limb within a prosthetic socket under somewhat realistic gait loading conditions. Maximum and minimum principal strains showed generally comparable distributions between DIC and FEA, especially in the anterior aspect of the residual limb. Although these preliminary results were only for a single participant, they support future investigation of DIC for informing the development of FEA models for prosthetic applications.

Supporting information

S1 Table. FEA strain results for tested Young’s modulus values.

(PDF)

pone.0353881.s001.pdf^{(115.2KB, pdf)}

S2 File. Mesh convergence analysis.

(PDF)

pone.0353881.s002.pdf^{(89.4KB, pdf)}

Acknowledgments

The authors acknowledge computational resources and technical support provided by Advanced Research Computing at Virginia Tech.

Data Availability

All relevant data have been stored in Virginia Tech research repository: https://doi.org/10.7294/32337195.

Funding Statement

This study was supported by the U.S. Army Medical Research and Development Command under award number W81XWH-21-1-0220. There was no additional external funding received for this study. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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PLoS One. doi: 10.1371/journal.pone.0353881.r001

Decision Letter 0

Alessandra Aldieri

22 Apr 2026

-->PONE-D-26-07309-->-->A Preliminary Comparison of Prosthetic Socket Liner Strain Determined Using Digital Image Correlation and Finite Element Analysis-->-->PLOS One

Dear Dr. Philen,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

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Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: Partly

**********

-->2. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: No

**********

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The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Key Strengths

First known attempt to measure liner strain in vivo under realistic loading conditions.

Strong methodological transparency in DIC setup, socket design, and FEA workflow.

Good numerical agreement between DIC and FEA strain patterns, supporting the feasibility of this validation approach.

Major Concerns

•Single participant, limiting generalizability.

•Simplified soft‑tissue modelling (linear elastic instead of hyperelastic).

•Limited DIC field-of-view, restricting strain measurement to a small region.

•Anatomical approximations due to generic bone models and tape‑based scaling.

•Artificial experimental conditions, including lubricant use and glare from the transparent socket.

•Simplified loading conditions with several neglected moments and assumptions.

Required Revisions

•Provide quantitative error metrics between DIC and FEA.

•Justify participant selection and modelling assumptions.

•Expand discussion of optical and mechanical limitations affecting DIC accuracy.

•Clarify why hyperelastic models failed, and better explain strain discrepancies.

•Temper conclusions to reflect the preliminary, single‑subject nature of the study.

Suggested improvement

Lines 19–37

•Comment: The abstract is clear and well structured, but it should acknowledge the single participant design explicitly, as this strongly limits generalizability.

•Suggestion: Add 1–2 sentences describing key limitations upfront to set realistic expectations.

Lines 40–81

•Lines 49–58: You highlight variability in FEA stress predictions due to a lack of validation. This is an excellent justification. However, more explanation of typical error magnitudes or clinical relevance thresholds would strengthen the rationale.

•Line 60: DIC is presented as widely accepted; consider citing more prosthetics-specific DIC applications to position the study within the field.

•Lines 74–81: The two research goals are clearly stated. However, consider emphasising that this is an exploratory single-subject feasibility study, not a validation study.

Lines 85–122

•Lines 85–89: Single participant; demographic justification is absent. Authors should state why this individual was chosen (e.g., typical limb geometry, availability).

•Line 100: Speckle pattern creation using fabric dye and thickener requires justification—does this alter liner compliance or friction properties?

Lines 105–122

•Lines 105–118: The two tasks (vertical loading, half step) are simple and controlled. However, they do not reflect everyday gait dynamics. Authors should justify why a more realistic gait was excluded.

•Lines 118–122: Because only two DIC cameras were available, separate trials were required for anterior and lateral views. This creates potential alignment inconsistencies between datasets and should be acknowledged earlier.

Lines 132–145

•Lines 137–140: More detail is needed on the DIC reconstruction error, stereocalibration accuracy, and noise filtering.

•Lines 140–145: The strain measurement region was extremely limited. This methodological constraint strongly weakens the validity of comparing full field FEA results with partial-field DIC data.

Lines 150–190

•Lines 155–157: Bone anatomy derived from an open-source model and scaled using tape measurements introduces significant geometric uncertainty. Consider quantifying potential anatomical mismatch.

•Lines 166–170: Soft tissues modelled as linear elastic contradict well-established nonlinear, viscoelastic behaviour. A more rigorous rationale is needed.

•Lines 183–190: The loading simplifications (no frontal/transverse plane moments, assumed COP alignment, no inertial effects) reduce ecological validity. Authors should evaluate how these simplifications might bias results.

Lines 199–234

•Lines 200–212: The agreement between DIC and FEA strains is well presented. However, statistical error metrics (e.g., RMSE, correlation, Bland–Altman plots) are missing.

•Lines 211–218: For the half-step task, a substantial discrepancy appears in the lateral minimum and maximum strains. Authors should explain this more clearly rather than briefly noting it.

•Figures: Clear, but inconsistent colour scaling between DIC and FEA maps makes direct visual comparison difficult.

Lines 235–286

•Lines 248–263: The authors compare their strain results to prior DIC studies. Suggest adding discussion on why magnitude differences occur (e.g., liner vs skin measurements).

•Lines 273–278: The explanation of task sensitivity is insightful; however, the discussion should address how the simplified load case compares to actual gait loading.

•Lines 282–285: The authors acknowledge the limitation of linear tissue modelling, but the dismissal of hyperelastic models requires more detail—what specific instabilities occurred?

Lines 288–316

1.Repeatability: No intra-trial variability analysis or repeated measures.

2.Liner nonuniformity: Real prosthetic liners vary locally in thickness and stiffness, unlike the modelled uniform shell.

3.Effect of lubricant and clear socket: The test conditions differ materially from real-world prosthesis use.

4.Region mismatch: The limited DIC area may not correspond perfectly to the FEA region assessed.

Lines 319–324

•Strong concluding summary; however, avoid overgeneralizing given the single participant nature.

•Suggest softening claims about “good agreement,” emphasising that findings are preliminary.

Reviewer #2: Review Comments to the Author:

The manuscript presents a preliminary comparison of prosthetic liner strains measured using digital image correlation (DIC) and predicted using finite element analysis (FEA) in a unilateral transtibial prosthesis user. The study addresses an important and longstanding challenge in prosthetic biomechanics: experimental validation of FEA models used to estimate interface mechanics. The integration of DIC with subject-specific FEA modeling under load-bearing conditions is novel and technically interesting.

Overall, the study demonstrates methodological feasibility and is clearly written. However, several issues related to validation rigor, experimental design, and interpretation must be addressed before the conclusions can be considered adequately supported.

Major Comments:

1. Calibration vs. Validation

The manuscript states that three values of Young’s modulus were evaluated and that 0.3 MPa was selected because it provided the closest match to DIC measurements. However, this approach constitutes calibration rather than independent validation. After tuning material properties to match DIC, the manuscript then concludes that FEA and DIC exhibit “good agreement.”

To strengthen the scientific rigor:

• Clearly distinguish between model calibration and model validation.

• Provide quantitative error metrics (e.g., RMSE, mean absolute error, percent difference, spatial correlation).

• Present strain comparisons for all tested material properties to show how sensitive agreement is to stiffness selection.

• Avoid language implying independent validation unless supported by independent data.

2. Sample Size and Generalizability

The study includes only one participant. While acceptable for a feasibility study, this limits the strength of conclusions. Anatomical variability, tissue properties, and socket fit vary substantially across individuals.

The manuscript should:

• Explicitly frame the study as a single-subject feasibility or proof-of-concept study.

• Avoid generalizable claims regarding prosthetic socket design.

• Clearly acknowledge that findings may be subject-specific.

3. Quantitative Assessment of Agreement

Agreement between DIC and FEA is described largely qualitatively (“good agreement”) and supported by selected peak strain values. However:

• No mesh convergence study is reported for FEA.

• No statistical or spatial comparison metrics are included.

I strongly recommend adding:

• Quantitative comparison metrics.

• A spatial difference map between DIC and FEA strain fields.

• Mesh refinement justification.

4. Modeling Assumptions and Sensitivity

The FEA model includes several simplifying assumptions:

• Linear elastic soft tissues

• Frictionless liner–socket interface

• Simplified loading (sagittal plane only)

• Assumed center-of-pressure alignment

• Non-subject-specific bone geometry

These assumptions may substantially influence strain distribution. While limitations are acknowledged, the manuscript would benefit from:

• A brief sensitivity analysis (e.g., effect of friction coefficient or stiffness variation on strain magnitude).

• Clarification of how loads were applied (to bone nodes, rigid body, distributed load).

• Discussion of how assumptions may bias agreement with DIC.

5. Limited DIC Measurement Region

The measurable strain region is approximately 7 cm in height and 8 cm circumferentially. This represents a limited portion of the liner surface.

The manuscript should:

• Clarify what percentage of total liner surface was analyzed.

• Discuss whether high-strain regions outside this window may have been missed.

• Ensure that claims of agreement are limited to the measured region.

Minor Comments:

• Provide additional DIC processing details (subset size, step size, smoothing, calibration error).

• Ensure identical color scales are used when comparing DIC and FEA strain maps.

• Soften statements such as “validate FEA model results” to reflect the preliminary nature of the study.

• Consider depositing raw DIC data and model inputs in a public repository to align with PLOS data transparency standards.

Reviewer #3: The present study demonstrates the use of DIC to measure prosthesis liner strains of a unilateral transtibial prosthesis user and conducts a preliminary comparison of these strains with those predicted from an FEA model.

The use of DIC has certain challenges as compared to the other experimental techniques, such as:

1. Unstable Speckle Pattern-Sweat or skin stretching alters the speckle pattern, Prosthetic socket friction can erase or distort the pattern, Long walking trials degrade pattern quality. It will be useful mentioning how a Stable Speckle pattern was assured for this study.

2. Secondly Walking involves Dynamic Motion and leads to Motion blurring if cameras are not high speed. Also, Synchronization errors between cameras and gait cycle phases. How are these Issues addressed?

3. Another major drawback of using DIC is that for minor changes in prostheses alignment cause large changes in stress distribution, which makes DIC results difficult to generalize. How is the alignment issue handled in the present study?

4. For a prostheses user, there is a movement of skin moves relative to the underlying bone and muscle known as soft tissue artifact. This phenomenon is known as soft tissue artifact. How present technique addresses this issue and what is the error percentage for the same.

Also, there are some studies done in past that uses DIC for Prostheses Socket Pressure Measurement. Refer to the following study -Evaluation of the influence of cyclic loading on a laser sintered transtibial prosthetic socket using Digital Image Correlation (DIC) by Saey et al. Annu Int Conf IEEE Eng Med Biol Soc, 2019

**********

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Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.-->

Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes: Amit Kumar Singh

**********

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PLoS One. 2026 Jul 14;21(7):e0353881. doi: 10.1371/journal.pone.0353881.r002

Author response to Decision Letter 1

28 May 2026

We would like to thank the editor and reviewers for their thoughtful review and constructive comments on our manuscript. We believe that the process of addressing these comments has improved the quality of our manuscript. Our point-by-point responses are indicated by >>>. Changes in the manuscript have been highlighted as requested by the journal.

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

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https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf.

>>> Thank you for sharing these guidelines. We updated our manuscript to adhere to the PLOS ONE style requirements.

2. Please note that PLOS One has specific guidelines on code sharing for submissions in which author-generated code underpins the findings in the manuscript. In these cases, we expect all author-generated code to be made available without restrictions upon publication of the work. Please review our guidelines at https://journals.plos.org/plosone/s/materials-andsoftware-sharing#loc-sharing-code and ensure that your code is shared in a way that follows best practice and facilitates reproducibility and reuse.

>>> Our model input file and data points have been stored in Virginia Tech research repository:

https://doi.org/10.7294/32337195

3. Thank you for stating in your Funding Statement:

“This study was supported by the U.S. Army Medical Research and Development Command under award number: W81XWH-21-1-0220. “

>>> We updated our cover letter.

4. Thank you for stating the following financial disclosure: “This study was supported by the U.S. Army Medical Research and Development Command under award number: W81XWH-21-1-0220. “ Please state what role the funders took in the study. If the funders had no role, please state: "The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript." If this statement is not correct you must amend it as needed. Please include this amended Role of Funder statement in your cover letter; we will change the online submission form on your behalf.

>>> We updated our cover letter.

5. We note that your Data Availability Statement is currently as follows: [All relevant data are within the manuscript.] Please confirm at this time whether or not your submission contains all raw data required to replicate the results of your study. Authors must share the “minimal data set” for their submission. PLOS defines the minimal data set to consist of the data required to replicate all study findings reported in the article, as well as related metadata and methods (https://journals.plos.org/plosone/s/data-availability#loc-minimal-data-set-definition). For example, authors should submit the following data: - The values behind the means, standard deviations and other measures reported; - The values used to build graphs; - The points extracted from images for analysis. Authors do not need to submit their entire data set if only a portion of the data was used in the reported study. If your submission does not contain these data, please either upload them as Supporting Information files or deposit them to a stable, public repository and provide us with the relevant URLs, DOIs, or accession numbers. For a list of recommended repositories, please see https://journals.plos.org/plosone/s/recommended-repositories. If there are ethical or legal restrictions on sharing a de-identified data set, please explain them in detail (e.g., data contain potentially sensitive information, data are owned by a third-party organization, etc.) and who has imposed them (e.g., an ethics committee). Please also provide contact information for a data access committee, ethics committee, or other institutional body to which data requests may be sent. If data are owned by a third party, please indicate how others may request data access.

>>> Our model input file and data points have been stored in Virginia Tech research repository:

https://doi.org/10.7294/32337195

Review Comments to the Author:

Reviewer #1: The manuscript presents a novel and valuable study that compares digital image correlation (DIC) and finite element analysis (FEA) for measuring strain in prosthetic liners. The work is well motivated, methodologically detailed, and demonstrates promising agreement between experimental and computational strain estimates. However, the reviewer identifies several important limitations requiring major revision. Key Strengths First known attempt to measure liner strain in vivo under realistic loading conditions. Strong methodological transparency in DIC setup, socket design, and FEA workflow. Good numerical agreement between DIC and FEA strain patterns, supporting the feasibility of this validation approach.

>>> Thank you for your thorough and constructive review. We appreciate the recognition of the novelty and methodological transparency of our work, and we have addressed each of the concerns and comments raised below.

Major Concerns:

•Single participant, limiting generalizability.

>>>Thank you for raising this concern. We agree that the single-participant design limits generalizability. We have revised the manuscript to explicitly acknowledge this limitation and to clarify that this study is a preliminary feasibility investigation.

•Simplified soft tissue modelling (linear elastic instead of hyperelastic).

>>> We agree that modeling soft tissues as linear elastic is a simplification that does not fully capture their nonlinear behavior. Hyperelastic models were explored; however, they resulted in numerical instabilities under the applied loading conditions and the model did not converge. This issue with hyperelastic models was also reported by Cagle et al. (2018). Due to the focus of this study on feasibility and our limited resources in quantifying subject-specific soft tissue behavior, linear elastic properties were used for modelling soft tissue. We have noted this in the manuscript in the fifth paragraph of the Discussion.

Reference:

“Cagle JC, Reinhall PG, Allyn KJ, McLean J, Hinrichs P, Hafner BJ, et al. A finite element model to assess transtibial prosthetic sockets with elastomeric liners. Medical and Biological Engineering and Computing. 2018;56(7):1227–40.”

Suggested improvement:

Lines 19–37 •Comment: The abstract is clear and well structured, but it should acknowledge the single participant design explicitly, as this strongly limits generalizability. •Suggestion: Add 1–2 sentences describing key limitations upfront to set realistic expectations.

>>> We agree that the single-participant design is an important limitation that should be mentioned upfront. We have revised the abstract to acknowledge this limitation and that the findings are preliminary.

>>> We have added a sentence to this section noting that FEA stress predictions have been experimentally validated using pressure sensors by other studies, with errors of up to 12 KPa, and that such errors are clinically significant given that repetitive interface stresses as low as 4–23 kPa have been associated with skin damage risk in prosthesis user.(Second paragraph of the Introduction)

•Line 60: DIC is presented as widely accepted; consider citing more prosthetics-specific DIC applications to position the study within the field.

>>> To be clear, DIC is widely accepted in engineering mechanics, but has not been used extensively in prosthesis-related work. In response to the reviewer’s comment, we have made this more clear and included an additional DIC study about prosthetic sockets by Saey et al. (2019). (Third paragraph of the Introduction)

•Lines 74–81: The two research goals are clearly stated. However, consider emphasising that this is an exploratory single subject feasibility study, not a validation study.

>>>We have revised the statement of the goals to explicitly indicate the single-participant and feasibility nature of the study. (Fourth paragraph of the Introduction)

•Lines 85–89: Single participant; demographic justification is absent. Authors should state why this individual was chosen (e.g., typical limb geometry, availability).

>>> The participant was selected based on a) having a below knee amputation at least one year prior; b) having a well-fitting prosthesis that was used daily; and c) schedule availability. We have added this to the paragraph.

•Line 100: Speckle pattern creation using fabric dye and thickener requires justification—does this alter liner compliance or friction properties?

>>> The speckled liner has a rougher surface than normal liner and this will increase the friction coefficient. For this reason, we decided to apply lubricant to remove this effect and have a frictionless liner-socket interface. We have discussed this as a potential limitation in the sixth paragraph of Discussion.

>>> We agree that selected tasks do not represent full gait dynamics. Full gait was excluded because glare and reflections on the transparent socket were more manageable under-controlled and quasi-static conditions than dynamic walking. Additionally, as a preliminary study, we focused on simple controlled tasks to establish a methodology prior to advancing to more ecologically valid conditions in future work. We have discussed this as a potential limitation in the sixth paragraph of Discussion.

>>> We agree that separate trials for anterior and lateral views could introduce inconsistencies across trials. To minimize the inconsistencies, the participant was provided with clear verbal instructions and visual markers on the forceplate for prosthetic foot positioning. We have added this explanation to the manuscript. We have added this in the third paragraph of Methods.

•Lines 137–140: More detail is needed on the DIC reconstruction error, stereocalibration accuracy, and noise filtering.

>>We have included more information about DIC calibration and filters in the Digital image correlation section.

•Lines 140–145: The strain measurement region was extremely limited. This methodological constraint strongly weakens the validity of comparing full field FEA results with partial-field DIC data.

>>> The measurable DIC region is limited due to proximal sleeve and distal wrap for maintaining the structural integrity of the socket. It is also worth noting that the approximate location of the corresponding region has been shown on FEA results, and all the comparisons were limited to only the corresponding region on the FEA. We acknowledge, however, that this approach limits the ability to draw conclusions about strain distributions across the full liner surface. This issue has been acknowledged as one of the study limitations (Sixth paragraph of the Discussion)

•Lines 155–157: Bone anatomy derived from an open-source model and scaled using tape measurements introduces significant geometric uncertainty. Consider quantifying potential anatomical mismatch.

>>> We agree that our method in bone sizes and positioning could introduce uncertainty. Formal quantification of anatomical mismatch was not possible for us due to lack of imaging data from the participant residual limb bones. We have acknowledged this as a limitation of our study. (Sixth paragraph of the Discussion)

•Lines 166–170: Soft tissues modelled as linear elastic contradict well-established nonlinear, viscoelastic behaviour. A more rigorous rationale is needed.

>>> We agree that linear elastic does not represent the full nonlinear behavior of soft tissues and have acknowledged this as a limitation. Hyperelastic material models were evaluated but could not be used due to solver convergence instability in the FEA software. Cagle et al. (2018) also reported the model convergence instability with hyperelastic models of soft tissues and alternatively adopted a linear elastic model. We have provided more justification in our discussion. (Fifth paragraph of the Discussion)

>>> Neglecting frontal/transverse plane moments could introduce bias of strain values, especially in the lateral side of the residual limb. These moments were neglected following the approach used in prior transtibial prosthetic FEA studies (Cagle et al. (2018) & Mbithi et al. (2022)). Assuming the center of pressure to be aligned with the tibial axis could introduce error in asymmetric strain distribution. Regarding inertial effects, the two loading tasks were intentionally selected quasi-static tasks that were performed slowly to minimize inertial effects, which is consistent with the feasibility scope of this study. We have added more information regarding these limitations to the manuscript. (Sixth paragraph of the Discussion)

•Lines 200–212: The agreement between DIC and FEA strains is well presented. However, statistical error metrics (e.g., RMSE, correlation, Bland–Altman plots) are missing.

>>> Due to differences in mesh discretization between FEA and DIC strain fields, point-wise comparison was not feasible. Gomez et al. (2018) proposed a methodology for such comparisons by comparing strain distribution histograms. In response to this comment, we have adapted their approach and generated probability distribution histograms of principal strains for both FEA and DIC and quantified their overlap using the Bhattacharyya coefficient (BC), a measure of overlap between two probability distributions where a value of 1 indicates complete overlap and 0 indicates no overlap. We additionally compared mean and standard deviation of principal strains between FEA and DIC. Accordingly, we have added a section to our Methods title as “DIC and FEA comparison” and updated our Results to report these comparison measures.

Reference:

Gomez AD, Stone ML, Bayly PV, Prince JL. Quantifying Tensor Field Similarity With Global Distributions and Optimal Transport. Med Image Comput Comput Assist Interv. 2018;11071:428–36.

•Lines 211–218: For the half-step task, a substantial discrepancy appears in the lateral minimum and maximum strains. Authors should explain this more clearly rather than briefly noting it.

>>> We agree that the lateral strain discrepancy during the half-step task needs more explanation. The higher lateral discrepancy between FEA and DIC during the half-step task could b

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PLoS One. doi: 10.1371/journal.pone.0353881.r003

Decision Letter 1

Alessandra Aldieri, Alessandra Aldieri

30 Jun 2026

A preliminary comparison of prosthetic socket liner strain determined using digital image correlation and finite element analysis

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PLoS One. doi: 10.1371/journal.pone.0353881.r004

Acceptance letter

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PONE-D-26-07309R1

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Associated Data

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Supplementary Materials

S1 Table. FEA strain results for tested Young’s modulus values.

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S2 File. Mesh convergence analysis.

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pone.0353881.s002.pdf^{(89.4KB, pdf)}

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Data Availability Statement

All relevant data have been stored in Virginia Tech research repository: https://doi.org/10.7294/32337195.

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PERMALINK

A preliminary comparison of prosthetic socket liner strain determined using digital image correlation and finite element analysis

Mohammadreza Freidouny

Michael L Madigan

Carson Squibb

Masaki Hada

Abbie Bailey

Trevor Johnson

Brian Kaluf

Michael K Philen

Roles

Abstract

Introduction

Methods

Human subject testing

Fig 1. Lateral views of the speckled liner (left) and diagnostic socket (right).

Fig 2. Anteroposterior and vertical components of ground reaction forces during vertical loading task (left) and the half-step task (right).

Fig 3. Experimental setup for collecting liner strain and ground reaction forces during the half-step task.

Digital image correlation

Fig 4. An illustration of the anterior (left) and lateral (right) views of the measurable strain region on the residual limb within the DaVis software.

Finite element analysis

Fig 5. Lateral view of the FEA model of the residual limb within the socket.

Table 1. Material properties and elements used for modelling FEA components.

Fig 6. Simulation phases of the donning process in the FEA model.

DIC and FEA comparison

Results

Fig 7. DIC measurements of principal strains on the liner surface during the vertical loading task when the vertical force was 810 N and the anteroposterior force was 50 N.

Fig 8. FEA measurements of principal strains on the liner surface when the vertical force was 810 N and the anteroposterior force was 50 N during the vertical loading task.

Fig 9. Probability distribution histograms of DIC and FEA measurements of principal strains on the liner surface during the vertical loading task when the vertical force was 810 N and the anteroposterior force was 50 N.

Fig 10. DIC measurements of principal strains on the liner surface when the vertical force was 780 N and the anteroposterior force was 130 N during the half-step loading task.

Fig 11. FEA measurements of principal strains on the liner surface when the vertical force was 760 N and the anteroposterior force was 160 N during the half-step loading task.

Fig 12. Probability distribution histograms of DIC and FEA measurements of principal strains on the liner surface during the half-step loading task when the vertical force was 760 N and the anteroposterior force was 160 N.

Discussion

Supporting information

Acknowledgments

Data Availability

Funding Statement

References

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Author response to Decision Letter 1

Decision Letter 1

Alessandra Aldieri

Alessandra Aldieri

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Acceptance letter

Alessandra Aldieri

Alessandra Aldieri

Roles

Associated Data

Supplementary Materials

Data Availability Statement

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