Functional Anatomy – Some Thoughts

© James Rooney, D.V.M.

In order to study such complex systems as the functional anatomy of the horse simplification is essential. The ultimate objective, of course, is to understand the entire system in detail, but that is rarely possible or even feasible. Where, for example, does one draw the line in such a reductive analysis? At what point has one left the animal behind and wandered off into particle physics?

If a simple model still looks slightly like a horse or at least a quadruped, I am content and feel that I am still dealing with the overall system. Blum 1967 showed that stick figures can have great generality as abstractions of real world systems. I first bruited the idea in 1989 that stick figures of the horse could be used together with graphical analysis to help pose and answer questions of static and dynamic stability. That theory of stability was further developed and described in Rooney and Robertson 1996 and Rooney 1998 and provides a general theory for the cause of many types of lameness in horses and, no doubt, in most other species including man.

The stick figures were traced from photographs of mounted skeletons for use in the graphical stability analysis. In this report I present some thoughts on these abstract figures and what they might mean for present and/or future study.

The foreleg and hindleg are represented by straight line segments as in Fig. 1.

These segments Blum 1967 has shown can contain all the information necessary for the reconstruction of the original shape provided that the information was stored as the line segment was being formed. In a sense the straight line segment is a template with the anatomy of specific regions encoded along its length.

In mathematical terms, the shape, Fig. 1, is the solution of the differential equation of the standing foreleg. That is, the solution is a trajectory which shows what happens when a system is subjected to a force. In the case of the leg the shape is determined by the force applied and the resistance of the leg to that force.

Fig.1 Stick figures of the fore and hind legs. The storing of information about leg shape in the bones is indicated by the red and blue lines in the foreleg.

While I know this will be off-putting for many, I do not see how I can present this argument without showing a differential equation:

There are three terms here, and we shall only go into them as far as absolutely necessary. The first term represents the weight on and of the leg. The second term is a damping term and is a measure of the loss of energy from the leg. The last term is called the spring constant and represents how stiff or resistant the leg is to the load (body weight) applied to it.

The first term, then, generally represents the load experienced by the leg while the other two terms determine what the actual shape of the leg will be when it is loaded by the first term. All this is simply to indicate how the leg attains and maintains the shape we see.

For our purposes one of the main reason for making stick figures and formulating an equation like that is to enable us to do a stability analysis and that is, in large part, a matter of formulating differential equations representing the physical system and then examining the solutions of those equations for stability, i.e., does the solution eventually stop changing, change continuously in a regular or irregular manner, or simply go on growing or decreasing without any evidence of coming to a conclusion. Example: does the clock eventually wind down and stop, continue to run periodically or aperiodically, or run wildly round and round, faster and faster until it flies to pieces?

The answer, Rooney 1998, Rooney and Robertson 1996, is that if the stick figure is, indeed, the solution of the differential equation of the leg, then the stability can be discovered by graphical analysis of the solution - the leg - without ever writing out the differential equation. That statement can be generalized to the entire skeleton of the horse or, indeed, any other organism with a skeleton.

Observe in Fig.1 that the overall shapes of the fore and hind legs are similar, so that what we learn from the one can be applied immediately to the other. We shall consider the legs first, followed by the vertebral column.

If a simple column is axially loaded, it will bend into a smooth curve, Fig. 2. If the column is “tied”, fastened at some point along its length to an external object, it will bend into an S-shaped sine curve, Fig. 2. It is immediately apparent that this shape mimics the configuration of the fore and hind leg skeletons reasonably well.

Fig. 2 The curved shape of a column axially loaded, to the left. The S curve of the column axially loaded with constraints (red). These constraints are the attachments of the pectoral muscles to the proximal end of the humerus in the foreleg and the multiple muscular insertions around the stifle in the hindleg.

The tie, for the foreleg, is the attachment of pectoral muscles from the thorax to the proximal end of the humerus. For the hindleg the attachment is the quadriceps femoris, adductor, obturator, biceps femoris, semimembranosus, and semitendinosus at the stifle joint.

This analysis does not, I hasten to say, provide the mechanism by which the leg assumes its characteristic shape. We are building a model of the leg from first premises. That is, we are taking the simplest system to adequately represent the complex leg.

Vertebral Column

The vertebral column presents somewhat more difficult problems. The cervical portion plus the head is a cantilever beam supported at the foreleg. The thoracolumbar column is a simple beam supported at the foreleg and hindleg. The sacrum and tail form another small cantilever beam.

Fig. 3 The shape of the vertebral column, black to red, caused by the acceleration of gravity acting at the mass centers, blue.

In basic form, Fig. 3, there are three centers of mass, one in the neck, thoracolumbar region, and croup. Left to its own devices the simple model assumes the shape of Fig.3 which is clearly not the shape of the standing horse. We add the supraspinous ligament and its continuation through the cervical region as the ligamentum nuchae. As is apparent in Fig.4 the tendency of the thoracolumbar center of mass to bow the back downward – into dorsiflexion – is countered by the moments exerted by the cervical and caudal cantilevers acting by way of the supraspinous ligament.

Fig.4 The resisting elements – supraspinous ligament, ligamentum nuchae – and the shape of the vertebral column.

The supraspinous ligament, then, is serving as the constraint for the vertebral column in the same manner as the muscles constrained the fore and hindlegs.

Again, this does not imply that this is an actual formative or developmental mechanism. It is an model, an analogy, which may help us to understand how the vertebral column was actually formed. Speaking in a scientifically unseemly manner, I might say that this formulation indicates what the development mechanism had in mind when it began to construct the legs and the back.

D’Arcy Thompson (1966) provided essentially the same analysis of the back of the horse as a twin cantilever bridge construction. Here the back is considered in more dynamic terms, but the basic static analysis of Thompson remains valid.

A pleasant feature of this model is that it can be reproduced easily with thin strips of wood, appropriate supports, weights, and rubber bands. That is not trivial. With these materials one can represent what cannot be readily represented mathematically since the horse is not a mathematically analyzable structure. Analyzable, here, has a distinct technical meaning.

Rooney JR and Robertson JL 1996 Equine Pathology. Iowa State University Press. Ames, Iowa.

Rooney JR 1998 The Lame Horse. Meerdink. Neenah, Wisconsin.

Return to Dr. Rooney's home page.