A Systematic Approach to Predicting the Risk of Unicompartmental Knee Arthroplasty Revision

Abstract

Objective

Unicompartmental knee arthroplasty (UKA) revision is usually due to the degenerative degree of knee articular osteochondral tissue in the untreated compartment. However, it is difficult to simulate the biomechanical behavior on this tissue accurately. This study presents and validates a reliable system to predict which osteoarthritis patients may suffer revision as a result of biomechanical reasons after having UKA.

Design

We collected all revision cases available (n=11) and randomly selected 67 UKA cases to keep the revision prevalence of almost 14%. All these 78 cases have been followed at least 2 years. An elastic model is designed to characterize the biomechanical behavior of the articular osteochondral tissue for each patient. After calculated the force on the tissue, finite element method (FEM) is applied to calculating the strain of each tissue node. Kernel Ridge Regression (KRR) method is used to model the relationship between the strain information and the risk of revision. Therefore, the risk of UKA revision can be predicted by this integrated model.

Results

Leave-one-out cross-validation is implemented to assess the prediction accuracy. As a result, the mean prediction accuracy is 93.58% for all these cases, demonstrating the high value of this model as a decision-making assistant for surgical plaining of knee osteoarthritis.

Conclusions

The results of this study demonstrated that this integrated model can predict the risk of UKA revision with theoretically high accuracy. It combines bio-mechanical and statistical learning approach to create a surgical planning tool which may support clinical decision in the future.

1. Introduction

Osteoarthritis (OA) is a progressive disease of the joints, known as “wear and tear” arthritis. The knee is the largest and strongest joint in human body. Knee OA onset usually occurs after 50 years of life, but may occur in younger people, too. Although the causes OA is proposed to relate to genetic, metabolic and mechanical loading. Joint angular deformity remains the most convincing determinants in OA patients. Other factors of OA such as age, obesity, trauma, repetitive loading, etc. are all mechanical-related¹. Unicompartmental knee arthroplasty (UKA)² has been developed over the years to treat osteoarthritis in patients with degenerative changes in a single knee compartment. Recently, robotic-assisted technology has been developed to facilitate UKA surgical procedures³. As part of the UKA procedure, preoperative CT scans are made to document the knee joint anatomy specific to each patient^4-6. There are advantages of UKA compared to total knee arthroplasty (TKA)⁷. Successful outcomes with UKA require proper patient selection⁸ and meticulous surgical technique to avoid revision from UKA to TKA. According to the Swedish knee arthroplasty register annual reports⁹, around 14% of UKA patients need revision during the following 3-5 years. Kozinn and Scott¹⁰ described the strict selection criteria for UKA, which is designed for patients with arthritic wear limited to a single medial or lateral tibiofemoral compartment. Indeed, to prevent the risk of rapid extension of osteoarthritis to the opposite compartment, the UKA procedure should be limited to restoring the patient's constitutional axis before degeneration phenomena had appeared in the opposite compartment. This increases the risk of failure of UKA due to micro degeneration in the opposite compartment. Heck's¹¹ work indicated that patients with higher weight have increased risk of revision rate after UKA, but some patients with normal weight may also undergo revision. This suggests there is no direct relationship between patients with normal weight and revision, but the behaviors of knee articular osteochondral tissue in the opposite compartment may vary with different loading forces. The loading force is mainly generated by the femoral bicondylar angle change after UKA and the individual body weight. It is worth pointing out that distribution of excessive strain will cause pain with degeneration. Thus we proposed to study the biomechanical properties of each patient who needs revision.

In this study, we established a statistical model to describe the relationship between the biomechanical strain information and the risk of UKA revision. The novelty of the proposed approach lies in: (1). design of equivalent material tissue properties in multiple layers of knee articular osteochondral tissue based on volumetric proportion of each layer; (2). calculation of the loading force on knee articular osteochondral tissue with patient body weight and angle change measured by femur center line correction of UKA; (3). use of a Kernel Ridge Regression (KRR) statistic model that relates the distributions of strain change information associate with the risk of the UKA revision in the knee articular osteochondral tissue finite elements.

The purpose of this paper is predicting which OA patients are going to fail due to biomechanical factors when they have UKA. We hypothesize that cartilage is microdamaged in the untreated compartment on account of initial stage of osteoarthritis degeneration, but the meniscus is considered to be intact in this stage. The biomechanical information of knee articular osteochondral tissue in the untreated compartment following virtual correction can be accurately simulated by integrating a FEM with statistical learning model.

2. Patients and Methods

This study presents an integrated approach to accurately simulate articular osteochondral tissue behavior in opposite compartment for pre and post operation respectively for the purpose of predicting of revision risk for osteoarthritis patient. Fig. 1 describes the flowchart of the whole process consisting of two phases. Both of the training phase and the prediction and validation phase having following steps: 1) a collection of patient body weight, pre-operative CT and preoperative and postoperative X-ray data (Section 2.1); 2) extraction of strain information from these data by FEM with the force calculated by patient body weight and femoral bicondylar angle change (Section 2.2).

Fig. 1.

Integrated system of finite element analysis approach to surgical decision-making. (A) both training and prediction need to use the force caused by body weight and femoral bicondylar angle change for extracting biomechanical features. (B) train the relationship between the biomechanical strain information and the risk factor of UKA revision. (C) predict and validate the risk factor of UKA revision.

2.1 Participants

From 2011-2013, over 100 OA patients have received robotic-assisted UKA and have been followed for at least 2 years to assess risk of UKA revision in the Wake Forest Baptist medical center. We collected all revision cases available (n=11) and randomly selected 67 UKA cases to keep the prevalence of UKA revision samples as about 14%, which has been reported in the Swedish knee arthroplasty register annual reports⁹ for the general population.

There are 78 cases, among which 35 are males and 43 are females with average age of 65 yrs, ranging from 42–88 yrs, and average body mass index (BMI) of 35.2 kg/m², ranging from 20.8–47.5 kg/m². The average time difference between primary operation and revision is 24.6 months, ranging from 20–36 months.

Although MRI data can assess the degree of osteoarthritis in both compartments by measuring the thickness of cartilage, as a practical matter, osteoarthritis diagnosis is mainly performed by x-rays and CT images prior to UKA surgery. In clinical practice, doctors monitor cases by x-ray data with severe osteoarthritis to determine whether immediate surgery is required or not, and CT data is primarily used to guide UKA surgery. The assessment of knee OA using X-ray has limited ability to discriminate conditions of the knee cartilage by grading joint space narrow visually. This method increases the risk of UKA failure due to the inappropriate patient selection.

Preoperative CT scans for 78 patients pre and post-operative X-rays, body weight in clinical database, Oxford Knee Score^{12, 13} (followed by 24-48 months) were collected at Wake Forest Baptist Medical Center (IRB00025566 has been approved prior to the study). All patients underwent UKA surgery with robotic-assisted (MSK, MAKO Surgical Corporation, Fort Lauderdale, FL, USA).

2.2 Feature Extraction

The basic idea to measure femoral bicondylar angle change by surgical correction from pre-operative and post-operative X-Ray images, and then calculate the force on knee articular osteochondral tissue, caused by individual body weight and femoral bicondylar angle change. Afterwards, the force is used to calculate the strain information by FEM in the knee articular osteochondral tissue mesh data, generated from pre-operative CT images. Individual biomechanical information, including stress, strain and displacement will be extracted based on the calculated force. Both stress and displacement have dense relations with strain, so the strain was used as biomechanical feature in this work.

The preoperative CT data is imported into the Mimics software (Materialise, Belgium), the knee articular osteochondral tissue were segmented in Mimics which would be further used to generate the mesh data for FEM computing.

2.2.1 Determine Tissue Material Property based on Multiple Layers Segmentation

Knee articular osteochondral tissue is composed of meniscus and cartilage layers. Different material parameters for these two layers were given by the previous work depending on characterization method and material model^14-18. To calculate knee articular osteochondral tissue property, we have to segment meniscus layer and cartilage layer; however it is extremely difficult to segment these two layers from clinical CT data. Fortunately, there is a template of meniscus which can be obtained from the Open Knee(s)¹⁹ at NIH. Thus we can calculate the volume of cartilage layer by subtracting the volume of a template of meniscus from the whole volume, and then the knee articular osteochondral tissue property by weighting the tissue properties of meniscus and cartilage based on their volumetric proportion in the mesh data. The details are described in below:

• 1)The whole knee articular osteochondral tissue composed of the meniscus and the cartilage is calculated by measuring the volume of whole tissue using Mimics software.
• 2)The volume of cartilage layer is calculated by subtracting the volume of a template of meniscus (the Open Knee(s)¹⁹) from the whole volume of knee articular osteochondral tissue. The geometry data of meniscus will be used for volume calculation, because we assume that cartilage is microdamaged in the untreated compartment on account of initial stage of osteoarthritis degeneration, which means the cartilage volume is various from different extent of degeneration, while as the meniscus is considered to be intact in this stage.
• 3)To obtain material properties according to volumetric proportion of each layer, then, assign them into each element of mesh data for FEM calculation. We set the Young's modulus to 50MPa and the Poisson ratio to 0.45 for cartilage. For meniscus, the Young's modulus and the Poisson ratio are set to 112MPa and 0.45, respectively^{17, 18}.

The equivalent material properties can be defined by the volumetric proportion of meniscus P_meniscus in each element of mesh data.

$$\begin{array}{cc}\hfill E& =E_{cartilage}(1-P_{meniscus})+E_{meniscus}{P}_{meniscus}\hfill \\ \hfill v& =v_{cartilage}(1-P_{meniscus})+v_{meniscus}{P}_{meniscus}\hfill \end{array}$$

where E denoted the Young's Modulus, v denoted the Poission's Ratio. They will be used to estimate tissue behavior based on Hooke's law in Section 2.2.4.

2.2.2 Hexahedral Mesh Generation

In order to establish the statistical model for characterize the relationship amongst all the strain changed information and the risk factor of UKA revision, we need to set up a dense correspondence between all input shapes of all patient CT data for strain extraction. In our experiment, mesh nodes were generated by TrueGrid (XYZ Scientific Applications, Inc., Livermore, CA). Thus, a natural correspondence between different mesh nodes was established based on the order of identical number of meshes. Fig. 2 presented the mesh data generated from the segmented knee articular osteochondral tissue. To limit the number of elements and reduce the computational complexity, we restricted to the zone for FEM calculation only in opposite compartment of knee joint which did not undergo arthroplasty surgery.

Fig. 2.

Mesh data generated from the segmented knee articular osteochondral tissue. (A) 3D object of knee articular osteochondral tissue was segmented based on CT images. (B) the mesh data includes 5948 hexahedral elements generated from the 3D object. (C) the shape of one element in the mesh data.

2.2.3 Loading Force Calculation and Determination of Boundary Condition

The displacement boundary condition^{20, 21}, consists of the displacements of all the boundary nodes lied in bone parts, will be simulated by FEM via adding a loading force on top surface and fixing a bottom surface of knee articular osteochondral tissue mesh data. Since the body weight and femoral bicondylar angle change²² caused by UKA for each patient will generate different forces to the knee articular osteochondral tissue. The loading force to the top tissue surface will be calculated as follows.

We used the functional weight-bearing X-ray's to determine the axis. The functional position of the knee joint is standing with weight-bearing, which provide the most accurate assessment of the functional bony anatomy of the knee joint. Both pre-operative and post-operative X-Ray images were imported into the Mimics software. We calculated Anatomischer femorotibialer Winkel (aFTW)^{23, 24} angular deviation to have the femoral bicondylar angle change for loading force calculation. The centerlines of femur and tibia are marked in Mimics, and the angles of intersection between two centerlines (i.e., aFTW in Fig. 3D) were measured preoperatively and postoperatively. Changes in the femoral bicondylar angle after UKA correction can be calculated by subtracting the preoperative aFTW angle from the postoperative aFTW angle. In Fig. 3A, B, C, the intersection angle α₁ and α₂ are measured pre-operatively and post-operatively in X-Rays. Also intersection angle equals 180° subtracting the aFTW angle. The femoral bicondylar angle change α after UKA correction can be calculated by α= α₁-α₂. Denote f as the frictional force produced by angle correction, 0.5G as the force of gravity from half body weight, F as the loading force after UKA. F can be calculated by femoral bicondylar angle change α and half body weight 0.5G. This study simulated the loading force on knee articular osteochondral tissue as patient stand up by one leg. The force after the UKA correction of femur could be calculated as:

$$F=0.5G∕cos\alpha =0.5G\cdot sec\alpha$$ (1)

Fig. 3.

Loading force calculation on knee articular osteochondral tissue.(A) preoperative X-Ray of intersection angle. (B) postoperative X-Ray of included angle. (C) calculation of loading force F by femoral bicondylar angle change α and half of patient body weight 0.5G. (D) aFTW angular deviation

The strain information after UKA extracted by FEM will be further simulated by this force brings to the top surface of knee articular osteochondral tissue mesh data (Section2.2.4). To determine how much correction of femoral bicondylar angle change occurs preoperatively for a new patient, a virtual correction takes average 6° angle change²⁵ for UKA in our experiment. We assumed the intersection angle of these two center line (one center line of femur; the other center line of tibia) would change to approximate 0°.

2.2.4 Calculation of Strain with FEM

According to the various geometric data and force calculated in different patients, we use FEM to extract the strain of each node as biomechanical information of individuals. Young's modulus and Poisson's ratio determined in Section 2.2.1 as tissue material property was applied to FEM calculation. The mechanical equilibrium equations were used to model the deformation behavior of knee articular osteochondral tissue:

$$\begin{array}{cc}\hfill \frac{\partial {\delta }_{xx}}{\partial x}+\frac{\partial {\eta }_{xy}}{\partial y}+\frac{\partial {\eta }_{xz}}{\partial z}+F_x& =0\hfill \\ \hfill \frac{\partial {\eta }_{xy}}{\partial x}+\frac{\partial {\delta }_{yy}}{\partial y}+\frac{\partial {\eta }_{yz}}{\partial z}+F_y& =0\hfill \\ \hfill \frac{\partial {\eta }_{xz}}{\partial x}+\frac{\partial {\eta }_{yz}}{\partial y}+\frac{\partial {\delta }_{zz}}{\partial z}+F_z& =0\hfill \end{array}$$ (2)

with δ_xx,δ_yy,δ_zz,η_xy,η_xz, and η_yz representing stress components and F(F_x, F_y, F_z) as the forces. Thereafter, we used Hooke's law to describe the relation between stress and strain.

$$\left[\begin{array}{c}\hfill {\delta }_{xx}\hfill \\ \hfill {\delta }_{yy}\hfill \\ \hfill {\delta }_{zz}\hfill \\ \hfill {\eta }_{xy}\hfill \\ \hfill {\eta }_{yz}\hfill \\ \hfill {\eta }_{xz}\hfill \end{array}\right]=\frac{E}{(1+v)(1-2v)}\times \left[\begin{array}{cccccc}\hfill 1-v\hfill & \hfill v\hfill & \hfill v\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill v\hfill & \hfill 1-v\hfill & \hfill v\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill v\hfill & \hfill v\hfill & \hfill 1-v\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{1-v}{2}\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{1-v}{2}\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{1-v}{2}\hfill \end{array}\right]\left[\begin{array}{c}\hfill {\omega }_{xx}\hfill \\ \hfill {\omega }_{yy}\hfill \\ \hfill {\omega }_{zz}\hfill \\ \hfill {\gamma }_{xy}\hfill \\ \hfill {\gamma }_{yz}\hfill \\ \hfill {\gamma }_{zx}\hfill \end{array}\right]\iff \delta =C\omega$$ (3)

with ω_xx,ω_yy,ω_zz,γ_xy,γ_xz, and γ_yz representing strain components, Young's modulus as E and Poisson coefficient as v.

After that, the mechanical equations were applied to calculating the nodal strain based on FEM. Since we merely focus on the opposite compartment of knee joint which did not undergo arthroplasty surgery, only nodes lying on the opposite compartment of knee joint were selected for calculation. In order get the strain pre-operation and post-operation, we first simulate the behavior response to different force F_pre=0.5G (half of body weight), F_post=F(calculated force), and then extract pre-operative and post-operative strain information. Here, we choose m=3885 nodes on the opposite compartment of knee joint. Each node has a strain vector of length six (ω_xx,ω_yy,ω_zz,γ_xy,γ_xz, γ_yz). The strain of 3885 selected nodes were stacked together (3885×6=23310) to generate the pre-operative strain vector${\omega }_q^{pre}\in {\mathcal{R}}^{23310}$ and post-operative strain vector ${\omega }_q^{post}\in {\mathcal{R}}^{23310}$ for the q th patient, q = 1, ... , h. The strain change vector ${\omega }_q={\omega }_q^{post}-{\omega }_q^{pre}$ was employed as the feature of qth patient.

In our work, the strain was calculated by the commercial FEM software ANSYS 12.0 (ANSYS Inc, Cecil Township, PA).

2.3 Kernel Ridge Regression Model Estimation

The outcome of UKA surgery is primarily judged by the patient feeling of pain during the recovery and the improvement in knee joint function. Each patient has an Oxford Knee Score to assess clinical outcomes. In our cases, all patients were followed up for a minimum of two years to evaluate need of UKA revision. We stratified the patients in two groups according to the need of revision. We labeled patients needing revision as 0 and those who did not as 1 in our model.

To model relationships between the strain information and the risk of UKA revision we used here a Kernel Ridge Regression (KRR) approach^{26, 27}. KRR is a nonlinear regression method which can detect subtle nonlinear dependencies present in the data by using the so called “kernel trick” which amounts to performing an implicit nonlinear transformation of the input data to a space of much higher dimension where the data can be linearly separated ²⁶.

Given the input and output training data pairs

$$({\omega }_q,{\theta }_q)\in {\mathcal{R}}^{23310}\times {\mathcal{R}}^{3885},q=1,\dots ,h$$ (4)

The true revision risk factor of the selected case was obtained from the doctor's following study. These revision risk factors of all nodes were stacked together to form a vector θ_q of length 3885.

Note that here we consider 3885 predicted factors estimated based on all nodes for one patient. The reason is that the degree of degeneration of different regions in the cartilage tissue is different. We have relatively small number of patients but each patient has 3885×6=23310 features. In order to model the strain change features of {ω_q} to predict revision risk factor {θ_q}, we use KRR model because it is a regularization approach that is well-known to perform well in undetermined problem like ours²⁸.

The prediction function of KRR²⁸ is defined as

$$f_{KRR}\left(\omega \right):\theta =W^T\phi \left(\omega \right)+e$$ (5)

where φ is a nonlinear mapping; e is additive white noise; W is the coefficient to be determined by minimizing an objective function as below:

$$L_{KRR}=f\left(W\right)=\frac{1}{2}\lambda W^{T}W+\frac{1}{2}{\sum }_{q=1}^n{\Vert W^T\phi \left({\omega }_q\right)-{\theta }_q\Vert }^2$$ (6)

This function consists of the mean square error L2 norm, a penalty term on W and λ> 0.

We use bootstrap method^{29, 30} to estimate the uncertainty of these parameters (coefficients) in Kernel Ridge Regression (KRR) model. We randomly choose 80% of total 78 cases for training each time, and repeat this procedure 1000 times. Then we have w₁, w₂, ···, w₁₀₀₀ as one certain feature's parameters (coefficients). We can calculate the uncertainty of the regression parameters using 95% confidence intervals, which is the 25^th percentile and 975^th percentile when we order w₁, w₂, ···, w₁₀₀₀ from the smallest to the largest. The 95% confidence intervals of regression coefficients W in Eq.(6) ranges from 0.325 to 0.348 in our model.

The regularization parameter λ in Eq.(6) is a fixed positive constant corresponding the sample size. It controls the over fitting of the model ²⁸. Here we set λ=0.001.

3. Results

When a new patient comes to hospital, we can accurately simulate the biomechanical behavior on knee articular osteochondral tissue with FEM, and predict his/her the risk of the UKA revision in other compartments of knee joint with learned KRR model and the new patient's biomechanical information. Thus the surgical decision-making could be done prior to the surgery, relieving the patient's unnecessary pain of re-operation.

Leave-one-out (LOO) cross-validation (CV) was implemented to assess the accuracy of our approach. To be more specific, the validation opts out a single patient from the 78 patients as the test data, while the remaining patients as training data to train the KRR model. Then repeat aforesaid procedure until each patient is used as the test data for once.

We evaluated the performance based on the difference between the prediction risk factor and the actual indicator recorded by clinician after UKA surgery in several years, given by:

$$E_{prediction}=\frac{1}{3885}{\sum }_{k=1}^{3885}\Vert X_k-\overline{X_k}\Vert$$ (7)

where X_k denoted the actual indicator (UKA or UKA revision, which is defined as 1 or 0 for kth node, respectively), $\overline{X_k}$ denoted the predicted revision risk factor of the kth node. Table 1 represents the prediction performance of our approach. Cases 1-67 are UKA only, and Cases 68-78 are UKA revision. The average of prediction accuracy is 93.58% for all these cases (73 out of 78 in Table 1).

Table 1.

Prediction Performance on Two Groups: UKA only and UKA revision.

Patient	True Type of Replacement	Body Weight (kg)	Force Calculated in opposite Compartment (N)	Post-OP Mean Strain (%)	Pre-OP Mean Strain (%)	Mean Strain Change	Predicted Results (1=UKA 0= Revision)
1	UKA Only	103.874	508.6	11.6	10.9	0.7	0.925 (UKA)
2	UKA Only	92.534	453.5	7.4	6.8	0.6	0.909(UKA)
3	UKA Only	121.564	595	11.2	9.8	1.4	0.832(UKA)
4	UKA Only	99.791	488.6	10.7	9.1	1.6	0.808(UKA)
5	UKA Only	145.877	732	20.9	18.8	2.1	0.745(UKA)
6	UKA Only	82.781	417	8.6	7.3	1.3	0.883(UKA)
7	UKA Only	61.281	322	9.1	7.3	1.8	0.824(UKA)
8	UKA Only	73.12	371	9.5	8.1	1.4	0.806(UKA)
9	UKA Only	65.772	348	10.9	7.5	3.4	0.655(UKA)
10	UKA Only	115.214	570	12.3	9.1	3.2	0.716(UKA)
11	UKA Only	108.863	539	11.7	8.2	3.5	0.687(UKA)
12	UKA Only	119.75	595	10.7	8.5	2.2	0.779(UKA)
13	UKA Only	112.038	551	11.5	10.9	0.6	0.857 (UKA)
14	UKA Only	116.175	571	11.1	10.3	0.8	0.815 (UKA)
15	UKA Only	58.968	290	9.3	8.2	1.1	0.798 (UKA)
16	UKA Only	90.719	446	10.2	7.5	2.7	0.772 (UKA)
17	UKA Only	86.183	424	10.5	8	2.5	0.782 (UKA)
18	UKA Only	62.143	306	9.4	7.3	2.1	0.778 (UKA)
19	UKA Only	81.285	400	10.1	8.3	1.8	0.802 (UKA)
20	UKA Only	114.533	564	11.7	10.2	1.5	0.790 (UKA)
21	UKA Only	91.037	449	10.5	9.1	1.4	0.813 (UKA)
22	UKA Only	74.5	368	9.2	7.1	2.1	0.795 (UKA)
23	UKA Only	66.679	329	9.7	7.3	2.4	0.786 (UKA)
24	UKA Only	96.637	476	10.7	8.8	1.9	0.851 (UKA)
25	UKA Only	119.296	587	11.2	8.5	2.7	0.725 (UKA)
26	UKA Only	139.118	685	12.5	8.8	3.7	0.583 (UKA)
27	UKA Only	76.9	379	9.9	7.1	1.8	0.778 (UKA)
28	UKA Only	90.719	447	10.8	9.2	1.6	0.795 (UKA)
29	UKA Only	122.925	605	12.2	8.7	3.5	0.432 (Revision)
30	UKA Only	88.905	438	10.3	8	2.3	0.791(UKA)
31	UKA Only	81.421	401	10.7	9.8	0.9	0.802 (UKA)
32	UKA Only	85.73	423	10.5	9.3	1.2	0.855 (UKA)
33	UKA Only	100.88	497	10.3	8.5	1.8	0.779 (UKA)
34	UKA Only	151.048	745	14.8	10.9	3.9	0.545 (UKA)
35	UKA Only	94.62	466	10.4	8.7	1.7	0.783 (UKA)
36	UKA Only	112.855	555	11.6	9.7	1.9	0.755 (UKA)
37	UKA Only	71.215	351	9.7	7.6	2.1	0.764 (UKA)
38	UKA Only	90.71	447	10.5	8	2.5	0.735 (UKA)
39	UKA Only	82.101	405	10.1	8.8	1.3	0.810 (UKA)
40	UKA Only	108.319	533	11.5	9.3	2.2	0.745 (UKA)
41	UKA Only	109.77	540	11.1	8.7	2.4	0.703 (UKA)
42	UKA Only	84.052	414	10.5	8.2	2.3	0.736 (UKA)
43	UKA Only	80.967	401	10.2	8.1	2.1	0.792 (UKA)
44	UKA Only	99.791	455	11	8.7	2.3	0.773 (UKA)
45	UKA Only	109.77	543	11.1	8.4	2.7	0.756 (UKA)
46	UKA Only	78.019	393	9.3	7.5	1.8	0.836 (UKA)
47	UKA Only	120.203	595	13.3	8.2	5.1	0.617 (UKA)
48	UKA Only	81.2	403	9.8	7.9	1.9	0.735 (UKA)
49	UKA Only	117.663	582	13.1	7.8	5.3	0.589 (UKA)
50	UKA Only	70.761	351	11.1	8.6	2.5	0.781 (UKA)
51	UKA Only	94.167	465	11.6	8.4	3.2	0.602 (UKA)
52	UKA Only	94	464	11.4	8.1	3.3	0.688 (UKA)
53	UKA Only	68.04	338	9.9	7.5	2.4	0.759 (UKA)
54	UKA Only	134.764	667	14	8.5	5.5	0.427 (Revision)
55	UKA Only	89.812	446	11.3	7.7	3.6	0.633 (UKA)
56	UKA Only	98.113	485	11	7.9	3.1	0.689 (UKA)
57	UKA Only	71.215	353	10.1	7.5	2.6	0.773 (UKA)
58	UKA Only	83.1	412	10.8	8.5	2.3	0.759 (UKA)
59	UKA Only	81.194	402	11.1	8.5	2.6	0.734 (UKA)
60	UKA Only	103.42	511	12.7	7.9	4.8	0.627 (UKA)
61	UKA Only	81.647	405	11.5	8.2	3.3	0.685 (UKA)
62	UKA Only	93.441	462	11.8	8.3	3.5	0.674 (UKA)
63	UKA Only	122.698	608	13.7	8.5	5.2	0.597(UKA)
64	UKA Only	91.627	453	10.9	7.7	3.2	0.721 (UKA)
65	UKA Only	118.661	584	11.7	8.2	3.5	0.704 (UKA)
66	UKA Only	110.224	545	12.1	7.8	4.3	0.615 (UKA)
67	UKA Only	96.616	478	10.8	7.9	2.9	0.703 (UKA)
68	Revision	104.6	516	12.7	8.3	4.4	0.296(Revision)
69	Revision	79.334	390	13.1	9.9	3.2	0.402(Revision)
70	Revision	79.833	393	13.7	10.8	2.9	0.438(Revision)
71	Revision	90.629	446	16.8	11.7	5.1	0.114(Revision)
72	Revision	90.402	447	14.2	10.9	3.5	0.597(UKA)
73	Revision	120.203	604.5	21.3	15.3	6	0.168(Revision)
74	Revision	80.105	395	14.5	10.4	4.1	0.287(Revision)
75	Revision	118.842	598	19.2	14.5	4.7	0.239(Revision)
76	Revision	86.183	425	9.3	7.1	2.2	0.736(UKA)
77	Revision	93.895	475	10.2	7.5	2.7	0.702(UKA)
78	Revision	90.719	478	17.1	13.7	3.4	0.308(Revision)

The ROC (receiver operating characteristic) curve is illustrated in the Fig. 4. The AUC (area under the curve) of prediction is 0.93. After fixed the cut-off point (the closest point to the upper left corner of this specific ROC curve and the highest achievable sensitivity and specificity of the test), such as (0.273, 0.97), we obtain the sensitivity as 0.97, specificity as 0.727.

Fig. 4.

ROC (receiver operating characteristic) curve based on 78 cases

There is evidence that our approach performs well when predicting risk of UKA revision caused by degeneration of knee articular osteochondral tissue in the opposite compartment for OA patients. The combination of the biomechanical information of an individual, the information gathered from the follow-up study and the use of a statistical learning method such as KRR substantially improved detection of UKA revision risk.

4. Discussion

The prediction in our model focuses on the risk factor of revision collected at the primary operation, and the purpose of this paper is to predict the possibility of failure (usually happen around 24 months after surgery) due to biomechanical factors when they have UKA. In clinical practice, many patients with one sided degenerative disease, one compartment is taking most of the load due to the angular deformity, and thus the opposite side of the knee is protected. However, after UKA correction, the loading force distribution changed from one compartment to the other. Therefore, the protection disappeared in the opposite compartment. The microdamaged cartilage in the untreated compartment will accelerate degeneration due to excessive strain, leading to premature failure of UKA. The clinical data available indicates that the revision is most likely to happen around 24 months after surgery.

In Table 1, we can see patient body weight has no direct relationship with the risk of the UKA revision; both groups have patients with high body weight and low body weight. In addition, the knee articular osteochondral tissue behavior could not be characterized only by the loading force, which also does not have a direct relationship with the risk of the UKA revision. Because other factors such as shape of tissue and tissue properties are need to be considered. Consequently, 3D FEM was applied to extracting biomechanical strain information for predicting the risk factor of UKA revision.

The mean strain change is calculated from pre-operative and post-operative strain (Table 1). In many cases, the strain change values in UKA revision group are greater than those in UKA only group. However, it can be seen that the mean strain change values of some UKA only cases (e.g.47^th, 49^h, and 63^th, et.al) are overlapped with the revision cases (69^th, 70^th, and 78^th). So no threshold value exists to distinguish these two groups. In our model, the prediction results shows cases 69^th, 70^th, and 78^th need revision, because the distribution of strain change for different regions in the cartilage is different. Some regions with high strain change will accelerate degeneration, although the mean strain change of all nodes seems normal in these cases. In the UKA only cases, the mean strain change of some case (e.g.47^th, 49^th, and 63^th, et.al) is bigger than the other cases, the patients still did not feel severe pain because about 60 to 80 percent of the load is distributed through the medial compartment of the normal knee²⁵. In lateral compartment, fewer loads will affect it, but strain feature of knee articular osteochondral tissue can still reflect its behaviors definitely. If the distribution of strain change is smooth, the pain with degeneration won't appear, regardless of the mean strain change. But in some area, if the cartilage is micro-damaged on account of initial stage of osteoarthritis degeneration and the distribution of strain change is irregular, the patient will suffer apparent pain with degeneration. Fig. 5 demonstrates the color map of strain and deformation simulated by ANSYS. Thus, KRR statistic model was selected to learn the distributions of strain change associating with the risk of the UKA revision.

Fig. 5.

The color map of strain and deformation simulated by ANSYS. (A) strain distribution color map. (B) deformation distribution color map.

The number of false positives in our model is 3 (72^th, 76^th and 77^th) with lower prevalence (14%)⁹. That because other non-biomechanical problems which were not collected are potentially better predictors. For the 72^th cases, severe deformity resulted in unbalance force in two compartments, and thus the Oxford Knee Score decreased by the pain from unbalance force. As for 76^th and 77^th cases, surgical failure resulted from implants loosening which is not our research object in this model.

In addition, the prediction in 29^th and 54^th failed, because patients in both cases are over weighted. For those obesity patients with difficulties in movement, they are less involved in exercise, which in turn delays the degeneration of the cartilage in the opposite compartment.

Leave-one-out (LOO) cross-validation (CV) was implemented to assess the accuracy of our approach as internal validity. Our model has a strong AUC of prediction (AUC=0.93) in ROC curve based on randomly selected 78 cases which showed in Fig. 4. Thus the result of the study at least can be fairly generalized to the other osteoarthritis patients in the Wake Forest Baptist medical center. If the demographic and clinical characteristics of OA patients are similar in other medical centers, our model can be generalized to other patients similarly situated medical centers. In addition, we will work with other institutes to validate our model in other different populations to establish the external validity in the future.

The limitations of our study are that there is very small numbers and we do not have the capability of accounting for factors other than biomechanical. The limitations in this study cause revision are no chronic pain syndrome; no severe angular deformity; the axis deformity of femur and tibia should be not exceed 10° varus or valgus; no fracture, infection, prosthesis instability, prosthesis loosening and stiffness, no lateral unicompartmental arthroplasty.

In conclusion, this study demonstrated a systematic approach to predict risk of UKA revision. A 3D FEM of the knee articular osteochondral tissue was constructed to extract biomechanical strain information. The KRR method was used to model the relationships between the biomechanical strain information and the risk of UKA revision. We have combined biomechanical and statistical learning modeling to create a surgical planning tool which may support clinical decision making to avoid UKA revisions prior to the surgery in the future.