A novel method of determining bone mineral density of the knee from a pre-surgical CT scan to aid in surgical planning

Abstract

Introduction

Patients with reduced bone mineral density (BMD) may have poorer outcomes after cementless joint replacement surgery. BMD phantoms may be used to calibrate Hounsfield units (HU) to BMD values, but BMD assessment with phantoms is not routine prior to surgery. We describe automated BMD calibration using air, fat and an aluminum motion-detection rod in Mako robotic-assisted knee arthroplasty 3D CT image volumes.

Methods

Using 6111 CT knee arthroplasty planning image volumes, including 133 with a BMD phantom (Mindways, TX), mean BMD values were determined for air, fat, and bone equivalent rods as calibration standards. Image voxels containing air were identified using histogram analysis. The rod surface was identified using an Active Appearance Model (AAM) search. At each point on the AAM-segmented femoral bone surface, lines perpendicular to the surface (“normal rays) were sampled and gaussian mixture model histogram analysis was used to identify fat. Ten iterations of 10-fold cross-validation were performed to compare calibration using either the phantom or the air, fat, and rod standards in tibial and femoral trabecular bone.

Results

Trabecular bone BMD from phantom calibrations were highly correlated with BMD values calculated using the air, fat, and rod standards for femur and tibia (r ≈ 0.98). Bland-Altman analysis showed negligible bias of ∼0.3 mg/cm3. The standard deviation of differences was 9.9. mg/cm3, suggesting an upper bound of precision of 9 mg/cm3 (precision error for Mindways phantom is 3.6 mg/cm3), which produces a coefficient of variation of 7.7% at mean BMD=117 mg/cm3.

Conclusion

Accurate volumetric BMD values may be derived at the knee from CT image volumes routinely acquired before robotic-assisted arthroplasty. This information may be useful in informing surgical decisions regarding the use of cementless implants, particularly in patients at risk of osteoporosis.

Introduction

Patients with a reduced bone mineral density (BMD) may have poorer outcomes after joint replacement surgery [1,2]. Some surgeons exercise caution in choosing cementless implants that rely on press-fit fixation for their primary stability in patients with reduced BMD [3]. Biomechanical studies using polyurethane bone analogues have suggested that implant stability is directly related to BMD for cementless implants. When BMD is reduced, fixation is greatly enhanced by the addition of cement [4].

During knee replacement surgery, the choice of cemented or cementless implantation may be made by the surgeon at the time of bone resection, by use of a “thumb test” in which the strength of the trabecular bone is manually judged by applying pressure with the tip of the thumb [5]. An objective measurement of BMD at the knee before surgery may help surgeons to choose between cementless and cemented implants.

Mako (Stryker, Mahwah, NJ) robotic-assisted knee arthroplasty utilizes a 3D CT scan of the joint acquired prior to surgery. The acquisition protocol requires the addition of an aluminum (Al) rod (15.8 mm diameter, 1.3 m in length) fixed to the lateral side of the leg to detect motion during scanning. This rod spans the ankle joint to above the femoral head.

BMD measurement for the diagnosis of low bone mass and osteoporosis is usually done using dual-energy x-ray absorptiometry (DXA) scanning [6]. However, BMD may also be measured using CT scans by using internal or external calibration standards to convert CT Hounsfield units (HU) to BMD values [7]; a technology known as Quantitative CT (QCT), that predates DXA scanning [8]. Although HU can be used to make a crude estimate of BMD tissue values directly, the make and model of scanner, reconstruction kernel, and table height during scanning can all influence the HU of a particular tissue type. For these reasons, the use of internal or external calibration standards will produce a more accurate BMD assessment [9].

Therefore, it is possible that BMD calibration using the CT image volume acquired as part of robotic surgical planning could inform a surgeon’s decision prior to surgery on whether to use cemented or cementless implants. Commercial QCT systems generally require the use of an external calibration phantom containing materials of known BMD values [10]. Internal standards from the patient image volume such as muscle or fat have also been used [11]. However, internal reference standards can be problematic because the effective BMD value of some tissues like muscle can change with hydration state and the dynamic BMD range spanned by these tissues is limited [12].

Here we describe an automated method of BMD calibration from a CT scan acquired for robotic surgery using a mixture of two external BMD reference standards (air and the aluminum motion rod) to provide a wide BMD calibration range, and the use of an internal reference standard (fat) as a third BMD reference value. Our objective was to test whether BMD values derived from these reference standards are equivalent in accuracy and precision to BMD values derived using a commercial phantom.

Methods

Image data

De-identified data sets (Stryker Performance Solutions LLC., Chicago, Illinois, USA) were collected from surgeons performing high-volume robotic-assisted total knee arthroplasty, or unicondylar knee arthroplasty, for knee OA using a standard CT protocol. Supine CT image volumes were available for 6111 knees. Patients had a mean age of 67 years (range, 35–95) and a mean body mass index of 32 (range, 17 – 62); 39.5 % were men [13]. Research on this image data was approved by the Institutional Review Board (IRB) with a waiver of informed consent for minimal risk clinical investigations.

All knee image volumes were acquired using the standard Mako knee arthroplasty protocol. Subjects were positioned supine, headfirst during CT acquisition, with both legs neutrally positioned and knees at full extension. The motion-detection rod was strapped to the affected leg to detect motion; if motion was present, the scan was repeated.. Antero-posterior and lateral views checked initial alignment. Three CT image volume acquisitions were performed at the hip, knee, and ankle joint as part of the Mako CT protocol. Knee joint acquisition included coverage superior to the patella to the tibial tuberosity with contiguous 0.5–1 mm slices. Scanning was performed using a bone reconstruction algorithm with tube voltage of 120–140 kVp and tube current of 200–400 mA with auto-exposure control. Coverage was 10 cm each side of the knee joint line. The motion-detection rod was secured to the lateral side of the joint (see Fig. 4). Of the scans, 133 from a single site contained a three-rod research version of the commercially available five-rod BMD calibration phantom used in the Mindways QCT Pro system (Mindways, Austin, TX), placed under the knee during scanning (the Phantom Set). The three rod phantom was used because of its smaller size, which is more suitable to the knee.

Fig. 4.

Left: Axial slice through the femur with rod above and BMD phantom below. Right: After detection, the rod is labelled in blue, and fat is labelled in green.

Air calibration standard

Image voxels containing air were identified using histogram analysis. In general, the intensity histogram of the entire CT image volume has the form shown in Fig. 1.

Fig. 1.

Histogram (log scale) of Mako knee image characteristics, with peaks corresponding to labeled image features.

Peak detection and filtering algorithms using peak prominence [14]. were used to identify the voxel intensities corresponding to air, based on the histogram of the entire 3D image volume voxel intensity, as demonstrated in Fig. 1.

This algorithm was tested on all 6111 image volumes by visual inspection of image histograms to determine which histogram peak corresponded to the air signal.

Motion rod calibration standard

To rapidly identify and segment the motion rod within the image volume, we developed a 3D active appearance model (AAM) (Imorphics, Manchester, UK), an established image analysis technique [15,16]. that enables accurate cartilage and bone segmentations in large datasets [17,18]. For the motion rod model, the AAM was trained using a random sample of 24 manually segmented image volumes from the dataset. The nonvarying shape of the motion rod meant that a small training set of image volumes could be used, since the training set needed only to provide variation in image appearance surrounding the rod margin. Rod surfaces identified by the AAM-based image search were eroded by a 4 mm radius to exclude partial voxels and beam hardening. To make the result robust to image noise, the median voxel intensity from the segmented rod volume was used as the rod HU value (Fig. 2). The median intensity was selected to provide a more robust estimate in the face of a wide range of image quality. For the majority of datapoints, there was negligible difference between the mean and median. The AAM search was applied to all 6111 CT scans and the resulting motion rod segmentation was inspected visually for accuracy.

Fig. 2.

Left: Normal rays are projected from the femoral surface; only a sparse subset is shown. Right: These normal rays are sampled until a discontinuity is detected, indicating a boundary between soft tissue and either air, bone or cartilage (shown in green).

Adipose tissue (Fat) calibration standard

As part of Mako knee arthroplasty planning, the entire femoral and tibial bone surface geometry is automatically segmented using AAMs. This geometry may be utilized for reliable identification of periarticular soft tissue. Surface-normal rays were projected from the centroids of the triangular elements of the AAM-segmented femoral bone surface (Fig. 2, left) and sampled until a discontinuity in image intensity was detected, representing a soft-tissue boundary to air, bone or cartilage (see Fig. 2, right). Histograms were produced from the combined samples collected along all the rays.

Several methods of detecting the soft-tissue boundary were tested. A simple test of a HU discontinuity of ± 300 HU along the surface-normal vector was able to reliably detect boundaries and discriminate between fat and muscle components. This method was chosen to allow for a range of image quality and would benefit from further development.

A two-gaussian mixture model was used to resolve the histogram of combined soft tissue voxel intensity into fat and muscle tissue along these normal rays (Fig. 3). The mixture model was initialized using the HU corresponding to the cumulative probability densities at 30 % and 70 % of the histogram. The mean value of the lower HU gaussian peak was reported as the fat HU value. An example of segmentation of fat using a lower and upper HU threshold of peak ± 1 SD is shown in Fig. 4.

Fig. 3.

Examples of HU histograms representing the collected signal of soft tissues surrounding four femoral surfaces. Each histogram is shown with curve fitting by a twin gaussian mixture model representing the two soft tissue components of fat (lower HU) and muscle (higher HU).

Determination of BMD calibration values

We used the 133 CT knee arthroplasty planning images that contained a commercial BMD phantom (the “Phantom Set”) to determine the average BMD equivalent values of air, fat and rod as calibration standards. The phantoms were segmented in 3D with a manually thresholded region of interest and the median value was used as the HU value for the three standard tubes within the phantom. Linear least squares fitting of the known equivalent BMD values of these tubes in mg/cm³ was used to determine the equivalent BMD values for the air, fat, and motion rod standards.

Testing the air-fat-rod calibration standard

We performed 10 iterations of 10-fold cross-validation to compare calibration from the commercial phantom tubes versus air-fat-rod standards in trabecular bone of the femur and tibia. Agreement was assessed using linear regression, Bland-Altman plots, and correlation analysis. Using the phantom-based BMD measurements as the reference standard, accuracy was quantified as the bias in the Bland-Altman plots, and precision from the variance around the bias. In each cross-validation iteration, the reference BMD values for air, fat, and motion rod from the 90 % training set (derived using the Mindways Phantom) were used to calibrate the 10 % test set, and the resulting trabecular bone BMD values were compared to the BMD values from the Mindways Phantom calibration in the test set. Trabecular bone samples were produced from all 133 images containing a phantom by eroding the bone volume defined by the previously segmented femoral and tibial surfaces by 4 mm, which is greater than the maximum cortical thickness that might be expected in the distal femur and proximal tibia [19]. Using the previously published precision error figures for the Mindways phantom, we determined the precision error of our method as the coefficient of variation.

Results

Air calibration standard

The air identification algorithm worked reliably in all of the 6111 image volumes and was notably robust, with visual inspection confirming reliable peak detection in several image volumes with partial corruption of pixel data.

Motion rod standard

The motion rod algorithm was determined by visual inspection to have successfully identified the surface of the rod in all 6111 image volumes except for two image volumes in which the motion rods were missing.

Adipose tissue (Fat) standard

The fat acquisition method was successful in all 133 phantom image volumes, and was visually verified using the histogram fits (Fig. 3) and thresholding (Fig. 4).

Determination of calibration standards

Fig. 5 shows the linear fit to the known calibration standards (Tubes A, B, and C) from the commercial phantom and our three image-derived calibration standards (air, fat, aluminum rod). The BMD values for the air, fat, and aluminum rod used as image-derived calibration standards were obtained from the linear fit to the known calibration standards. Table 1 shows the known BMD-equivalent values of the three phantom rods, the BMD-equivalent values for the air, fat, and motion rod from these phantom values, and for comparison, the BMD-equivalent values of the phantom tubes derived using the air–fat–rod standards. These values were computed as the median values from the 133 image volumes of the Phantom Set to ensure robustness against outliers.

Fig. 5.

Phantom BMD values converted from HU for three-tube phantom standards and air–fat–rod standards in 133 image volumes containing phantoms. To demonstrate linearity, a line was constructed between the centers of the air and aluminum rod clusters.

Table 1.

HU values; BMD–equivalent values of the three phantom rods; derived BMD equivalent values for the air, fat and motion rods using the phantom values; and the derived BMD equivalent values for the phantom tubes using the air, fat, and rod standards. BMD values in mg/cm³.

Image feature	Mindways BMD tube values (mg/cm3)	HU values mean (SD)	BMD derived w/ air/fat/rod median (IQR) (mg/cm3)	BMD derived w/ phantom median (IQR) (mg/cm3)
Phantom tube A	−46.91	−70.95 (9.63)	−50.91 (−58.08, −44.31)	-
Phantom tube B	151.80	194.83 (9.28)	147.21 (141.88, 156.50)	-
Phantom tube C	379.65	506.85 (13.64)	382.17 (373.67, 389.12)	-
Air	-	−994.5 (3.02)	-	−742.05 (−753.15, −730.76)
Fat	-	−103.1 (17.72)	-	−76.76 (−83.93, −70.26)
Motion rod	-	2228.67 (32.42)	-	1669.06 (1643.27, 1683.68)

To demonstrate that the phantom based calibration is linear, we have constructed a line between the centers of the air and aluminum rod clusters. Note that this line passes through the centers of the original phantom tube clusters, as well as the fat cluster.

Testing the calibration standards

Results from the 10-fold cross-validation comparisons of the 133 image volumes that included a phantom are shown for trabecular bone at the femur and tibia in Fig. 6. Trabecular bone BMD values from the phantom calibration were highly correlated with BMD values calculated using the air, fat, and rod standards for both femur and tibia (r ≈ 0.98) (Fig. 6 Left). Bland-Altman analysis showed negligible bias of ∼0.2–0.3mg/cm³ (Fig. 6 Right) demonstrating good accuracy of the method. The standard deviation of differences is 9.9 mg/cm³, suggesting an upper bound for short-term precision error of 9 mg/cm³, calculated from combined variances (the precision error for the Mindways phantom is 3.6 mg/cm³)[19], which produces a coefficient of variation of 7.7 % at mean BMD of 117 mg/cm³, similar to the short-term precision reported for a commercial QCT system using internal calibration.

Fig. 6.

Comparison of trabecular bone BMD from phantom calibration and air–fat–rod calibration. Left: Correlation of femur (top) and tibia (bottom). Right: Bland–Altman plots of agreement for femur and tibia.

Discussion

We have shown that accurate volumetric BMD values can be derived at the knee from CT image volumes acquired for robotic arthroplasty planning and that these values are equivalent to those derived from a commercial QCT phantom. Fully automated algorithms have been developed to identify air, motion detection rod and adipose tissue surrounding the knee joint in CT scans. These algorithms demonstrated accuracy and resilience to variability in image acquisition parameters and HU encoding in a large test set of 6111 image volumes.

Air and aluminum calibration standards provided equivalent BMD values that were used to define a linear conversion of HU to BMD equivalent values over a wide dynamic range. The use of adipose tissue as a third standard, with a BMD value between the other two, produces a more accurate linear fit during image calibration. It may also be used in error checking in the determination of these standard in the image volume by evaluating the magnitudes of the three residuals of linear least squares fit. The BMD values calculated using a commercial phantom compared with our method demonstrated minimal bias with a difference of ∼0.2–0.3 mg/cm³, which is clinically negligible.

The standards we have used for our BMD calibration method are a hybrid of an external phantom-based method (air and the motion rod) and an internal calibration standard (fat). We calculated the reproducibility of our method, rather than the test-retest repeatability on the same subject. The coefficient of variation of 7.7 % precision of our method compares favorably to the short-term precision figure of 8.4 % reported for a commercial internal calibration (“phantomless”) system, which used the subject’s paraspinal muscle and subcutaneous fat as calibration standards [12]. Although phantom-based BMD calibration methods may have superior precision, both phantomless and phantom-based systems have proven useful for routine clinical diagnosis and monitoring of osteoporosis. In our case, the proposed application is not the clinical diagnosis of osteoporosis, but rather the identification of poor bone quality prior to surgery. Despite the poorer precision of our system compared to the phantom-based method, we believe it could be useful for binary determination of bone quality; however, more work is needed to construct and test a bone quality classification.

Diagnosis of low BMD depends on comparing measured values to normative reference values. At the spine, these values have already been established for QT-based diagnosis of osteoporosis and low bone mass. However, unlike the wrist, hip or spine, the knee joint is not usually susceptible to osteoporotic fracture, and normative values for BMD have not been established for diagnostic thresholds. Nonetheless, there has been considerable effort devoted to measuring BMD at the knee in individuals with spinal cord injury. In a study of 99 patients with motor-complete spinal cord injury (21 femoral or tibial fractures), trabecular BMD thresholds of 114 mg/cm³ at the distal femur and 72 mg/cm³ at the proximal tibia were associated with fracture, with both measurements obtained at a position 4 % of the length of the bone from the articulating surface [20]. Both of these BMD fracture values are approximately four standard deviations below the mean of the healthy reference cohort. This is a pattern also observed in BMD of the spine, in which the QCT guidelines [21]. provide a threshold for osteoporosis as 80 mg/cm³ which is also approximately four standard deviation below the peak bone mass of healthy individuals. Using this method, it is possible that a threshold could be derived for various depths from the articulating surface in the femur or tibia using the normative data, although additional work would be required to determine whether cemented or cementless knee arthroplasty is appropriate.

The study does have some obvious limitations. First, all development and testing was done on a single scanner. As discussed in the introduction, the make and model of the scanner, reconstruction kernels, table height, and other factors can affect the HU values of particular tissues. In addition, the testing sample size was small (133 image volumes). The choice of boundary detection method allowed for a range of image quality and would benefit from further development. The calibration method introduced here would benefit from further development and testing using a larger, more diverse dataset from multiple sites. Our air, fat, and rod BMD values have been derived from Mako pre-planning CT scans that are acquired according to a protocol specifying an x-ray tube potential of 120 – 140 kV. We would expect energy-dependent equivalent BMD differences in aluminum and the plastics used in the phantom because of energy-related differences in x-ray attenuation characteristics. Therefore, while this may not be an issue for BMD calibration in Mako scans, further work would be required if different CT tube potentials were to be used.

Conclusions

Accurate volumetric BMD values may be derived at the knee from CT image volumes acquired for use in robotic-assisted arthroplasty planning. Algorithms can accurately and autonomously identify air, motion rod, and fat regions on CT image volumes and BMD information may be useful to surgeons when deciding whether to use cementless implants in robotic-assisted knee arthroplasty.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Declaration of the use of generative AI and AI assisted technologies in the writing process

No generative AI or AI assisted technologies were used in the process of writing this manuscript.

Editor Disclosure

The peer review process did not involve Editorial Board Member Alan Brett, and the editorial decision-making was led by editors not involved in the creation of this manuscript.

Declaration of competing interest

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.