Biomechanics

Introduction

Biomechanics combines engineering and the life sciences by applying principles from classical mechanics to the study of living systems. This relatively new field covers a broad range of topics, including strength of biological materials, biofluid mechanics in the cardiovascular and respiratory systems, material properties and interactions of medical implants and the body, heat and mass transfer into biological tissues, biocontrol systems regulating metabolism or voluntary motion, and kinematics and kinetics applied to study human gait. The great breadth of the field of biomechanics arises from the complexities and variety of biological organisms and systems.

The goals of this chapter are twofold: to apply basic engineering principles to biological structures and to develop clinical applications. Section 4.2 provides a review of concepts from introductory statics and dynamics. Section 4.3 presents concepts from mechanics of material that are fundamental for engineers and accessible to those with only a statics/ dynamics background. Section 4.4 introduces viscoelastic complexities characteristic of biological materials, with the concepts further applied in Section 4.5. The last two sections bring all of this information together in two “real-world” biomechanics applications: human gait analysis and cardiovascular dynamics. The human body is a complex machine, with the skeletal system and ligaments forming the framework and the muscles and tendons serving as the motors and cables. Human gait biomechanics may be viewed as a structure (skeleton) composed of levers (bones) with pivots (joints) that move as the result of net forces produced by pairs of agonist and antagonist muscles, a concept with origins as early as 1680, as depicted in Figure 4.1 from Borelli’s De Motu Animalium (On the Motion of Animals). Consequently, the strength of the structure and the action of muscles will be of fundamental importance. Using a similar functional model, the cardiovascular system may be viewed as a complex pump (heart) pumping a complex fluid (blood) into a complex set of pipes (blood vessels). An extensive suggested reading list for both gait and cardiovascular dynamics permits the reader to go beyond the very introductory nature of this textbook.

The discipline of mechanics has a long history. For lack of more ancient records, the history of mechanics starts with the ancient Greeks and Aristotle (384–322 BC). Hellenic mechanics devised a correct concept of statics, but those of dynamics, fundamental in living systems, did not begin until the end of the Middle Ages and the beginning of the modern era. Starting in the sixteenth century, the field of dynamics advanced rapidly with work by Kepler, Galileo, Descartes, Huygens, and Newton. Dynamic laws were subsequently codified by Euler, LaGrange, and Laplace (see A History of Mechanics by Dugas).

FIGURE 4.1 Plate reproduced from Borelli’s De Motu Animalium, showing animal (human) motion resulting from the action of muscle pairs on bones, serving as levers, allowed to move at joints.

In Galileo’s Two New Sciences (1638), the subtitle Attenenti all Mechanical & i Movement Locale (Pertaining to Mechanics and Local Motions) refers to force, motion, and strength of materials. Since then, “mechanics” has been extended to describe the forces and motions of any system, ranging from quanta, atoms, molecules, gases, liquids, solids, structures, stars, and galaxies. The biological world is consequently a natural object for the study of mechanics.

The relatively new field of biomechanics applies mechanical principles to the study of living systems. The eminent professor of biomechanics Dr. Y. C. Fung describes the role of biomechanics in biology, physiology, and medicine as follows:

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 an organ, biomechanics helps us to understand its normal function, predict changes due to alteration, and propose methods of artificial intervention. Thus, diagnosis, surgery, and prosthesis are closely associated with biomechanics.

Clearly, biomechanics is essential to assessing and improving human health. The following is a brief list of biomechanical milestones, especially those related to the topics in this chapter:

• Galen of Pergamon (129–199) Published extensively in medicine, including De Motu Muscularum (On the Movements of Muscles). He realized that motion requires muscle contraction.

• Leonardo da Vinci (1452–1519) Made the first accurate descriptions of ball-and-socket joints, such as the shoulder and hip, calling the latter the “polo dell’omo” (pole of man). His drawings depicted mechanical force acting along the line of muscle filaments.

• Andreas Vesalius (1514–1564) Published De Humani Corporis Fabrica (The Fabric of the Human Body). Based on human cadaver dissections, his work led to a more accurate anatomical description of human musculature than Galen’s and demonstrated that motion results from the contraction of muscles that shorten and thicken.

• Galileo Galilei (1564–1642) Studied medicine and physics, integrated measurement and observation in science, and concluded that mathematics is an essential tool of science. His analyses included the biomechanics of jumping and the gait analysis of horses and insects, as well as dimensional analysis of animal bones.

• Santorio (1561–1636) Used Galileo’s method of measurement and analysis and found that the human body changes weight with time. This observation led to the study of metabolism and, thereby, ushered in the scientific study of medicine.

• William Harvey (1578–1657) Developed an experimental basis for the modern circulation concept of a closed path between arteries and veins. The structural basis, the capillary, was discovered by Malpighi in 1661.

• Giovanni Borelli (1608–1679) A mathematician who studied body dynamics, muscle contraction, animal movement, and motion of the heart and intestines. He published De Motu Animalium (On the Motion of Animals) in 1680.

• Jan Swammerdam (1637–1680) Introduced the nerve-muscle preparation, stimulating muscle contraction by pinching the attached nerve in the frog leg. He also showed that muscles contract with little change in volume, refuting the previous belief that muscles contract when “animal spirits” fill them, causing bulging.

• Robert Hooke (1635–1703) Devised Hooke’s Law, relating the stress and elongation of elastic materials, and used the term “cell” in biology.

• Isaac Newton (1642–1727) Not known for biomechanics work, but he developed calculus, the classical laws of motion, and the constitutive equation for viscous fluid, all of which are fundamental to biomechanics.

• Nicholas Andre´ (1658–1742) Coined the term “orthopaedics” at the age of 80 and believed that muscular imbalances cause skeletal deformities.

• Stephen Hales (1677–1761) Was likely the first to measure blood pressure, as described in his book Statistical Essays: Containing Haemostatics, or an Account of Some Hydraulic and Hydrostatical Experiments Made on the Blood and Blood-Vessels of Animals; etc., in 1733.

• Leonard Euler (1707–1783) Generalized Newton’s laws of motion to continuum representations that are used extensively to describe rigid body motion and studied pulse waves in arteries.

• Thomas Young (1773–1829) Studied vibrations and voice, wave theory of light and vision, and devised Young’s modulus of elasticity.

• Ernst Weber (1795–1878) and Eduard Weber (1806–1871) Published Die Mechanic der meschlichen Gerwerkzeuge (On the Mechanics of the Human Gait Tools) in 1836, pioneering the scientific study of human gait.

• Hermann von Helmholtz (1821–1894) Studied an immense array of topics, including optics, acoustics, thermodynamics, electrodynamics, physiology, and medicine, including ophthalmoscopy, fluid mechanics, nerve conduction speed, and the heat of muscle contraction.

• Etienne Marey (1830–1904) Analysed the motion of horses, birds, insects, fish, and humans. His inventions included force plates to measure ground reaction forces and the “Chronophotograph a pellicle,” or motion picture camera.

• Wilhelm Braune and Otto Fischer (research conducted from 1895–1904) Published Der Gang des Menschen (The Human Gait), containing the mathematical analysis of human gait and introducing methods still in use. They invented “cyclograph” (now called interrupted-light photography with active markers), pioneered the use of multiple cameras to reconstruct 3-D motion data, and applied Newtonian mechanics to estimate joint forces and limb accelerations.

Basic Mechanics

This section reviews some of the main points from any standard introductory mechanics (statics and dynamics) course. Good references abound, such as Engineering Mechanics by Merriam and Kraige (2008). A review of vector mathematics is followed by matrix coordinate transformations, a topic new to some students. Euler’s equations of motion (see Section 4.2.5) may also be new material. For both topics, Principles of Dynamics by Greenwood provides a comprehensive reference.

FIGURE 4.2 Two-dimensional representation of vector F.