Given the geometry of the biplane x-ray system and a 3D bone, joint prosthesis and socket model from a CT scan, a pair of digitally reconstructed radiographs (DRRs) can be produced via ray-traced projection through the 3D bone model (Figure 3).64 In the next step, the similarity between the two DRRs and the actual 2D biplane radiographic images is tuned using optimization, so that the in vivo position and the orientation of the socket or residual bone can be estimated. Laplacian enhancement masks, Gaussian blur filters, Canny edge, and Sobel edge-detector output are added to the base images for both the DRRs and the radiographs to improve the matching process. The quality of matching is measured by calculating the correlation coefficient of each DRR with its corresponding radiograph and then multiplying the two view correlations to get total system correlation.
The first step in the model-based tracking involved developing and separating the 3D volumetric bone, prosthesis, and socket model. First, the residual bone and joint prosthesis CT images were manually segmented from soft tissue and the socket information. The implanted tantalum beads were manually removed from the CT images so that the presence of implanted beads did not improve the model-based tracking. The CT volume was then interpolated using a feature-based interpolation technique and scaled to have cubic voxels with dimensions similar to the 2D pixel size in the biplane x-ray system images.
The model-based tracking process uses a homegrown operator-friendly interface of graphical tools. This graphical interface includes the following tools: 1) a visual overlay of the DRRs on the radiographs that empowers the operator's initial guesses and provides contrasting enhancements to help the operator match position and orientation; 2) an array of six position buttons that control the position and orientation of the model; 3) a low-resolution 2D search tool that performs a broad exhaustive search by translating and rotating each DRR to maximize the correlation with its radiograph; 4) a high-resolution but finer narrower local six-axis search tool to refine alignments in position and orientation; 5) similarity between the DRR and the radiographic image is determined with a correlation and an optimization71–73 iterates motion parameters until the maximum similarity is obtained. Estimating 3D kinematics requires simultaneous optimization of all the six motion parameters (three positions and three rotations). Once 6 df of the center point of the bone, prosthesis, or socket model are estimated from each single-plane system, the absolute 3D position and orientation of the bone in the reference coordinate system are determined using a 3D line intersection method and the known imaging geometry of the biplane system; and 6) visualization tools for evaluation of quality of the motion.
In addition, the new MBT and markerless tracking algorithms apply image-processing routines (Laplacian enhancement masks, Gaussian blur filters, and Canny edge detection; Figure 4), so that enhanced tracking of the orthogonal skin-mesh based on its geometrical properties is possible.74 This allows characterization of 3D displacement/deformation and skewness, i.e., relative strain and relative engineering shear strain of the skin mesh from the sequences of DRSA images. Two different methods were used to estimate the relative “resting” initial length (3D distance) between the skin-mesh markers. In the unloaded (without the socket) mode, the 3D distance was obtained from the laser scan measurements. In the unloaded but donned socket mode, we averaged the 3D distances from DRSA data collected from a total of 10 to 20 frames. This “skin resting initial length” is then combined with the DRSA skin mesh deformation data to produce relative strain/shear assessments. This is repeated for all critical regions of the residual limb during the impact phase of the strenuous tasks. The kinematic relationships of the socket, residual bone edges, TKR prosthesis, and several skin-meshes were analyzed using data from the two tasks from touchdown to up to 0.4 seconds (or up to the time point when data existed). Clinically relevant joint kinematics was calculated from each of the marker-based and model-based tracking results. Translation was defined as the three-dimensional distance between the femoral and tibial prosthesis component's most distal edge and expressed in the tibia anatomical coordinate system. Previously described anatomic coordinate systems were adopted.73 Segmental rotations were calculated using ordered rotations.75 Accuracy measures (bias, precision, and root mean square [RMS] error) for clinically relevant kinematic variables were calculated as described earlier for the 2.4 seconds after foot impact. One-sample, two-tailed, t-tests with alpha set at 0.05 were used to test for bias. 3D pathways or proximity maps (using software tools from MATLAB [The Mathworks Inc., MA], Autodesk 3ds max studio 2009, Autodesk Autocad 2008 [Autodesk Inc., CA], Geomagic Studio 10 [Geomagic US Corporate, NC], and Mimics [The Materialise Group, Leuven, Belgium]) between the socket-skin-TKR-bone-edge markers at critical socket areas were plotted for the tasks in question. Areas of kinematic importance were further animated and presented with visualization paradigms that the clinician is trained to interpret.
Reassessing the static and dynamic accuracy method of DRSA of the marker-based method was possible by estimating the difference between the known 3D distance of two rigidly fixed socket markers and the respective measured 3D distances during the static standing and dynamic tasks (from all trials). Static accuracy was 0.03 ± 0.06 mm and dynamic accuracy was 0.09 ± 0.05 mm. Minimum and maximum dynamic errors in determining the 3D distance were between 1% and 2.3% of the original known distance between the two socket markers (SoMMAnt and SoMLPos).
Estimation of the efficiency of the model-based tracking technique relative to dynamic RSA was established by quantified accuracy in terms of bias and precision as reported elsewhere.62,65,76 Measurement bias was assessed by determining the average difference in 3D tantalum marker locations between the two techniques across all trials. It was assumed that the tantalum markers were rigidly fixed in all structures in question. Therefore, a direct estimate of the uncertainty in the model-based tracking measurements independent of residual bone, prosthesis, or socket motion was possible. The standard deviation of the difference between the two techniques during the motion trials represents the dynamic precision. We also assessed the overall dynamic accuracy of the model-based tracking technique by computing the RMS error between the two techniques across all trials.
Excellent agreement was found between the results produced by the model-based tracking and the DRSA technique. Quantitatively, measurement bias ranged from 0.012 to 0.11 mm (depending on coordinate axis) for the femoral prosthesis and ranged from 0.004 to 0.048 mm for the socket (Table 6). Dynamic measurement precision was better than 0.49 mm for the femoral prosthesis and 0.37 mm for the socket. The assessment of overall dynamic accuracy indicated that RMS errors in any one direction were <0.50 mm for the femoral prosthesis and <0.40 mm for the socket. Finally, the assessment of overall dynamic rotational accuracy indicated that RMS errors in flexion extension, ab-adduction, and internal-external rotation were <1.03, 0.29, and 1.12 degrees, respectively.
Dynamic skin slippage was assessed by plotting the relative 3D displacement of a skin-marker with respect to the socket. Figure 5 shows the respective proximity 3D pathway for characteristic skin markers and the 3D kinematics (telescoping motion) of the femoral/tibia prosthetic components at four time instants (t1: 0.0 seconds, t2: 1.46 seconds, t3: 1.8 seconds, and t4: 2.14 seconds) after impact with the ground during the step-down trial 2. It was observed that the characteristic slippage patterns of skin markers skDAnt, skDL, skDPos, and the femur and tibia prosthesis 3D displacement were the most amplified immediately after impact. All skin markers inside the socket demonstrated the largest displacement in the X-direction of progression (3.51 to 5.6 mm), whereas vertical displacement ranged between 1.2 and 4.3 mm. The skin marker skPPos that is outside the socket and just at the edge of the socket's upper rim demonstrated the highest magnitudes in the displacements in all three directions (X: 11.3 mm, Y: 5.073 mm, Z: 7.883 mm). There was a significant amount of perturbation in these areas of the skin that occurs between time instant t1 that the foot impacts the ground and time instants t2–t4 when the skin settles and the impact has been absorbed by the skin-residual limb-socket complex. In addition, the femoral/tibia prosthesis components moved 25 mm vertically (a clear telescoping type of motion) with respect to the socket (Figures 1, 5). The femoral component translated almost twice as much in the X and Y direction when compared with the tibia motion. These plots can be used as visualization assistants to demonstrate large dynamic slippage of the skin tissue at critical regions. The 3D maximum, minimum, and average distance (millimeter) as well as relative strain and engineering shear strain values between selected residual limb-socket-markers and the residual bone-edge for fast-stop and step-down trials are given in Tables 2 to 5. The maximum 3D distance between several socket-skin-marker pairs ranges from 3 to 16 mm for the fast-stop task and from 2 to 8 mm for the step-down task. Marker pair soDMAnt-skDPos demonstrated the maximum 3D distance of 16 mm in fast-stop trial: this is the pair representing the distal medial-anterior side of the residual limb-socket complex. It should be noted that for all trials, the highest maximum 3D distance is observed between the residual femoral prosthesis component and socket-or-skin-marker pairs located at the distal residual limb. The highest telescoping motion of the residual bone with respect to the skin marker skDAnt reached a value of 28 mm for the step-down trial 2. Higher magnitude ranges were observed between the most proximal skin markers that were outside the socket. Skin-marker pairs reach relative strain values that range between 0.01 and 0.1 for step-down and fast-stop trials, respectively (Table 4). The relative engineering shear (γ) between selected marker clusters that form orthonormal meshes (skPAnt, skMAnt, skDAnt, skDL, and skDPos) ranged between 81.5 and 129 degrees. Table 5 demonstrates the highest relative engineering shear (γ) values from all skin markers measured for marker skDAnt.
The results demonstrate a downward, anterior-posterior shift of a whole group of distal, and a lateral and posterior region skin markers after impact. Figures 6 to 8 present the worst-case scenarios of overall “deformation” between adjacent pairs of skin-to-socket to bone edge (joint prosthesis) and skin-to-skin markers for both tasks. Maximum deformation of up to 12.5% is observed for the fast-stop trials and step-down trials between skin-to-skin-marker pairs (markers with highest deformations for both tasks are shown in Figure 6). The respective deformation between skin-to-socket marker pairs reached maximum values of almost 22% (markers with highest deformations for both tasks are shown in Figure 7). The deformation between the tibia prosthetic component and skin/socket marker pairs reached maximum values of almost 100% (Figure 8).
Socket fitting and evaluation is a skill that remains an art today, depending on the accumulated expertise of the practitioner/prosthetist. A new method for the evaluation of dynamic fitting of prosthetic sockets is presented here. Marker- based assessment of dynamic socket-residual limb and bone-socket telescoping motion with as much as ±0.03 mm translational and 1.3 degrees rotational accuracy (one order of magnitude higher than current techniques) using DRSA was demonstrated. The in-vivo dynamic accuracy for the markerless tracking method was further improved from that reported previously.61,64,77 Excellent agreement was found between the results produced by the model-based tracking and the DRSA technique. In particular, the position and orientation of the femoral prosthesis component and socket component were qualitatively acceptable when superimposed over the original biplane images (Figure 3). Quantitatively, measurement bias ranged from −0.012 to −0.11 mm (depending on coordinate axis) for the femoral prosthesis and from 0.004 to 0.048 mm for the socket (Table 6). This is due a) to the enhanced out-of-plane CT resolution used in this study (an improvement in slice thickness from 1.5 to 0.5 mm) and b) to the improved DRSA image resolution (1440 × 1200 pixels matrix). This in turn was the result of improved x-ray tube focal spot (0.3 to 0.8mm) and increased image intensifier size (19"). These hardware and camera improvements resulted in almost complete reduction in blurriness due to motion and significantly more information on the image for the tracking algorithms.
No operator bias data are available because only one operator processed and analyzed the data. It should be noted that the marker placement protocol must be kept identical as much as possible so that differences in the geometry and shape-morphology of socket/residual limb complex will not introduce discrepancies when comparing data from different patients. Another critical challenging aspect of this method is that in very dynamic tasks such as the fast-stop task the critical socket regions of interest might get out of the field of view (40 cm intensifier diameter). They might also get occluded by the other limb while trying to perform the task naturally and without familiarization. It is recommended that large image intensifiers and alternative x-ray beam penetration angle orientations be in use.
Our results showed that deformations (from an initial “resting unloaded length”) between selected skin-socket pairs of markers and joint prosthesis-bone-edge exceeded 100% for both strenuous trials. These deformations relate to 3D distances that reached values of up to 25 mm for some marker pairs for both tasks. These tasks demonstrate a large envelope of magnitude in socket marker and bone kinematics as well as an abrupt slope immediately after the impact phase. Deformations of up to 12.5% and 22% were observed for both trials between skin-to-skin marker pairs and between skin-to-socket marker pairs, respectively. These deformations succeed a huge vertical downward displacement (telescoping motion) of the joint prosthesis immediately after the impact followed predominantly by an AP movement of all skin markers. This information on the telescoping behavior of the residual bone and slippage mapping is critical in one's effort to further rectify the socket toward improved AP stability. This is further supported from the fact that the prosthetist now has more detailed information demonstrating that the most affected skin areas are those at the distal posterior part of the socket for this subject.
Tracking of 3D skin surface mesh markers indicated that skin deformed (through a characteristic skewness of the mesh) during the support/impact phase of both tasks (Figure 4). Maximum strains were observed for skin-marker pair skDM-skDPos and were 0.07 and 0.1 for the step-down and fast-stop tasks, respectively. These are the markers placed distally and posteriorly on the residual limb that reflect the vertical (distal-to-proximal movement) axes and signify the topology of the more severe tissue deformations occurring during these strenuous activities. Strains of all other skin marker pairs range from 0.01 to 0.1. Relative engineering shear strain for skin-marker meshes associated with marker skDAnt (worst case) reached values ranging from 81 to 130 degrees (range for other marker clusters: 81.5 to 129 degrees). Engineering shear strain is defined as the change in the angle between two material line elements initially perpendicular to each other in the nondeformed or initial configuration. In this study, this change in the initial configuration was represented by the change in the orthonormal lines of the skin mesh. Because complete initial orthonormality in the skin-mesh was not always met in this study after socket donning, the shear strain data should be viewed with precaution. It is apparent that for this protocol special attention must be given to the size and density of the skin meshes and their position on critical residual limb locations.
Assessing the dynamic skin 3D slippage was possible by plotting the relative displacement of a skin marker with respect to the 3D inner-socket mesh of the area around an adjacent socket marker. The method is capable of describing with the use of a 3D visualization tool the large dynamic slippage of skin tissue at critical regions. In the fast-stop and step-down trials, skin slippage of up to 16 mm and residual bone telescoping motion of up to 25 mm was observed. Figure 5 shows the 3D direction of skin slippage with respect to the patient-specific inner-socket geometry. The maximum slippage of 16 mm occurs in the fast stop-trial from a skin marker pair representing the distal medial and anterior side of the residual limb-socket complex. It should also be stressed here that for this subject and for all trials, the highest deformation was observed between the residual bone edge and tibial prosthesis component and socket-or-skin marker pairs located at the distal residual limb. It is important to note that this skin slippage is associated and synchronous to the significant telescoping motion of both components of the internal prosthesis. Information obtained from a proximal posterior-medio-lateral skin-marker above and outside the posterior socket rim indicates that in the step-down trials, the skin marker is moving downward and in the AP direction during impact and then away from the socket rim as the load is absorbed and the residual limb settles in the new position. Overall displacement in the outside the socket markers is twice that of the markers inside the socket. The above findings are interesting knowing that the PTB socket is expected to be a characteristically tight-fit socket design. It should be noted however that this particular amputee was wearing a silicon liner and had excessive residual skin and adipose tissue on the residual limb. The subject was capable of performing these activities but complained for discomfort and pain. This might be an explanation for the increased residual limb mobility, slippage, and instability even at the given tight-fit socket design.
We are in the process of further calibrating patient-specific, whole lower limb (socket-residual limb-prosthesis) finite element (FE) models driven by DRSA high-accuracy kinematics. In the past, the preferred protocol used for most socket rectification simulation studies relies on prescribing the displacement boundary conditions at the nodes on the outer surface of the socket or liner.17,78–80 Displacement boundary conditions corresponding to the shape of a given socket design are applied to deform the residual limb soft tissue or the liner to conform to the rectified socket shape. Data available from this study provide accurate dynamic in-vivo patient-specific displacement boundary conditions at the nodes on the inner surface of the socket. Adding tantalum meshes at the liner would also improve our current protocol and provide information on the liner dynamics. In a very complicated residual bone-residual limb-socket FE model, this information can be critical in improving contact solution and the explicit or implicit model convergence.
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