The extrapolation of biological damage from a biomechanical model requires that a closed-form mathematical damage threshold function (DTF) be included in the model. A DTF typically includes a generic load variable, being the critical load (e.g., pressure, strain, temperature) causing irreversible tissue or cell damage, and a generic time variable, which represents the exposure to the load (e.g., duration, strain rate). Despite the central role that DTFs play in biomechanical studies, there is no coherent literature on how to formulate a DTF, excluding the field of heat-induced damage studies. This technical note describes six mathematical function types (Richards, Boltzmann, Morgan-Mercer-Flodin, Gompertz, Weibull, Bertalanffy) that are suitable for formulating a wide range of DTFs. These functions were adapted from the theory of restricted growth, and were fitted herein to describe biomechanical damage phenomena. Relevant properties of each adapted function type were extracted to allow efficient fitting of its parameters to empirical biomechanical data, and some practical examples are provided.
Amit Gefen and Ron Neulander
Bone is a living tissue, which undergoes continuous renewal to repair local defects. Two separate processes, adaptation and remodeling, are involved when a defect appears. The defect produces stress concentrations that provoke regional adaptation, and is gradually repaired, first by resorption and then by deposition of new bone. Using a mathematical formulation of the adaptation mechanism in trabeculae of cancellous bone, we hypothesize that in some cases, where a microcrack is small enough relative to the dimensions of the trabecula, the adaptation response of the whole trabecula may be sufficient to regain homeostatic mechanical conditions (with no need for a remodeling process). The simulation results showed that for trabeculae with nominal length of 900 µm and nominal thickness of 80–800 µm, a microcrack with minimal length of 48 µm and minimal depth of 13% of the trabecula’s thickness was required to initiate a remodeling process. A longer (100 µm) but shallower (depth of 7% of the trabecula’s thickness) crack also triggered remodeling. These computational results support our hypothesis that when a microcrack small enough relative to the dimensions of the trabecula occurs, adaptation of the whole trabecula may be sufficient to regain homeostatic mechanical conditions with no need for a local remodeling process.
Yaara Nadiv, Ricki Vachbroit, Amit Gefen, David Elad, Uri Zaretsky, Dani Moran, Pinchas Halpern, and Anat Ratnovsky
The respiratory muscles may fatigue during prolonged exercises and thereby become a factor that limits extreme physical activity. The aim of the current study was to determine whether respiratory muscle fatigue imposes a limitation on extreme physical activity of well-trained young men. Electromyography (EMG) signals of respiratory (external intercostal and sternomastoid) and calf muscles (gastrocnemius) were measured (N = 8) during 1 hr of treadmill marching at a speed of 8 km/hr with and without a 15 kg backpack. The root mean square (RMS) and the mean power frequency of the EMG signals were evaluated for calculating fatigue indices. The EMG RMS revealed that the respiratory and calf muscles did not fatigue during the marching without a backpack load. The study did show, however, a significant rise in the EMG values when a backpack was carried with respect to the no-load condition (p < .05), which suggests that respiratory muscles should be trained in military recruits who are required to carry loaded backpacks while marching.