Hierarchical cluster analysis of area and length of foot and ankle ligaments
C Mkandawire, S.B., WR Ledoux, Ph.D., BJ Sangeorzan, M.D., RP Ching, Ph.D.
RR&D Center of Excellence for Limb Loss Prevention and Prosthetic Engineering, VA Puget Sound Health Care System
Objectives: A computational model of the human foot and ankle has been developed by our research group to assist in the treatment of diabetic foot ulcers. The model currently includes 51 ligaments, with each ligament modeled as a spring and dashpot in parallel. Materials testing has been conducted on ankle ligaments (Funk 2000, Siegler 1988), but little work has been done on foot ligaments. Thus, mechanical properties for the 51 modeled ligaments were extrapolated from Sieglerís ankle ligament data (1988). We hypothesize that the mechanical properties of a representative sample of ligaments, based on similar area and length relationships, can be used to predict the properties of all ligaments in our computational model. The purpose of this research was to identify such groups for mechanical testing.
Methods: Ligament geometry was obtained from the right foot of the female specimen of the NIH Visible Human Project (National Library of Medicine, Bethesda, MD). Digital image analysis software (NIH Image, National Institutes of Health, Bethesda, MD) was used to identify the three-dimensional cross-sectional area and length from the anatomical image set. Resolution in the plane of each microtome was 0.33 mm, with 0.33 mm slice thickness. Thirty-nine of the 51 ligaments in our model were clearly identified with distinct origins and insertions. A hierarchical cluster analysis was performed using SPSS 7.5 (SPSS Inc., Chicago, IL) to group ligaments based on their area and length.
Results: Figure 1 shows seven clusters (1-7) were generated from the cluster analysis. They were plotted as mean area by mean length. Membership of each cluster was as follows, Cluster 1 had 1 member; cluster 2, 2; Cluster 3, 6; Cluster 4, 8; Cluster 5, 11; Cluster 6, 2; and Cluster 7, 9. Figure 1 also includes Sieglerís ligament data (S1-S6) for comparison.
Conclusions: Sieglerís data demonstrates that the stiffness of ligaments can be related to the area and length ratio. Specifically, his data had three groupings of ligaments: S1, S2-S5 and S6. S1, with the smallest area and longest length, was the least stiff, while S6, which had the largest area and smallest length, predictably had the largest stiffness. The members of the last group had similar stiffness, which, as expected, were values between S1 and S6. We have identified a broader spectrum of ligament area and length ratios, and are currently testing these ligaments to prove our hypothesis that ligament geometry can be used to estimate mechanical properties.
References: Funk J.R., Hall G.W. (2000). et al. J Biomech Eng. 122(1):15-22.
Siegler S., Block J., et al. (1988). Foot & Ankle. 8(5):234-242.
Funding Acknowledgment: Supported by Rehabilitation Research and Development Service, project number A0806C and the 2000-2001 VA Predoctoral Fellowship Award.