What Is Biomechanics? imply stated, biomechanics is mechanics applied to biology. The word “mechanics” itself was used by Galileo as a subtitle to his book Two New Sciences (1638) to describe force, motion, and strength of materials. Through the years its meaning has been extended to cover the study of the motions of all kinds of particles and continua, including quanta, atoms, molecules, gases, liquids, solids, structures, stars, and galaxies. In a generalized sense it is applied to the analysis of any dynamic system. Thus thermodynamics, heat and mass transfer, cybernetics, computing methods, etc., are considered proper provinces of mechanics. The biological world is part of the physical world around us and naturally is an object of inquiry in mechanics. Biomechanics seeks to understand the mechanics of living systems. The motivation for research in this area comes from the realization that physiology can no more be understood without biomechanics than an airplane can without aerodynamics. For an airplane, mechanics enables us to design its structure and predict its performance. For all organ biomechanics helps us to understand its normal function, predict changes due to alterations, and propose methods of artificial intervention. Thus diagnosis, surgery, and prosthesis are closely associated with biomechanics. The Finite Element Method The finite element technique was invented in 1956 as an extension of the matrix displacement method and the term finite element analysis first used by Clough who applied the process for the purpose of calculating structural integrity.[28, 29] However, the relative scarcity of computers at that time limited its general application. The introduction of personal computers in the 1970's initiated widespread employment of matrix analysis particularly the finite element method to a wide variety of real-world problems. By using a computer to sum the many elements, a total solution can be reached and this solution made as accurate as desired by simply creating smaller and smaller elements. While some of the methods employed in this work are not suited for use with soft tissue, such as the cornea, the underlying process can certainly be applied in ophthalmology. These methods, relying as they do on proven techniques of hypothesis, experimentation, and comparison of data to hypothetical models, yield quantitative data in distinction to the morphologic, qualitative measurements more commonly employed in ophthalmology today. Thus, a rigorous model of the cornea and eye can be constructed and vigorously tested in detailed studies — in ways which may not even have been envisioned in forming the original model. These studies can then, at least in theory, be carried over into actual surgery. There are, nonetheless, caveats in a too rigorous acceptance of such data because of certain shortcomings of method (see Caveats for the Prudent and Thoughtful). The mathematical process to bring this data together in one coherent whole must first be established. Traditional descriptions of physical phenomena have often been limited to a single equation or set of equations which yields a single number or multiple well defined numbers as described for radial keratotomy by Durnev.[24] Such a method is a closed solution to the problem since the variables are all known and the result is tied to these variables by means of the equations. Another approach is through regression analysis. In this method the postoperative results for a given group of patients is used to predict the outcome of surgery for a similar group using statistics and curve fitting. However, since the regression model depicts the outcome for a group of patients with a wide standard deviation — it is difficult if not impossible to predict individual cases. Furthermore, different regression models may identify different variables as important in determining outcome thereby increasing the confusion. This underscores Bores’ Fourth Rule of Refractive Surgery: one guru at a time is plenty . Figure 2. A model containing finite elements Figure 3. A finite element In a system as complex as the human cornea, it is not surprising that, although a number of closed mathematical models have been proposed for the prediction of various procedures on the cornea, their reliability has been limited by the complexity of the corneal structure.[13, 25-27] A different approach is the so called iterative or open solution in which a complex structure is broken into many small simpler components or finite elements. Here the cornea is assumed to be a structure that conforms in a predictable way to accepted laws of physics in response to applied forces. Such a model, however, requires foreknowledge of the geometry of the cornea and supporting tissue along with the material properties of the constituent soft tissues making up the eye. An analogy would be a wall constructed of bricks — said bricks being the small bits or elements constituting the wall. We can say something about the wall by knowing something about the bricks. Besides, it's easier to handle and test one brick than the entire wall. As can be seen, the number of such elements could be quite large. In a typical corneal model, for example, there will be as few as 300 elements although there are usually many times that number. Each of the elements (bricks) has nodes at each corner and at each midpoint (Figures 2 & 3). It is at these nodes that each brick is attached to another. In the model, each of these nodes is conceived as being perfectly joined forming a continuum — each element deforming in synchrony to every other element. Within each separate element, a simple displacement field is assumed and the continuity of these fields rigorously enforced within the polynomial interpolation. © Leo D. Bores, MD - 2002