Diabetes is Associated with a Lower Minimum Moment of Inertia Among Older Women: An Analysis of 3D Reconstructions of Clinical CT Scans

Abstract

Hip fractures are a heavy burden on the aging population, often resulting in reduced mobility, loss of independence, and even death. While fracture risk is generally inversely related to bone mineral density (BMD), people with diabetes suffer a higher fracture rate despite having a higher BMD. To better understand the connection between diabetes and fracture risk, we developed a method to measure the minimum moment of inertia (mMOI; a geometric factor associated with fracture risk) from clinical CT scans of the pelvis. Since hip fractures are most prevalent along the femoral neck and in female adults, we hypothesized that females with diabetes would have a lower mMOI along the femoral neck than those without diabetes, indicative of a higher fracture risk. Three-dimensional models of each hip were created from clinical CT scans of 40 older women (27 with diabetes: 10 fracture/17 non-fractured; 13 without diabetes: non-fractured controls). The mMOI of each hip (n=80) was reported as the average from three trials. People with diabetes had an 18% lower mMOI as compared to those without diabetes after adjusting for age and BMI (p=0.02). No differences in the mMOIs between the fractured hips of people with diabetes (3.4±1.2 cm⁴) and the contralateral non-fractured hips (3.4±0.9 cm⁴; p=0.78) or those of the non-fractured hips of people with diabetes (2.8±0.7 cm⁴; p=0.12) were observed. This suggests structural differences in the hips of individuals with and without diabetes (measured by the mMOI) may be associated with the elevated fracture rate among adults with diabetes.

INTRODUCTION

The one-year mortality rate after suffering a hip fracture is approximately 30%, which is due to decreased mobility, loss of independence, and multiple comorbidities associated with these injuries (Bentler et al., 2009; Moran et al., 2005). Hip fractures are also commonly associated with pain and disability in the elderly population (Bentler et al., 2009; Moran et al., 2005). Thus, hip fracture prevention is of the utmost importance. Specifically, identifying factors that may increase one’s likelihood of suffering a hip fracture is critical to these prevention efforts. One factor that is often linked to an increased fracture risk is a decreased bone mineral density (BMD), as is seen in individuals with osteoporosis (Unnanuntana et al., 2010). Interestingly, individuals with diabetes (approximately 27% of US adults 65 years or older (Centers for Disease Control and Prevention, 2020)) are at a higher fracture risk despite having an elevated BMD as compared to healthy controls (Oei et al., 2013), yet the reason for this apparent contradiction is currently unclear. Thus, a better understanding of hip fracture mechanics may help to predict and prevent these severe injuries.

Potentially important factors related to fractures include altered structural properties and bony geometries. Specifically, the quantity and geometric distribution of bone are essential for maintaining its rigidity and strength (Bouxsein and Karasik, 2006). The moment of inertia (MOI) is a quantitative material property based on the geometric distribution of a given material with respect to a central axis. Stress increases as the MOI decreases (Hibbeler, 2014); thus, the minimum MOI (mMOI) may be a component of fracture risk (Lambert et al., 2011; Russo et al., 2003). As hip fractures most commonly occur along the femoral neck (53% of all cases) (Fajar et al., 2018; Thorngren et al., 2002), and women account for 70-75% of all hip fractures (Orwig et al., 2006; Sterling, 2011), the primary objective of this investigation was to develop a technique to calculate the mMOI along the femoral neck from computed tomography (CT) scans of older women. Additionally, due to the possible association between the mMOI, diabetes, and fracture risk, we sought to compare the mMOIs between (1) females with diabetes who did and did not suffer a hip fracture and (2) females with and without diabetes. We hypothesized that lower mMOIs would be associated with fracture status in the cohort with diabetes. We further hypothesized that adults with diabetes would have lower mMOIs as compared to their counterparts without diabetes, indicative of a higher risk of hip fracture.

METHODS

Demographics & Image Acquisition

Forty female participants were retrospectively selected for inclusion in this Duke University Institutional Review Board-approved study. Bilateral hip CT images were acquired of each individual’s abdomen prior to any sustained injury for non-musculoskeletal-related complaints. The cohort included 10 women with diabetes who suffered a unilateral hip fracture within 5 years of their CT scan, as well as groups of 17 and 13 women with and without diabetes, respectively, who did not suffer a hip fracture in that same timespan.

Due to differences in fracture incidence and hormones between sexes and between pre- and post-menopausal women, only post-menopausal women were included in this study. Women comprise 70-75% of all hip fracture cases (Orwig et al., 2006; Sterling, 2011). Furthermore, although post-menopausal women have a higher hip fracture risk than pre-menopausal women, age is the primary predictor of hip fracture incidence in these women (Banks et al., 2009). As the primary objective of this work was to develop an algorithm capable of measuring the mMOI along the femoral neck, the current study specifically targeted a high-risk fracture group. Further details about these individuals can be found in Table 1.

Table 1.

Participant Demographics (mean [range])

	Diabetes		No Diabetes	Overall	Diabetes vs. No Diabetes
	Fracture	Non-Fractured	Non-Fractured
Group Size (n)	10	17	13	40	--
Age (years)	77 [60-89]	77 [60-89]	76 [62-84]	76 [60-89]	p = 0.53
Body Mass Index (BMI) (kg/m2)	27.5 [24.4-32.3]	28.9 [21.8-41.3]	29.6 [21.8-29.6]	28.8 [21.8-41.3]	p = 0.37

Image Acquisition & Analysis

Clinical bilateral hip CT images were acquired at four different hospitals within the Duke Health Network on General Electric (GE; Chicago, IL) and Siemens (Erlangen, Germany) systems with varying scan parameters (x- and y-resolution: 0.57-0.94 mm; slice thickness 2.5-7.5 mm; matrix size: 512x512 pixels; voltage potential (peak): 100-140 kVp; tube current: 72-744 mA). The CT images were imported into custom image processing software (MATLAB; The MathWorks, Inc.; Natick, MA). To account for differences between in-plane (x/y) vs. out-of-plane (z, slice thickness) resolution, the images were linearly interpolated along the z-axis to yield isotropic voxels. Next, a patient-specific threshold was selected to optimize the isolation of the bony regions from the CT images to construct a 3D point cloud. The same image threshold was used for all analyses pertaining to a single participant. The resulting point cloud was then manually cropped from both a coronal and an axial perspective to remove points outside of the anatomy of interest (either the left or right hip).

Two lines were then manually drawn along the femoral neck from both the coronal and axial perspectives, respectively (Figure 1A). These lines were used to define the planes perpendicular to the imaging plane, and the axis of the femoral neck was subsequently defined as the intersection of these two planes (Figure 1B). Next, the 3D point cloud was rotated and translated such that the axis of the femoral neck was parallel to the z-axis of the original coordinate system and centered about the origin (Figure 1C). Following this re-orientation, the 3D point cloud was again manually cropped to isolate the femoral neck from the rest of the model.

Figure 1.

(A) Two orthogonal planes were drawn along the femoral neck (from axial and coronal perspectives). (B) The femoral neck axis was defined as the intersection of these orthogonal planes. (C) The 3D bone model was translated and rotated such that the femoral neck axis was parallel with the z-axis and centered about the origin.

Next, the resulting femoral neck point cloud was resliced axially (slice thickness = 1 mm). A 2D moment of inertia matrix, I, was computed with respect to the femoral neck axis for each cross section using the following formulae:

$$I=\left[\begin{array}{cc}{I}_{xx}& -I_{xy}\\ -I_{xy}& I_{yy}\end{array}\right]=\left[\begin{array}{cc}\iint y^{2}dA& -\iint xydA\\ -\iint xydA& \iint x^{2}dA\end{array}\right]$$ (1)

Next, the eigenvalues and eigenvectors of the moment of inertia matrix were calculated. These eigenvalues corresponded to the minimum and maximum moments of inertia within each cross section.

After each femoral neck cross section was analyzed, the global minimum MOI (mMOI) and its corresponding cross section were subsequently identified. This process was repeated three times for each participant, and the resulting mMOIs were averaged to improve the precision of the reported measurements. An additional three trials were run on the contralateral hip for each participant.

Repeatability

All mMOI calculations were performed by a single investigator to eliminate inter-rater variations. To assess the intra-rater repeatability of this technique, this investigator completed three triplicate trials (9 total) on each hip of a randomly selected participant. Each group of three trials were averaged, as described previously. Overall, this technique was shown to be repeatable in quantifying the mMOI along the femoral neck to within a standard deviation of 2% of the mean.

Statistical Analysis

Unpaired t-tests were used to compare BMIs and ages between the cohorts with and without diabetes. A paired t-test was used to compare the mean mMOIs between the fractured and contralateral hips within the injured cohort of adults with diabetes. Next, the mMOIs of both hips were averaged for each participant in the non-fractured cohort of adults with diabetes to yield a single value per person. Then, an unpaired t-test was used to compare the mean mMOIs between fractured and non-fractured hips in the adults with diabetes. Additionally, to account for differences in BMI and age between participants, a multivariate linear regression was performed to compare the mean mMOIs between the cohorts with and without diabetes. All statistical analyses were performed using R (https://www.r-project.org). Significance was determined where p<0.05. All results are presented as the mean±standard deviation.

RESULTS

Participants with and without diabetes had unadjusted mean mMOIs of 3.0±0.9 cm⁴ and 3.4±0.9 cm⁴, respectively (Figure 2A). After adjusting for age and BMI via a multivariate linear regression, individuals with diabetes had on average, an 18% lower mMOI as compared to individuals without diabetes (p = 0.02; Table 2). No differences in the mean mMOIs between the fractured hips in adults with diabetes (3.4±1.2 cm⁴) and their contralateral hips (3.4±0.9 cm⁴; p=0.78) nor those of the non-fractured hips in adults with diabetes (2.8±0.7 cm⁴; p=0.12) were observed (Figure 2B).

Figure 2.

(A) The mean (±standard deviation) mMOI was 18% lower in adults with diabetes as compared to those without diabetes after adjusting for age and BMI using a multivariate linear regression (*p=0.02). (B) No significant differences between the mean (±standard deviation) minimum moment of inertia (mMOI) in contralateral versus fractured hips were observed via a paired t-test (p=0.78). There were also no differences observed between the mean mMOIs in fractured versus non-fractured hips within the cohort of individuals with diabetes via an unpaired t-test (p=0.12).

Table 2.

Multivariate linear regression of mMOI outcome

Variable	Beta coefficient	Standard Deviation	p-value
Diabetes	−0.602	0.248	0.02*
BMI	0.029	0.029	0.32
Age	0.029	0.014	0.05*

^*p<0.05

DISCUSSION

The purpose of this investigation was to develop a method to compute the mMOI along the femoral neck from clinical CT scans. This method was repeatable to within a standard deviation of 2% of the mean, suggesting that this technique may be a viable clinical tool for quantifying hip fracture risk. We observed significantly reduced mMOIs along the femoral necks in individuals with diabetes as compared to those without diabetes. Interestingly, no significant differences were observed between the mMOIs in the fractured and non-fractured hips within the cohort of adults with diabetes. Thus, it is possible that there are systemic changes in bone structure in both hips of individuals with diabetes that predispose them to a higher fracture risk.

Our finding of reduced mMOIs along the femoral necks in individuals with diabetes is in consilience with the literature that suggests that individuals with diabetes have a higher fracture risk (de et al., 2005; Garg et al., 2012; Oei et al., 2013). These differences may be due to differing physical activity levels, mechanical loading, body mass distribution, hormonal differences, or bone metabolic rates (Meisinger et al., 2006; Zhao et al., 2020). Furthermore, other comorbidities associated with diabetes including nerve damage, hypoglycemic episodes, muscle weakness, and vision impairments may predispose these individuals to falls (Lee et al., 2017; Lee et al., 2019). This increased likelihood of a fall coupled with a decreased mMOI may contribute to the elevated risk of hip fracture in adults with diabetes.

Interestingly, despite the elevated risk of fracture in individuals with diabetes, BMD values reported in the literature for patients with diabetes are often elevated as compared to healthy individuals (de et al., 2005; Garg et al., 2012; Oei et al., 2013). This clinical paradox may be due to how BMD is quantified clinically. Specifically, BMD is often measured using dual x-ray absorptiometry (DXA), which relies on 2D projections of bones (Garg et al., 2012). Importantly, BMD is a scalar quantity that does not account for 3D joint geometries (Fonseca et al., 2014; Lakhwani et al., 2017). In contrast, the method developed in this work utilized bilateral clinical CT scans to assess the mMOI along the femoral neck of each hip in 3D.

Researchers have previously used DXA and quantitative computed tomography (qCT) to assess the cross-sectional moment of inertia (CSMI) of the femoral neck. Specifically, the mMOIs quantified in this study (mean=3.1 cm⁴ overall) are similar to values reported by previous studies in the literature. For example, Ramamurthi et al. (2012) measured CSMIs ranging between approximately 1-4 cm⁴ using qCT in a group of 48 older women (Ramamurthi et al., 2012). Using DXA, Li et al. (2019) reported a mean femoral neck CSMI of 2.1 cm⁴ in a cohort of adult Chinese women who suffered a femoral neck fracture (Li et al., 2019). Also using DXA, Ahlborg et al. (2005) measured mean CSMIs of 0.99 cm⁴ and 1.33 cm⁴ in adult females with and without hip fractures, respectively (Ahlborg et al., 2005). Thus, our findings are within the range of previously reported mMOI values in the literature.

Furthermore, we did not stratify our cohort of adults with diabetes based on decreased insulin production (Maahs et al., 2010) versus insulin resistance (Reaven, 2004), which are often characteristic of Type 1 and Type 2 diabetes, respectively. Insulin resistance, in particular, has been associated with decreased bone turnover (decreased C-telopeptide of Type 1 collagen (CTx-1)) (Tonks et al., 2017), which may moderately decrease the fracture risk in these individuals (Tian et al., 2019). Future studies may seek to investigate how these different presentations of diabetes influence the mMOI and fracture risk. Additionally, while we retrospectively followed each study participant over a 5-year period, it is possible that some hip fractures may not have been identified. Specifically, it is possible that our participants may have moved out-of-town or visited a non-Duke medical facility for treatment. Thus, some of our non-fracture cases may have been misclassified. Nonetheless, we were able to differentiate between the mMOIs in the cohorts of individuals with and without diabetes.

In summary, we developed a highly repeatable method to measure the mMOI along the femoral necks of female adults from clinical bilateral CT scans of the pelvis. We demonstrated that the mMOI was decreased in individuals with diabetes compared to those without diabetes, which may contribute to the elevated fracture risk associated with diabetes. Thus, this technique may be a valuable quantitative tool for estimating one’s fracture risk for clinical applications.