Bone and skin

Perhaps the most obvious biological application of finite-element modelling, given the popularity of the technique in mechanical engineering, is in bone mechanics. The structural properties of bone are determined by non-cellular organic and inorganic components. It is only these components that are included in the simplest models. The potential exists to assess quantitatively an individual patient's risk of bone fracture, which has significant clinical implications in an ageing population. Currently, estimates of this risk are limited by the inability to allow for complex structural features within the bone. However, if the internal structure of a bone was determined in vivo, using X-ray-based computed tomography, an accurate finite-element model could be built to estimate the maximum load that can be borne before fracture. Finite-element models can aid in surgical spine-stabilisation procedures, thanks to their ability to cope well with the irregular geometry and composite nature of the vertebrae and intervertebral discs.

The acellular structure of real bone is modified continuously according to the internal stresses caused by applied loads. This process, which represents an attempt to optimize the strength-to-weight ratio in a biological structure, is achieved by the interaction between two types of cell, one that absorbs bone and the other that synthesises new bone. New bone is added where internal stresses are high, and bone is removed where stresses are low. An accurate finite-element model of this combined process could be used clinically to determine the course of traction that will maximise bone strength after recovery from a fracture.

Another well-established area of mechanical finite-element analysis is in the motion of the structures of the human middle ear (Figure 9.3). Of particular interest are comparisons between the vibration pattern of the eardrum, and the mode of vibration of the middle-ear bones under normal and diseased conditions. Serious middle-ear infections and blows to the head can cause partial or complete detachment of the bones, and can restrict their motion. Draining of the middle ear, to remove these products, is usually achieved by cutting a hole in the eardrum. This invariably results in the formation of scar tissue. Finite-element models of the dynamic motion of the eardrum can help in the determination of the best ways of achieving drainage without affecting significantly the motion of the eardrum. Finite-element models can also be used to optimise prostheses when replacement of the middle-ear bones is necessary.

Figure 9.3. The human ear is divided into three main parts. The outer ear collects sound and directs it down the ear canal towards the eardrum. The size of the eardrum, combined with the lever action of the three bones of the middle ear, ensures the efficient conduction of sound from the ear canal, which is filled with air, to the inner ear, which is filled with a liquid. Very small muscles, not shown here, are connected to these bones to protect the ear from very loud sounds. The inner ear consists of two parts. Only the cochlea is shown, which is the part of the human ear that is responsible for converting sound into electrical signals in the auditory nerve. The other part of the inner ear, the vestibular organ, is involved in balance.

outer

Figure 9.3. The human ear is divided into three main parts. The outer ear collects sound and directs it down the ear canal towards the eardrum. The size of the eardrum, combined with the lever action of the three bones of the middle ear, ensures the efficient conduction of sound from the ear canal, which is filled with air, to the inner ear, which is filled with a liquid. Very small muscles, not shown here, are connected to these bones to protect the ear from very loud sounds. The inner ear consists of two parts. Only the cochlea is shown, which is the part of the human ear that is responsible for converting sound into electrical signals in the auditory nerve. The other part of the inner ear, the vestibular organ, is involved in balance.

Finite-element techniques can cope with large, highly non-linear deformations, making it possible to model soft tissues such as skin. When relatively large areas of skin are replaced during plastic surgery, there is a problem that excessive distortion of the applied skin will prevent adequate adhesion. Finite-element models can be used to determine, either by rapid trial-and-error modelling or by mathematical optimisation, the best way of covering a lesion with the available skin graft. The brain is another organ that is mechanically soft. Certain brain disorders are associated with variations in pressure in the cerebrospinal fluid that protects the brain from the hard skull. Imaging techniques can provide information about the resulting changes in brain shape, but finite-element models of the fluid-structure interactions have the potential to provide quantitative information about the forces exerted on the tissue itself.

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