Biomechanics and methods of structural analysis

The man had an approximate awareness of his own anatomy until the late Middle Ages, in fact up to 1300 religious taboos prevented the dissection of corpses to increase anatomical knowledge.
After the medieval period, in the humanistic period, the first attempts to give a mechanical justification of the behavior of the human body took place.
Leonardo da Vinci (1452-1519) first turned his interest to the anatomy of the head and brain, and later, around 1490, he studied the proportions of the human body, perhaps passing from a simple descriptor of human nature to a curious discoverer of mathematical relationships that they bind it. In the second half of the first decade of the fifteenth century he investigated the skeleton by studying limbs, entire apparatus, from the hand to the spine, drawing bony elements seen from each side and in section, investigating the musculature and tendons, as well as being interested in other organs.
Criticism has often wondered if Leonardo was only an observer of Nature or an anatomist or even more a physiologist; on the other hand he warned in a piece of the Atlantic Code: “We must understand what is homo, what is life”, not stopping therefore at the organ itself, but taking an interest in its functioning. He, although he did not yet possess the basic elements of Galileo’s modern science, used his knowledge of mechanics and anatomy to deepen the mechanics of walking, jumping, sitting down and getting up from a chair, and he therefore took care to describe shape and function.
The reference point for the classification of biomechanics goes back to the Iatromeccanica School, which had the merit of considering the human organism subject to immutable physical laws. As known, Santorio Santorio (1561-1630), Gian Alfonso Borelli (1608-1679), Giacomo Baglivi (1666-1707) (fig.1) were leaders of this movement.

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Figure 1. Drawing taken from the book “De Motu Animalium”, published posthumously in 1680, by Gian Alfonso Borelli

The most important intuition of the Iatromeccanica School, resulting in the most exasperated and theoretical conception of Giacomo Baglivi, is the so-called “human machine”, that is a mechanical system, composed of a large number of small machines constituting the various organs, whose faulty functioning mechanical is the cause of malaise.
After this period of lively intuitions, which were not followed by concrete applications due to the difficulties of investigation, both biological and mechanical, there was a gradual detachment of engineering and medical research, which continued in different and autonomous ways up to the present day.
Biomechanics, in its current meaning, originates, thanks to technological progress, towards the end of the Second World War, when in the United States substantial resources were placed at the service of systematic investigations aimed at the rehabilitation of veterans; of these resources the scholars culturally linked to the natural sciences, engineers, physicists and mathematicians made significant use. Therefore biomechanics, which characterizes the transition from qualitative to quantitative, is reborn for humanitarian purposes for health care and not as a cultural exercise [1].

First mechanical observations on the bone

The interest in the mechanical properties of bone dates back to at least 1638 when Galileo Galilei made some observations on the mechanical meaning of the shape of bones and on the resistance to bending of solid hollow bodies. After this first interest the subject was more or less forgotten until the end of the first half of the nineteenth century, when the studies of Bourgery (1832) [2], Bell (1834) [3], Wertheim (1847) appeared [4 ], Wyman (1857) [5] and Humphrey (1858) [6].
Bourgery first observed the architectural structure of cancellous bone; Bell stated that in nature the structure of bone segments is optimized in relation to their function, so resistance is achieved with the minimum amount of material.
Historically the first attempt to explain, from the mechanical point of view, the structure of cancellous bone was made by Meyer in 1867 [7]. In that year he published an article entitled “Die Architektur der Spongiosa” in which he reported, representing it on boards, the architecture of cancellous bone found in different skeletal segments (fig. 2).

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Figure 2. Drawings of the trabecular structure in bone segments executed by Meyer (from a table by Meyer, 1867)

Observations of this kind had already been made in previous years, but the originality and also the success of Meyer’s work lie in the fact that he tried to relate the architecture of the bone with its mechanical behavior; he also had the good fortune of being perhaps the protagonist of the first historic collaboration between an anatomist and an engineer; in fact Culmann, stimulated by Meyer’s observations, in the same year reconstructed the geometrical and loading situation of a femur with a curved bar, suitably modeled at one end, known in literature as “Culmann crane” and obtained, with the methods of statics graphic, the trajectories of the main tensions, that is the trajectories identified by the directions of the tensile and compression tensions indicative of the path followed by the transmission of the tensile and compressive forces in the structure subjected to a determined external load (fig. 3) [7].

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Figure 3. On the left is the “Culmann crane” with the trajectories of the main tensions indicated; on the right is a Meyer sketch of the trabecular architecture of a longitudinal section of a proximal human femur. Both the femur and the “Culmann crane” are loaded on their cantilevered ends, as illustrated below on the right (from a Wolff table, 1872) [11]

Wolff, observing the similarity between the trends of the main tensions in the curved bar and the trajectories followed by the cancellous bone, became convinced of the correspondence between the structure of the bone and the trajectories designed by Culmann. On this basis he founded his “law of bone transformation”, which together with the “hypothesis of the trajectory structure” of the trabecular bone is known as Wolff’s law (developed between 1869 and 1892); in it Wollf states that “under load and following pathological alterations of the external form of the bone elements, the transformation of the architecture of the bone follows mathematical laws” (1984) [13]. In the trajectory hypothesis of trabecular bone he argues that the distribution and orientation of the trabeculae alters with varying loading history [9] [10] [11] [12] [13] (fig. 4).

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Figure 4. Trabecular trajectory structure in rachitic bones and in bones that have suffered a fracture that has not been reduced [11]

Roux in 1880 [14] developed the principle of functional adaptation, trying to interpret Wolff’s trajectories as a result of a functional adaptation of the bone; even if this theory was later not entirely convincing, an important basic idea emerges in his work: the formation and reabsorption of bone are controlled by a biological process that depends on a state of local tension.
In those years also the works of Rauber (1876) [15] appeared, whose studies revealed the viscoelastic nature of bone tissue, by Messerer (1880) [16], who was the first to analyze the behavior at break under different stresses of whole bone elements (mandibles, femurs, shins, clavicles, skulls, etc.), observing their dependence on age and sex and introducing the concept of fracture mechanics, by Hülsen (1896) [17], who first recognized bone as anisotropic material; later the topic lost interest, until it became an active field of research in the 1960s.
It can now be considered proven that the bone can be studied, from the mechanical point of view, as a material of engineering. This conviction was reached when the possibility of carrying out measurements on human body tissues that were able to characterize them mechanically occurred, providing results in numerical and graphic form similar to those available for engineering materials; in other words when it was possible to move from a qualitative study of the human body to its quantitative study [18] [19] [20].
The knowledge of the mechanical characteristics of the bone tissue, in particular as regards its behavior under load, is undoubtedly fundamental both to be able to carry out the study in the various physiological and pathological conditions, and to be able to search for replacement materials, and to be able to study the possibility of coupling with other materials.