10.4. Applications in Biomechanics of Deformable Bodies

The biomechanics of deformable bodies deals with the forces that cause a change in the dimensions of a body structure (e.g., bone, tendons, ligaments, or muscles). These forces can be tensile, compressive, shear, bend, or torsion, and deformations are classified as elastic, if reversible, or plastic, when irreversible. Biomechanical materials testing makes it possible to assess the mechanical properties (e.g., Young's modulus, Poisson's ratio) of simple or complex body structures and/or of the objects with which they interact (e.g., prostheses or implants), under either normal or pathological conditions. Naturally, test results depend on many factors, such as the geometric properties of the material/structure, how it is handled, or the way the test is performed. Thus, standardization (e.g., ASTM, ISO) and guidelines for testing are mandatory [126,127].
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Figure 10.7 Biomechanics and bioenergetics analysis with XSENS and COSMED K4b2. Courtesy of the Porto Biomechanics Laboratory, www.labiomep.pt.
Broken bones, tendon sprains, and muscle strains happen. Therefore, studying their behavior is important to understand limits, prevent injury, or find compatible materials that could replace them. Moreover, it will allow the optimization of their function and make self-overcoming possible as it occurs in Olympic sports.
SGs are considered the gold standard for bone surface strain measurements [26,128]. In contrast, their use in soft tissues (e.g., ligaments, tendons, or muscles) has been rarely reported, particularly when glued directly to the tissue. The high water content of soft tissues seems to interfere with SG adhesion. In fact, the surface for bonding an SG should be chemically clean, waterproof, and sufficiently rough, and a faulty adhesion could lead to underestimation or erroneous strain readings. Moreover, soft tissues can withstand larger strains and a compliant interface device, such as a buckle, to which the SG can be bonded should it be necessary [4]. The majority of SGs used in biomechanics are of the foil type. Nevertheless, other configurations have been explored, such as the liquid metal SG [4]. Under proper calibration SGs can also be used for sensing of pressure, force, torque, position, etc. The most common transducers that have been used in biomechanics are the implantable force transducer and the modified pressure transducer [4]. In conclusion, FOSs must compete with SGs.
Many applications can be found in reports of the use of FOSs in monitoring force and strain, particularly in dental biomechanics. One of the first applications was a mouthpiece system instrumented with a microbending sensor capable of measuring the bite force [129]. The bite force was also measured with FBG sensors [130]. Another study reports the use of FBG sensors to measure strain and temperature in dental splints during and after placement within the mouth [71,131]. More applications include the use of high-birefringence FBG sensors to measure in vitro orthodontic forces [132], bracket polymer photonic crystal fiber sensors to measure the forces applied in the teeth during realistic orthodontic treatments [133], and FBG sensors to monitor tension at the tooth roots and the maxilla's surface [134].
In the study of Carvalho et al. [135] SGs and FBG sensors were compared and used to understand how the mandible behaves under static and impact loads acting on dental implants. Uncoated FBGs and standard SGs were glued directly to the surface of a human cadaveric mandible (Fig. 10.8). In addition to an excellent correlation between both sensors, the FBG sensor was considered to be more precise in predicting load transfer from the implant to the bone [135]. Fresvig et al. [26] also demonstrated that SGs and FBG sensors are well correlated when measuring strain in acrylic and bone samples.
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Figure 10.8 Schematic representation of the fiber Bragg grating and strain gauge sensors used to measure bone strain at the surface of an implanted cadaveric mandible [4]Reprinted with permission from Elsevier.
The loading effect of several dental implant materials on the stress–strain patterns of different supporting structures (bovine cancellous bone and silicone) was studied using FBG sensors and finite element analysis (FEA). A good agreement was obtained between experimental and numerical results [136].
Usually SGs are applied to measure surface strain. However, FOS properties make them attractive for embedding in the material. This advantage has been explored with FBG sensors to monitor the curing process of dental resin cements [137140] (Fig. 10.9).
Traumatic head and dental injuries can be avoided through the use of protective devices, such as helmets and mouth guards. In the study of Tiwari et al. [141] the absorption capability of mouth guards was studied using pairs of FBG sensors that were bonded in parallel on a mouth guard and a jaw model. The mouth guard was submitted to several impact loads and the absorbed impact energy was calculated. The results reinforced the use of mouth guards as effective protective devices.
Bone cements play an important role in the fixation of implants or prostheses, and their long-term stability is a critical issue in joint biomechanics. In vitro strain and temperature characterization of PMMA-based bone cements of femoral prostheses was studied by Frias et al. [142] at different temperatures and load conditions using FBG sensors. A similar study has contributed to confirming that FBGs are easier to implement and are less time consuming than standard SGs, making them suitable for use in preclinical tests of prostheses and implants [143].
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Figure 10.9 Schematic representation of the setup used to measure the setting expansion and temperature variation that occurred during the setting reaction of dental gypsum. The compensation fiber Bragg grating was placed freely inside a needle to isolate it from the strain. The other was placed directly in contact with the dental material [4]Reprinted with permission from Elsevier.
A large number of implants and prostheses are metallic or incorporate metallic components. In such types of materials, particularly those with significant electrical conductivity, the signal-to-noise ratio can be maximized using FBG sensors, as suggested by Talaia et al. [144]. Seven FBG sensors were glued directly to stainless steel bone plates and the effects of these fracture fixation plates were studied in synthetic femurs (Fig. 10.10).
FBG sensors were also used to classify the stage of in vitro bone decalcification [145]. In this study it was argued that the strain response of bone under loading at a particular site gives a direct indication of the degree of calcium present in the bone.
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Figure 10.10 Schematic drawing of fiber Bragg gratings glued to a stainless steel bone plate [4]Reprinted with permission from Elsevier.
The first contribution of FOSs to measuring the force of ligaments and tendons was an attempt to reduce the errors associated with the large geometry of conventional sensors and to minimize subjects' complaints. This was pursued in the ex vivo experiment by Komi et al. [146] through the use of a PMMA fiber and an intensity-modulated interrogation scheme. The group of Paavo Komi (Biology of Physical Activity Department, University of Jyväskyla, Finland), collaborating with researchers from the Laboratoire de Physiologie, GIP Exercise (Lyon, France), also performed in vivo studies on the Achilles tendon in a variety of activities such as walking and jumping [147151] (Fig. 10.11).
Contradicting the original findings of Komi et al. [146], Erdemir et al. [152] observed a nonlinear relationship between the OF output and the tendon force. The calibration protocol, hysteresis, cable migration, loading rate, joint angle, skin movement, or tendon creep were also pointed out as possible sources of error in force prediction [152155].
FBG sensors could represent a step forward in sensing soft tissue strain or force, but few studies have been published. In the study by Vilimek [156] the force of porcine leg tendons was estimated under loads applied by a tensile machine. It has been argued that FBG measurements are more accurate than those obtained with intensity modulated sensors. FBG sensors were also used by Goh et al. [157] to measure the axial load within the menisci of porcine knee joints. A transverse load was applied and, to relate it better to the measured axial load, the FBG sensor was placed between uneven layers of carbon–epoxy composites using a buckle configuration [71,157]. Behrmann et al. [158] also proposed a novel sensor based on microfabricated stainless steel housings used to convert radial forces into axial forces that were measured by FBG sensors. The sensor was inserted into the Achilles tendon and in vitro experiments were performed using a dynamic gait simulator [158].
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Figure 10.11 Schematic representation of the intensity-modulated force sensor proposed by Komi et al. [146] to be implanted into the human Achilles tendon [4]. IC, integrated circuit; LED, light-emitting diode. Reprinted with permission from Elsevier.
Ren et al. [159] proposed a displacement sensor based on an FBG and shape memory alloy technology to monitor cadaveric tendon and ligament strains. Roriz et al. [160] embedded an FBG sensor into the intervertebral disc (IVD) of a cadaveric porcine spine and measured disc bulging under axial compression (Fig. 10.12).
Roriz et al. [161] also explored the use of FBGs in buckle transducers for tendon strain measurements.
The chest behaves as a deformable body, changing its perimeter and volume during breathing. Macrobending technology has been used to monitor respiratory function using the fiber optical respiratory plethysmography (FORP) technique [162165]. Essentially, the FORP system comprises an expandable belt encircling the chest and an OF loop that changes its radius of curvature as a function of the chest perimeter. This noninvasive technique was first described by Augousti and Raza [166] and presented as an alternative to the respiratory inductive plethysmography technique. Other FORP configurations include long-period grating arrays, which are more sensitive to curvature [167,168]. Or, as in the case of the Wehrle et al. [24] experiment, FBG sensors were used to trigger the pulse burst of electrically assisted ventilation processes and monitor high-frequency respiratory movements (up to 10 Hz).
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Figure 10.12 Schematic representation of the fiber Bragg grating sensor used to measure intervertebral disc bulging under compression [4]Reprinted with permission from Elsevier.
The possibility of embedding FOSs into technical textiles and monitoring the respiratory rate as well as other vital functions was also explored [169]. In fact, a €2.3 million European-funded project (Optical Fiber Sensors Embedded into Technical Textile for Healthcare, or OFSETH) was initiated for that purpose [170] (Fig. 10.13).
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