Computational study of the influence of callus porosity on ultrasound propagation in healing bones

Ultrasound Radiation Force for the Assessment of Bone Fracture Healing in Children: An In Vivo Pilot Study

Vibrational characteristics of bone are directly dependent on its physical properties. In this study, a vibrational method for bone evaluation is introduced. We propose a new type of quantitative vibro-acoustic method based on the acoustic radiation force of ultrasound for bone characterization in persons with fracture. Using this method, we excited the clavicle or ulna by an ultrasound radiation force pulse which induces vibrations in the bone, resulting in an acoustic wave that is measured by a hydrophone placed on the skin. The acoustic signals were used for wave velocity estimation based on a cross-correlation technique. To further separate different vibration characteristics, we adopted a variational mode decomposition technique to decompose the received signal into an ensemble of band-limited intrinsic mode functions, allowing analysis of the acoustic signals by their constitutive components. This prospective study included 15 patients: 12 with clavicle fractures and three with ulna fractures. Contralateral intact bones were used as controls. Statistical analysis demonstrated that fractured bones can be differentiated from intact ones with a detection probability of 80%. Additionally, we introduce a “healing factor” to quantify the bone healing progress which successfully tracked the progress of healing in 80% of the clavicle fractures in the study.

Computational Study of the Effect of Cortical Porosity on Ultrasound Wave Propagation in Healthy and Osteoporotic Long Bones

Computational studies on the evaluation of bone status in cases of pathologies have gained significant interest in recent years. This work presents a parametric and systematic numerical study on ultrasound propagation in cortical bone models to investigate the effect of changes in cortical porosity and the occurrence of large basic multicellular units, simply called non-refilled resorption lacunae (RL), on the velocity of the first arriving signal (FAS). Two-dimensional geometries of cortical bone are established for various microstructural models mimicking normal and pathological tissue states. Emphasis is given on the detection of RL formation which may provoke the thinning of the cortical cortex and the increase of porosity at a later stage of the disease. The central excitation frequencies 0.5 and 1 MHz are examined. The proposed configuration consists of one point source and multiple successive receivers in order to calculate the FAS velocity in small propagation paths (local velocity) and derive a variation profile along the cortical surface. It was shown that: (a) the local FAS velocity can capture porosity changes including the occurrence of RL with different number, size and depth of formation; and (b) the excitation frequency 0.5 MHz is more sensitive for the assessment of cortical microstructure.

In vivo standardization of bone ultrasonometry of the clavicle

OBJECTIVE

The assessment of fracture union includes physical examination and radiographic imaging, which depend on the examiner's experience. The development of ancillary methods may avoid prolonged treatments and the improper removal of implants. Quantitative bone ultrasonometry has been studied for this purpose and will soon be included in clinical practice. The aims of the present study were to assess the feasibility of using this technique on the clavicle and to standardize its in vivo application.

METHODS

Twenty adult volunteers, including 10 men and 10 women without medical conditions or a previous history of clavicle fracture, underwent axial quantitative ultrasonometric assessment using transducers in various positions (different distances between the transducers and different angulations relative to the clavicle).

RESULTS

Similar values of wave propagation velocity were obtained in the different tested set-ups, which included distinct distances between the transducers and angular positions relative to the clavicle. There were significant differences only in the transducers positioned at 0° and at 5 or 7 cm apart.

CONCLUSIONS

The use of bone ultrasonometry on the clavicle is feasible and the standardization of the technique proposed in this study (transducers placed at 45° and at 7 cm apart) will allow its future application in clinical trials to evaluate the healing process of diaphyseal fractures of the clavicle.

Computational modeling of ultrasonic backscattering to evaluate fracture healing

Fracture healing is a complex, regenerative procedure including several phases of recovery as the original mechanical and geometrical features of bone are gradually restored. Ultrasonic evaluation of bone pathologies such as osteoporosis and fracture healing has recently gained significant interest due to the non-invasive and non-radiating nature of the method. In this study, we present numerical simulations of ultrasonic backscattering in simple, two dimensional geometries of healing long bones to investigate the monitoring capacity of the acoustic pressure in the backward direction. The fracture process was modeled as a 7-stage procedure and the results were compared to the acoustic pressure derived for the case of intact bone. A 100 kHz plane wave was used as the excitation frequency and multiple receivers were placed at a distance of 20 mm from the cortical cortex. It was found that the acoustic pressure profile is gradually restored at the final healing stages approaching the values of intact bone.

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.