Effect of ultrasound on bone fracture healing: A computational mechanobioregulatory model.

Bone healing process is a complicated phenomenon regulated by biochemical and mechanical signals. Experimental studies have shown that ultrasound (US) accelerates bone ossification and has a multiple influence on cell differentiation and angiogenesis. In a recent work of the authors, a bioregulatory model for providing bone-healing predictions was addressed, taking into account for the first time the salutary effect of US on the involved angiogenesis. In the present work, a mechanobioregulatory model of bone solidification under the US presence incorporating also the mechanical environment on the regeneration process, which is known to affect cellular processes, is presented. An iterative procedure is adopted, where the finite element method is employed to compute the mechanical stimuli at the linear elastic phases of the poroelastic callus region and a coupled system of partial differential equations to simulate the enhancement by the US cell angiogenesis process and thus the oxygen concentration in the fractured area. Numerical simulations with and without the presence of US that illustrate the influence of progenitor cells' origin in the healing pattern and the healing rate and simultaneously demonstrate the salutary effect of US on bone repair are presented and discussed.

Effect of ultrasound on bone fracture healing: A computational bioregulatory model.

Bone healing is a complex biological procedure in which several cellular actions, directed by biochemical and mechanical signals, take place. Experimental studies have shown that ultrasound accelerates bone ossification and has a multiple influence on angiogenesis. In this study a mathematical model predicting bone healing under the presence of ultrasound is demonstrated. The primary objective is to account for the ultrasound effect on angiogenesis and more specifically on the transport of the Vascular Endothelial Growth Factor (VEGF). Partial differential equations describing the spatiotemporal evolution of cells, growth factors, tissues and ultrasound acoustic pressure and velocity equations determining the development of the blood vessel network constitute the present model. The effect of the ultrasound characteristics on angiogenesis and bone healing is investigated by applying different boundary conditions of acoustic pressure at the periosteal region of the bone model, which correspond to different intensity values. The results made clear that ultrasound enhances angiogenesis mechanisms during bone healing. The proposed model could be regarded as a step towards the monitoring of the effect of ultrasound on bone regeneration.

Evaluation of ultrasonic scattering for different cortical bone porosities and excitation frequencies: A numerical study.

Quantitative ultrasound is a promising and relative recent method for the assessment of bone. In this work, the interaction of ultrasound with the porosity of cortical bone is investigated for different frequencies. Emphasis is given on the study of complex scattering effects induced by the propagation of an ultrasonic wave in osseous tissues. Numerical models of cortical bone are established with a porosity of 0, 5 and 10% corresponding to healthy homogeneous bone, healthy inhomogeneous bone and normal ageing, respectively. Different excitation frequencies are applied in the range 0.2-1 MHz. The scattering amplitude and the acoustic pressure are calculated for multiple angles and receiving positions focusing on the backward direction. The results indicate that the application of higher frequencies can better distinguish changes in the energy distribution in the backward direction due to alterations of the cortical porosity.

Numerical evaluation of the backward propagating acoustic field in healing long bones.

The propagation of ultrasound in healing long bones induces complex scattering phenomena due to the interaction of an ultrasonic wave with the composite nature of callus and osseous tissues. This work presents numerical simulations of ultrasonic propagation in healing long bones using the boundary element method aiming to provide insight into the complex scattering mechanisms and better comprehend the state of bone regeneration. Numerical models of healing long bones are established based on scanning acoustic microscopy images from successive postoperative weeks considering the effect of the nonhomogeneous callus structure. More specifically, the scattering amplitude and the acoustic pressure variation are calculated in the backward direction to investigate their potential to serve as quantitative and qualitative indicators for the monitoring of the bone healing process. The role of the excitation frequency is also examined considering frequencies in the range 0.2-1 MHz. The results indicate that the scattering amplitude decreases at later stages of healing compared to earlier stages of healing. Also, the acoustic pressure could provide supplementary qualitative information on the interaction of the scattered energy with bone and callus.

Boundary element simulation of ultrasonic backscattering during the fracture healing process.

Competent fracture healing monitoring and treatment requires an extensive knowledge of bone biology and microstructure. The use of non-invasive and non-radiating means for the monitoring of the bone healing process has gained significant interest in recent years. Ultrasound is considered as a modality which can contribute to the assessment of bone status during the healing process, as well as, enhance the rate of the tissues' ossification. This work presents boundary element simulations of ultrasound propagation in healing long bones to investigate the monitoring potential of backscattering parameters. The interaction of a plane wave at 100 kHz with the bone and the callus is examined by calculating the acoustic pressure and scattering amplitude in the backward direction. Callus is considered as a two-dimensional, non-homogeneous medium consisted of multiple layers with evolving material properties. It was shown that the backscattering parameters could potentially reflect the fracture healing progress.

A mechano-regulatory model for bone healing predictions under the influence of ultrasound.

The bone healing process involves a sequence of cellular action and interaction, regulated by biochemical and mechanical signals. Experimental studies have shown that ultrasound accelerates bone solidification and enhances the underlying healing mechanisms. An integrated computational model is presented for deriving predictions of bone healing under the presence of ultrasound.

Ultrasound propagation in cortical bone: Axial transmission and backscattering simulations.

Cortical bone is a heterogeneous, composite medium with a porosity from 5-10%. The characterization of cortical bone using ultrasonic techniques is a complicated procedure especially in numerical studies as several assumptions must be made to describe the concentration and size of pores. This study presents numerical simulations of ultrasound propagation in two-dimensional numerical models of cortical bone to investigate the effect of porosity on: a) the propagation of the first arriving signal (FAS) velocity using the axial transmission method, and b) the displacement and scattering amplitude in the backward direction. The excitation frequency 1 MHz was used and different receiving positions were examined to provide a variation profile of the examined parameters along cortical bone. Cortical porosity was simulated using ellipsoid scatterers and the concentrations of 0-10% were examined. The results indicate that the backscattering method is more appropriate for the evaluation of cortical porosity in comparison to the axial transmission method.

Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones.

Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.

A meshless Local Boundary Integral Equation (LBIE) method for cell proliferation predictions in bone healing.

Bone healing involves a series of complicated cellular and molecular mechanisms that result in bone formation. Several mechanobiological models have been developed to simulate these cellular mechanisms via diffusive processes. In most cases solution to diffusion equations is accomplished using the Finite Element Method (FEM) which however requires global remeshing in problems with moving or new born surfaces or material phases. This limitation is addressed in meshless methods in which no background cells are needed for the numerical solution of the integrals. In this study a new meshless Local Boundary Integral Equation (LBIE) method is employed for deriving predictions of cell proliferation during bone healing. First a benchmark problem is presented to assess the accuracy of the method. Then the LBIE method is utilized for the solution of cell diffusion problem in a two-dimensional (2D) model of fractured model. Our findings indicate that the proposed here LBIE method can successfully predict cell distributions during fracture healing.