Seeing the Big Picture: Improving The Prosthetic Design Cycle Using 360° 3D Digital Image Correlation

Additive manufacturing is one of the most promising emerging technologies for building prosthetic sockets. However, there is no reliable way to estimate the factor of safety and the lifetime of 3D printed prosthetic sockets. Here, we explore 360° 3D digital image correlation (DIC) and discover how this new tool can increase our understanding of prosthetic structural failures. We establish that this new technology can dramatically improve the prosthetic design cycle by identifying local strain concentrations and by highlighting limitations in current simulated models. Overall, 360° 3D DIC technology empowers prosthetic engineers to characterize the performance of new materials and create innovative designs that are both safe and affordable.


Introduction
Every year in the United States, more than 185,000 people lose their limbs to trauma, infection, malignancy, diabetes or other conditions and this number is projected to keep growing [1]. Around the globe, approximately 40 million individuals are amputees and as many as 95% of them do not wear a prosthetic [2]. Amputees who do not wear a prosthetic suffer from limited mobility as well as limited access to education, employment, and financial support [3]. 3D printing has been identified as a breakthrough technology that can dramatically improve access to affordable prosthetic limbs [4]. It can be used to manufacture customized prosthetics faster and more affordably than traditional shaping methods (Figure 1). Unfortunately, 3D printed prosthetic sockets are not currently safe enough to use in clinical practice. No polymeric 3D printed prosthetic socket to date has been sufficiently strong to comply with the loads specified by ISO 10328, the standard for structural testing of lower limb prosthetics [5]. For this reason, engineers need to understand how and why 3D printed sockets fail in order to improve their designs to the point where they can be utilized safely by amputees.

Structural Analysis of Lower Limb Prosthetics
Prosthetic sockets are a critical structural component in lower limb prosthetics; however, they have not been tested or simulated to the same extent as other prosthetic components. This stems from the fact that prosthetic sockets are omitted from ISO 10328. These prosthetic sockets do not have the degree of mechanical analysis that load bearing structures should have. However, previous research on the topic yielded valuable insights into how to conduct experiments and analyze the failure of these prosthetic sockets. This previous work is framed in terms of the typical engineering design cycle: Simulation → Experiment → Simulation.

Prior Simulations
There are a significant number of simulations that seek to model the mechanical behavior of prosthetic sockets. Modeling prosthetic sockets is a challenge because it is a complex multi-body problem that involves interactions between multiple surfaces and materials with both linear elastic and viscoelastic behavior [6]. This has led to many different approaches for solving this complex simulation challenge dependent on some critical biomechanical assumptions. These simulations generally model this system to understand how a residual limb deforms in response to loading [6]. This perspective is limited because it does not evaluate the prosthetic sockets themselves for failure. However, the simulation parameters and boundary conditions can be modified to take this a step further for socket failure analysis.
Simulations of prosthetic sockets begin with obtaining a sample geometry. The most common approach utilizes magnetic resonance imaging (MRI) scans to obtain the hard and soft tissue geometry of a residual limb for simulations [7][8][9][10]. Material properties in these simulations are commonly simplified to homogeneous isotropic linear elastic behavior. More sophisticated models utilize hyperelastic or viscoelastic formulations of material behavior [6,7]. Loading and boundary conditions vary considerably based on the phase of the gait cycle. Most simulations utilize a pre-stress at a magnitude of 50 N. Standing yields static and vertical loading conditions while running or walking require ground reaction forces and moments [13,14]. Simulations of donning, the act of putting on a socket, do not require pre-stresses [15]. The magnitude of stresses simulated was most commonly 800 N which is approximately 110% of an ideal patient's body weight [14][15][16]. In almost all cases of multibody simulations, the interface between the limb and socket was represented by a coefficient of friction (typically of value 0.5) [6,7].

Prior Experiments
Failure in prosthetic sockets can be catastrophic. Amputees rely on sockets to maintain the link between their body and the prosthesis and they can be seriously injured in the event of failure. Therefore, engineers need to be able to verify and quantify the level of safety in prosthetic sockets. Simulations are useful tools for predicting these catastrophic events. However, because so many assumptions are made, experimental data is needed to validate these models. Despite the fact that ISO 10328 omits protocols for testing prosthetic sockets, several research teams have attempted to develop valid methods for testing the strength of these sockets. These tests are all inspired by ISO 10328 to specify the loading conditions for yield stress, ultimate strength, and fatigue strength of these sockets.
Current et al. [17] characterized the failure modes of composite prosthetic sockets in 1999. They developed a custom socket loading fixture (SLF) which enabled them to apply loads to a prosthetic socket with a 100kN hydraulic load cell. They identified three primary failure modes for the prosthetic socket material: inter-laminate shear, buckling, and tension. Significantly, they also noted that the prosthetic sockets failed near the pyramidal adapter. Most importantly, they noted that "none of the composite sockets in the study were able to meet the specified parameters set [by ISO 10328] for other prosthetic componentry." Goh et al. [18] tested the mechanical strength of additively manufactured prosthetic sockets in 2002. They characterized the material properties of polypropylene sockets using ASTM D638 [19] and then tested for the strength of the prosthetic socket using ISO 10328 as a guideline. Both the static and cyclic (250,000 cycles) behavior was tested on prosthetic sockets in two loading configurations (standing and walking). The additively manufactured sockets failed catastrophically after the material reached its ultimate tensile strength.
Gerschutz et al. [20] performed an extensive strength evaluation of prosthetic sockets in 2012 (which is still the most comprehensive analysis to date). They developed a custom apparatus to test the static compressive strength of prosthetic sockets using an instrumented load cell and a standardized limb shape. Following this, they tested sockets manufactured by different providers around the United States. Their experiments revealed that check sockets (prototype sockets typically used for fitting) and copolymer sockets failed to meet the loading conditions specified by ISO 10328. This is significant because prosthetic sockets fabricated with 3D printing are very similar in strength to these check sockets.
Skoglund [21] built a custom apparatus to test the mechanical strength of prosthetic sockets manufactured by selective laser sintering (SLS) in 2015. This new apparatus represents a significant improvement; it can apply compressive loads in a more biomechanically accurate manner by utilizing multiple ball joints. This new design also enables prosthetic sockets to be tested without geometrical modification. Using this new apparatus, Skoglund [21] was able to design a titanium alloy prosthetic socket to satisfy the ISO 10328 loading conditions.

Strain Characterization Advances
To understand how prosthetic sockets deform and fail, the most important tools for characterizing failure are experimental strain techniques. Strain gauges have been the primary method of characterizing mechanical performance of prosthetic sockets. However, new techniques for strain characterization have the potential to significantly improve the quality and quantity of experimental data.

Strain Gauges
Strain gauges have historically been the most frequently utilized tools for characterizing strain in prosthetics. Strain gauges work by outputting a voltage reading which changes over the course of an experiment; this voltage reading will decrease when a strain gauge undergoes extension because the resistance of the strain gauge increases. This technique has many advantages. Most importantly, it is relatively inexpensive and quantitative strain performance is very well documented. Strain gauges can be used on arbitrarily large structures as well as built into arrays to give information on the local strain field. Finally, strain gauges can be used in hollow structures to obtain interior strain information [22]. Disadvantages of strain gauges are that they fundamentally only give local uniaxial strain information, require perfect bonding for measurements, and can be complex to set up for large installations. These limitations have frustrated prosthetic researchers in the past who noted significant challenges in obtaining useful strain data [23].

Photoelasticity
The photoelasticity technique is equally well established for strain characterization being utilized as far back as 1932 [24]. In photoelasticity, light waves pass through a material that exhibits birefringence behavior under stress. The indices of refraction change in the material based on the induced polarization and which shifts the wavelength of light passing through a material and creates different colors which are used to determine stress and strain. The main advantage of this technique is that it can visualize stress and strain over an entire surface (including 3D surfaces), which yields significantly more information about a structure as a whole [25]. However, the photoelastic technique has its own limitations. It requires a part be made of a birefringent material. Otherwise, a relatively thick (~3 mm) uniform photoelastic coating must be adhered to the surface, possibly leading to reinforcement issues. Additionally, it can be tedious to calculate values of principal stress since it requires expensive equipment that is time consuming for 3D work [25,26]. These factors have made photoelasticity unsuitable for use in prosthetic research.

Digital Image Correlation
Digital image correlation (DIC) is a relatively new technique for strain characterization, dating back to 1985 [27]. DIC works by tracking the displacement of an image pixel block on the surface of a sample. Simply by tracking these pixels, a computer can construct deformation vector fields and strain maps in both 2D and 3D. DIC only requires that the samples surface exhibit a unique pattern that can be easily tracked [28]. One main advantage of DIC is that the numerical strain is calculated automatically during the analysis, saving a great deal of time compared to photoelasticity. DIC has the additional advantage of not requiring a specialized coating. Some disadvantages of the technique are that it has primarily been restricted to 2D analysis because most implemented DIC algorithms assume plane strain and stress conditions [29]. 3D analysis has been dramatically improving in recent years, but the majority of analyses utilize small surfaces generated from a single stereo camera pair [30,31]. 360° DIC systems have been developed commercially such as by Dantec Dynamics; however these solutions are extremely expensive. Two recent papers by Solav et al. [32,33] outlined a new method called MultiDIC to stitch together an arbitrary number of stereo camera pairs. This new method has the potential to take advantage of DIC's strengths (low cost equipment and sample preparation) while eliminating its major weaknesses (limited 3D analysis). These benefits make this new method a powerful tool for studying prosthetic design.

Experimental and Computational Methods
Based on our literature review of existing technologies for structural analysis, we determined that the MultiDIC technology developed by Solav et al. [33] was a promising tool to calculate the factor of safety in prosthetic socket designs. However, since that paper did not address failure analysis, we needed to determine if the tool was capable of characterizing structural failures. A validation study (outlined in Appendix A.1) was conducted which demonstrated that MultiDIC was an effective tool for structural failure analysis. Subsequent experiments were conducted to understand how prosthetic sockets fail in compression. In the first stage, a socket loading fixture was simulated using ABAQUS CAE. This simulation represents how current simulation model parameters predict the stress and strain distribution of prosthetic sockets. This computational work was followed by an experiment where a 3D printed polylactic acid (PLA) socket was compressed in the socket loading fixture until failure. This event was captured with a synchronized camera array. This analysis was limited to a single prosthetic socket to determine the viability of the 360º 3D DIC method. The MultiDIC software used the camera data to reconstruct a 360º strain map of a prosthetic socket. Finally, the simulated data was compared to the experimental data to understand the current limitations of existing structural analysis methods.

Simulation
ABAQUS CAE requires objects to be represented by a parametric CAD file before it can simulate their mechanical behavior. To create a parametric CAD file of an amputee's limb, a geometry was generated using spline decomposition of a parent .STL file. This decomposition method was used to generate parametric CAD files of all the socket loading fixture components. Once all of the geometries were created, the CAD files were imported into ABAQUS CAE for analysis (Figure 2).
Dickinson et al. [6] presented several references where researchers assumed that the material behavior was homogeneous and isotropic when simulating prosthetic sockets. Based on previous assumptions [6], the following simulations also utilize homogenous and isotropic material properties ( Table 1). The interaction between the socket and residual limb was defined as surface to surface with finite sliding. The behavior of the contact surface simulation was set as tangential with zero tolerance for adjustment. Additionally, a zero frictional penalty was defined resulting in rigid and perfect contact between simulated surfaces.
Both models for the residual limb and socket had a tetrahedral mesh geometry and a global seed size of 0.0075. The model components had 40405 and 13649 elements respectively which was sufficient to enable convergence of simulated results. To avoid convergence errors mentioned in previous work [8], the number of iterative attempts was increased from the default of 5. A load of 2240 N was applied to the top surface of the residual limb model under the assumption that the aluminum rod used was able to transfer loads perfectly. This force value is the structural proof strength as specified by ISO 10328. Finally, the flat plane at the bottom of the distal end of the socket was specified as a fixed boundary condition.

Physical Experiment
A physical experiment was conducted to characterize the full surface strain of a 3D printed prosthetic socket in pure compression using MultiDIC. Using the camera system built by Solav et al. [33] as inspiration, a synchronized camera system capable of capturing image data in a 360º field of view was built. Two rings of LED lights ensure that samples are evenly illuminated. 16 Raspberry Pi 3 B+ and cameras were arranged radially on an adjustable mounting system (Figure 3). All of the Raspberry Pi computers are connected on a local network via a network switch. A separate Raspberry Pi computer with a real time clock (RTC) module set the global time for the system using Network Time Protocol (NTP). A host PC initiates a Python script over Secure Shell Protocol (SSH) for capturing images at 1640x1232 resolution and 1 frame per second (Appendix A.2). Figure 4 shows the network configuration.
The same socket design was analyzed in both the simulations and physical experiment. A polylactic acid (PLA) test specimen utilizing 100% infill was manufactured by a Raise3d Pro 2 Plus FDM 3D printer. To prepare the socket for DIC analysis, the specimen's surface was coated with white spray paint to which a speckle pattern was applied. Finally, a pyramidal adapter was attached to the base of the socket to allow for mounting into the socket loading fixture.
This socket loading fixture, based on the Skoglund [21] design, uses two ball and socket joints to isolate the prosthetic socket specimen from bending moments when loaded in compression (Figure 5). The fixture applies a uniform load to the prosthetic socket through a replica of a patient's limb cast in epoxy. An instrumented load cell (Instron 3367) transfers the load to the epoxy limb via an aluminum rod fixed centrally in the limb. The separate components of the apparatus connect to each other using standard prosthetic pyramidal adapters.
During the experiment, an instrumented load cell first applied a preload of 5 N to the socket specimen, then compressed this specimen at a quasistatic velocity of 0.11mm/s to a maximum extension of 45mm. The synchronized camera array captured images of the deformation for the MultiDIC analysis. The socket exhibited a structural failure during this loading cycle.

Results and Discussion
The simulated and experimental strain maps were plotted using ABAQUS CAE and the MultiDIC MATLAB toolbox. When compared, these two strain maps showed similar strain profiles (Figure 6). This agreement suggests that the multibody simulation model is able to accurately impose a loading condition similar to the real-world experiment. However, comparing the numerical data between the two profiles, the simulated strain is significantly smaller than the observed experimental strain (Figure 6) The maximum simulated strain was 2.5*10 -4 while the maximum experimental strain was 5.7*10 -3 , one order of magnitude higher. This difference implies that the homogeneous isotropic material properties assumed by many previous researchers are not sufficient to accurately characterize the structural behavior of prosthetic sockets. Thus, one way to improve simulated models is to determine the anisotropic material properties of printed specimens and incorporate this data into simulations. Following this result, the mechanical properties of the PLA specimens were measured using ASTM D638 [19] and found to have a lower Young's modulus and tensile strength than expected from the bulk material (Table 2).
Interestingly, the ultimate failure and delamination of the socket occurred at the bottom of the distal end, even though the simulated model and the experimental model show the highest surface strain concentration in a different location (Figures 6 & 7). This discrepancy means that the true strain concentration that led to failure occurred on the inside of the socket. Figure 8 shows several small breaks before the large delamination event. These breaks could potentially be from the attachment screws destroying individual printed layers on the inside of the socket. The prosthetic socket specimen failed at 694.4 N which is lower than the 2240 N proof strength required by ISO 10328. Since the prosthetic socket failed at a low force under quasistatic loading conditions, it would not be capable of surviving the 1330 N cyclic loading requirement. Based on this observation, a new boundary condition for the distal end attachment should be utilized to identify interior stress concentrations. Clearly, there are both structural and material deficiencies that need to be addressed in 3D printed prosthetic sockets.
One limitation of the 360º 3D strain analysis is that the surfaces did not perfectly align during reconstruction (Figure 9). This could be due to the prosthetic socket being positioned off the central axis whereas the calibration object was positioned in the center of the camera array. The calibration object was slightly smaller than the prosthetic socket, but this should not have had any effect on calculating camera parameters because the calibration object was equally within the field of view of all cameras. It is important to note that while changing these factors can improve the quality of the visualization, the quantitative strain values will remain unchanged. Engineers can utilize this quantitative strain data to make design adjustments to improve the safety and mechanical performance of prosthetic sockets. Overall, 360° 3D DIC improves the testing phase of the prosthetic socket design cycle by precisely identifying limitations in assumptions for simulated models and by generating full field quantitative strain maps to highlight local strain concentrations.

Conclusions
This research offers several significant advances to the field of prosthetics. A synchronized 360⁰ camera array was built to record deformations on the surface of a prosthetic socket under compressive loading. Using MultiDIC and this camera data, a full field 360⁰ strain map was reconstructed on a prosthetic socket specimen. These experimental strain maps are useful because they pinpoint specific strain concentrations on a sample. However, their greatest strength comes from comparisons with simulated strain maps. The prosthetic socket specimen was simulated using homogeneous isotropic material properties. Comparisons between the simulated strain data and the experimental strain data indicate that these assumptions are not sufficient to calculate an accurate numerical strain value. This insight would not have been possible without this new strain characterization technology. In conclusion, 360° 3D DIC enables engineers to have a clearer view of how an entire mechanical system performs. This technology allows them to make a distinction between failures due to material properties and failures due to structural design. 360⁰ 3D DIC is useful for the field of prosthetics research and will empower engineers to create stronger, lighter, and safer designs.

Future Work
One limitation of the work reported herein is that the experimental socket model only accounts for a quasistatic loading condition. This stands in contrast with the dynamic nature of the human gait cycle. In addition, the model only accounts for failures under compressive loading conditions and does not account for failures due to bending or fatigue. Future research is needed to test prosthetic sockets under dynamic loading conditions and long term fatigue conditions. Additionally, future simulations must incorporate anisotropic material properties. Significant computational resources will be needed to visualize the dynamic experimental and simulation results. In future studies, 360° 3D DIC will be a critical tool to create accurate simulations and achieve a greater understanding of these complex mechanical systems. Ultimately, this technology will guide prosthetic safety research by allowing engineers to find innovative materials and improve the quality of all prosthetic designs.

Acknowledgements
Funding for this research was provided by the Alfred P. Sloan Foundation, UC San Diego Graduate Division, UC LEADS, Summer Training Academy for Research Success (STARS), Research Experience for Undergraduates Program in Biomaterials (REU), UCSD Center for Human Frontiers, and the Qualcomm Institute at UCSD. This work is dedicated to the late Professor Joanna McKittrick, without her support this research would not have been possible. We would like to thank the generous support of the Center for Human Frontiers and the Qualcomm Institute at UC San Diego for providing resources for this research project. In addition, we would like to give thanks to Brett Butler and Alex Grant in the UCSD Prototyping Lab for helping to machine the custom mechanical testing equipment utilized in this paper. We were very generously helped with the MultiDIC toolbox by Dr. Dana Solav and Aaron Jaeger of the Herr Group in the MIT Media Lab. We also want to thank Benjamin Cabrera of Stater Bros. Markets for helping us to create a network configuration for our synchronized camera arrays. Finally, we would like to thank all of the other students involved on the Project Lim(b)itless team for their incredible support and positive energy which led to the successful completion of this research. Figure 1: Two lower limb (trans-tibial) prosthetics manufactured using traditional shaping methods. a) The socket on the left is made of a laminated carbon fiber composite which is expensive but common in developed nations. b) The socket on the right is manufactured at a low cost out of high density polyethylene (HDPE) by Jaipur Foot in India     This socket loading fixture is surrounded by our 360° synchronized camera array to facilitate 3D digital image correlation analysis.

Figure 6:
Image showing a comparison between experimentally generated strain maps and simulated strain maps. These two graphics show great agreement as to the strain distribution, but the simulated strain is much smaller than the experimental strain.    The sample was twisted at a rate of 0.002 radian/s and we ran our experiment until we reached 1 radian of extension. This was sufficient to consistently generate cracks.

A.1.3 Results and Implications for Prosthetic Research
Once we finished the torsional experiment, we visualized the strain results using the MultiDIC toolbox developed by Solav et al. [33]. This required that we calculate lens distortion, calibrate our camera positions, calculate the 2D DIC maps for each stereo camera pair, reconstruct our 3D surface geometry, before we could project these strain maps onto the 3D surface. We evaluated the torsional specimen from its zero deformation state until right before failure. We were able to successfully visualize the results on an entire 180° surface; these are presented in Figure A2.
In Figure A2, we can clearly see that a crack propagated longitudinally across the sample. This behavior was entirely expected based off of the work by Chen et al. [37]. Looking at the principal strain map, we can observe that the MultiDIC system was able to keep track of the surface strain over the entire testing period. The system is able to show the strain concentration leading to the crack. This means that we were able to successfully observe strain concentrations in the sample even before they presented themselves as macroscopic cracks.
Overall, this validation was a success and we were able to visualize the strain field on the surface of an object in torsion utilizing multiple stereo camera pairs. This allowed us to capture the failure mechanism in our torsionally loaded balsa wood samples. Our system is extremely useful in observing strain concentrations on complex structures and can show us exactly where a structure will fail. This in turn tells us where a structure can be redesigned to increase safety. Since we were able to successfully characterize a structural failure mechanism using an instrumented load cell and the MultiDIC toolbox, we were confident to continue our work and begin to characterize the failure mechanisms of a prosthetic socket. Figure A1: Image showing the assembled 180° synchronized camera array with a precision machined calibration object. This camera array is designed to analyze torsional failure modes in materials.

Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: