Nonlinear dynamics stability measurements of locomotion in healthy Greyhounds

Dan B. Marghitu From the Department of Mechanical Engineering, College of Engineering (Marghitu), and Department of Anatomy and Histology, College of Veterinary Medicine (Kincaid, Rumph). Auburn University, AL 36849.

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Steven A. Kincaid From the Department of Mechanical Engineering, College of Engineering (Marghitu), and Department of Anatomy and Histology, College of Veterinary Medicine (Kincaid, Rumph). Auburn University, AL 36849.

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Paul F. Rumph From the Department of Mechanical Engineering, College of Engineering (Marghitu), and Department of Anatomy and Histology, College of Veterinary Medicine (Kincaid, Rumph). Auburn University, AL 36849.

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Abstract

Objective

To characterize normal locomotion of dogs, using nonlinear dynamic stability measurements to analyze two-dimensional kinematic data.

Animals

5 healthy, orthopedically sound Greyhounds.

Procedure

Data were studied by sequentially constructing phase plane portraits from the angular velocity and displacement data; creating first-return (Poincare) maps from periodically sampled data; and evaluating the dynamic stability of the gait, using Floquet multipliers calculated from the assembled data. Retroreflective markers were placed on the left craniodorsal aspect of the iliac spine, greater trochanter, lateral epicondyle of the femur, lateral malleolus, and fifth metatarsophalangeal joint. Each dog was repeatedly led at a trot along a 10-m runway. Data were collected, using a video-based, two-dimensional motion measurement and analysis system. Dogs were considered a nonlinear system and were represented by the joint angular displacements and velocities. Phase plane portraits and first-return maps were constructed to analyze the smoothed data. The Floquet theory was then used to investigate the local stability of critical points of the discrete map.

Results

The femorotibial joint had the highest angular velocity, ranging from −2.5 to 4.9 radians/s. Tarsal joint velocity ranged from −2.7 to 3.2 radians/s, and the coxofemoral angle had the lowest range of −2.2 to 2.2 radians/s. The points on the first-return maps converged to the 45° diagonal line and were clustered together. The largest Floquet multiplier averaged 0.452, which characterized the stability of this population and will be used to draw a comparison between this and future work.

Conclusions

Nonlinear dynamics can be effectively used to analyze two-dimensional kinematic data from animal models to quantify the dynamic stability of animal locomotion through precise mathematical measurements. The method is general and can be applied to normal or abnormal gaits.

Clinical Relevance

Point mapping and quantitative measurement of joint movement have several advantages associated with the application to animal and human locomotion. The clinician can visually distinguish the normal gait pattern from abnormal patterns to assist in the diagnosis of musculoskeletal abnormalities (diseases). (Am J Vet Res 1996;57:1529–1535)

Abstract

Objective

To characterize normal locomotion of dogs, using nonlinear dynamic stability measurements to analyze two-dimensional kinematic data.

Animals

5 healthy, orthopedically sound Greyhounds.

Procedure

Data were studied by sequentially constructing phase plane portraits from the angular velocity and displacement data; creating first-return (Poincare) maps from periodically sampled data; and evaluating the dynamic stability of the gait, using Floquet multipliers calculated from the assembled data. Retroreflective markers were placed on the left craniodorsal aspect of the iliac spine, greater trochanter, lateral epicondyle of the femur, lateral malleolus, and fifth metatarsophalangeal joint. Each dog was repeatedly led at a trot along a 10-m runway. Data were collected, using a video-based, two-dimensional motion measurement and analysis system. Dogs were considered a nonlinear system and were represented by the joint angular displacements and velocities. Phase plane portraits and first-return maps were constructed to analyze the smoothed data. The Floquet theory was then used to investigate the local stability of critical points of the discrete map.

Results

The femorotibial joint had the highest angular velocity, ranging from −2.5 to 4.9 radians/s. Tarsal joint velocity ranged from −2.7 to 3.2 radians/s, and the coxofemoral angle had the lowest range of −2.2 to 2.2 radians/s. The points on the first-return maps converged to the 45° diagonal line and were clustered together. The largest Floquet multiplier averaged 0.452, which characterized the stability of this population and will be used to draw a comparison between this and future work.

Conclusions

Nonlinear dynamics can be effectively used to analyze two-dimensional kinematic data from animal models to quantify the dynamic stability of animal locomotion through precise mathematical measurements. The method is general and can be applied to normal or abnormal gaits.

Clinical Relevance

Point mapping and quantitative measurement of joint movement have several advantages associated with the application to animal and human locomotion. The clinician can visually distinguish the normal gait pattern from abnormal patterns to assist in the diagnosis of musculoskeletal abnormalities (diseases). (Am J Vet Res 1996;57:1529–1535)

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