RESEARCH

If you are a student looking for a research project, please contact me for specific projects related to the ideas outlined here. If you are interested in a full list of publications, click here.

Computer-Assisted Musculoskeletal Medicine

Computers have had a profound impact on medicine and that trend will likely continue. Their influence was first seen on the business side of medicine, but computers are increasingly becoming an integral part of the clinical practice of medicine. LOCOS seeks to develop computer-based decision support tools for surgery and rehabilitation. The LOCOS approach is to formulate clinical planning problems as optimization models. This work is done in close collaboration with clinicians. Two examples of this are optimizing shoulder rehabilitation and optimizing distal humerus fracture fixation.

Optimization modeling of rehabilitation. One fundamental fact we all live with is a 24-hour day. Each of us seeks to get as much as possible of out the available time. What exercises should a patient do to maximize the rehabilitation benefit if a person has a limited amount of time for physical therapy exercises? The approach is to formulate an integer programming model to optimally choose a set of exercises to perform. The model is based on a three-dimensional biomechanical model of the shoulder developed by the Delft Shoulder Group and implemented in AnyBody modeling software. This project is being conducted in collaboration with James Carpenter, M.D., who is an orthopaedic surgeon.

Selected relevant publications:

1. Hughes, R.E., Rock, M.G., and An, K-N (1999) Identification of optimal strategies for increasing whole arm strength using Karush-Kuhn-Tucker multipliers.  Clinical Biomechanics  14: 628-634.  This is an early paper and describes my first attempt at formulating an optimal rehabilitation project as a mathematical program. Abstract

Optimization modeling of distal humerus fracture fixation. Consider the problem of placing screws in the distal humerus in an effort to provide stability to a comminuted distal humerus fracture. The surgeon faces may possible screw placement combinations. Some combinations of screws are not feasible because the screws would intersect. Moreover, not all plate holes must have screws placed through them. However, no hole may have more than one screw. We can formulate the problem of determining optimal screw placement by formulating and solving an integer programming model in which the decision variables are Boolean (one 1 if there is a screw; 0 otherwise). The results of one model simulation is illustrated in the figure to the right. This research is too recent to provide references.

Selected resources:

1. If you are not familiar with mathematical optimization, you may want to check out an online educational tool for linear programming.

2. We use an optimization-based method known as support vector machine (SVM) modeling. A good website to learn more about SVM modeling is LS-SVM Lab.

Systems Biology in Musculoskeletal Medicine

Cells are highly complex biochemical networks, and many important musculoskeletal disorders are the result of cellular mechanisms. Therefore, we seek to develop greater understanding of musculoskeletal medicine through the application of systems biology tools and techniques. We focus on developing mathematical models using methods ranging from ordinary differential equations to convex analysis and game theory. In essence, this work involves applying operations research to the study of cells that are major players in the musculoskeletal system. Current work focuses on modeling differentiation of mesenchymal stem cells. Collaborators on these projects include Josh Miller, M.D., Ph.D., and Andrea Alford, Ph.D.

Stochastic Biomechanical Simulation

Most biomechanical models are deterministic. They use one set of model inputs and produce one set of outputs. The inputs may be external loadings and the outputs are typically internal force estimates. However, human performance and human anatomy have a random component. If you perform the same task many times you will not reproduce the same force profile each time. For example, many shoulder disorders are related to the mechanics of the glenohumeral joint, and much of shoulder mechanics is dictated by the shallow geometry of the glenoid fossa. A mathematical analysis of the glenohumeral joint indicates that angulation of the glenoid in the plane of the scapula, which we term "glenoid inclination," affects the ability of the rotator cuff muscles to prevent superior humeral head translation (the figure to the right illustrates glenoid inclination on a radiograph of a human shoulder).  Deterministic models do not explain superior humeral head migration well, as they tend to predict that the net force acting on the humerus points into the glenoid.  However, a stochastic computational model has been developed to investigate the relationship between glenoid inclination and the probability of superior humeral head migration.  The model accounts for the random component of muscle activation, and it predicts that that the probability of superior migration depends on glenoid angle.

The overall objective of our research is to develop and validate a stochastic biomechanical model of the shoulder and elbow to be used in robust design of orthopaedic implants, instrumentation, and techniques for disorders of the shoulder and elbow.

Selected relevant publications:

1. Hughes, R.E. and An, K-N. (1997) Monte Carlo simulation of a planar shoulder model.  Medical and Biological Engineering and Computing 35: 544-548.   Abstract

2. Langenderfer, J., Hughes, R.E., and Carpenter, J.E. (2005) A stochastic model of elbow flexion strength for subjects with and without long head biceps tear. Computer Methods in Biomechanics and Biomedical Engineering 8(5): 315-322. Abstract

3. Langenderfer, J.E., Carpenter, J.E., Johnson, M.E., An, K-N, and Hughes, R.E. (2006) A probabilistic model of glenohumeral external rotation strength for healthy normals and rotator cuff tear cases. Annals of Biomedical Engineering 34(3):465-476. Abstract

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Last updated 10/19/07