Vasilios C. Protopappas

Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.

An ultrasound wearable system for the monitoring and acceleration of fracture healing in long bones

An ultrasound wearable system for remote monitoring and acceleration of the healing process in fractured long bones is presented. The so-called USBone system consists of a pair of ultrasound transducers, implanted into the fracture region, a wearable device and a centralized unit. The wearable device is responsible to carry out ultrasound measurements using the axial-transmission technique and initiate therapy sessions of low-intensity pulsed ultrasound. The acquired measurements and other data are wirelessly transferred from the patient-site to the centralized unit, which is located in a clinical setting. The evaluation of the system on an animal tibial osteotomy model is also presented. A dataset was constructed for monitoring purposes consisting of serial ultrasound measurements, follow-up radiographs, quantitative computed tomography-based densitometry and biomechanical data. The animal study demonstrated the ability of the system to collect ultrasound measurements in an effective and reliable fashion and participating orthopaedic surgeons accepted the system for future clinical application. Analysis of the acquired measurements showed that the pattern of evolution of the ultrasound velocity through healing bones over the postoperative period monitors a dynamic healing process. Furthermore, the ultrasound velocity of radiographically healed bones returns to 80% of the intact bone value, whereas the correlation coefficient of the velocity with the material and mechanical properties of the healing bone ranges from 0.699 to 0.814. The USBone system constitutes the first telemedicine system for the out-hospital management of patients sustained open fractures and treated with external fixation devices.

Velocity dispersion of guided waves propagating in a free gradient elastic plate: Application to cortical bone

The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study, the simplest form of gradient theory (Mindlin Form-II) is used to theoretically determine the velocity dispersion curves of guided modes propagating in isotropic bone-mimicking plates. Two additional terms are included in the constitutive equations representing the characteristic length in bone: (a) the gradient coefficient g, introduced in the strain energy, and (b) the micro-inertia term h, in the kinetic energy. The plate was assumed free of stresses and of double stresses. Two cases were studied for the characteristic length: h=10(-4) m and h=10(-5) m. For each case, three subcases for g were assumed, namely, g>h, g<h, and g=h. The values of g and h were of the order of the osteons size. The velocity dispersion curves of guided waves were numerically obtained and compared with the Lamb modes. The results indicate that when g was not equal to h (i.e., g not equal h), microstructure affects mode dispersion by inducing both material and geometrical dispersion. In conclusion, gradient elasticity can provide supplementary information to better understand guided waves in bones.

Ultrasonic monitoring of bone fracture healing

Quantitative ultrasound has attracted significant interest in the evaluation of bone fracture healing. Animal and clinical studies have demonstrated that the propagation velocity across fractured bones can be used as an indicator of healing. Researchers have recently employed computational methods for modeling wave propagation in bones, aiming to gain insight into the underlying mechanisms of wave propagation and to further enhance the monitoring capabilities of ultrasound. In this paper, we review the relevant literature and present the current status of knowledge.

Multivariate Prediction of Subcutaneous Glucose Concentration in Type 1 Diabetes Patients Based on Support Vector Regression

Data-driven techniques have recently drawn significant interest in the predictive modeling of subcutaneous (s.c.) glucose concentration in type 1 diabetes. In this study, the s.c. glucose prediction is treated as a multivariate regression problem, which is addressed using support vector regression (SVR). The proposed method is based on variables concerning: 1) the s.c. glucose profile; 2) the plasma insulin concentration; 3) the appearance of meal-derived glucose in the systemic circulation; and 4) the energy expenditure during physical activities. Six cases corresponding to different combinations of the aforementioned variables are used to investigate the influence of the input on the daily glucose prediction. The proposed method is evaluated using a dataset of 27 patients in free-living conditions. Tenfold cross validation is applied to each dataset individually to both optimize and test the SVR model. In the case, where all the input variables are considered, the average prediction errors are 5.21, 6.03, 7.14, and 7.62 mg/dl for 15-, 30-, 60-, and 120-min prediction horizons, respectively. The results clearly indicate that the availability of multivariable data and their effective combination can significantly increase the accuracy of both short-term and long-term predictions.

The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone.

Guided wave propagation has recently drawn significant interest in the ultrasonic characterization of bone. In this work, we present a two-dimensional computational study of ultrasound propagation in healing bones aiming at monitoring the fracture healing process. In particular, we address the effect of fluid loading boundary conditions on the characteristics of guided wave propagation, using both time and time-frequency (t-f) signal analysis techniques, for three study cases. In the first case, the bone was assumed immersed in blood which occupied the semi-infinite spaces of the upper and lower surfaces of the plate. In the second case, the bone model was assumed to have the upper surface loaded by a 2mm thick layer of blood and the lower surface loaded by a semi-infinite fluid with properties close to those of bone marrow. The third case, involves a three-layer model in which the upper surface of the plate was again loaded by a layer of blood, whereas the lower surface was loaded by a 2mm layer of a fluid which simulated bone marrow. The callus tissue was modeled as an inhomogeneous material and fracture healing was simulated as a three-stage process. The results clearly indicate that the application of realistic boundary conditions has a significant effect on the dispersion of guided waves when compared to simplified models in which the bones surfaces are assumed free.

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 numerical study on the propagation of Rayleigh and guided waves in cortical bone according to Mindlin’s Form II gradient elastic theory

Cortical bone is a multiscale heterogeneous natural material characterized by microstructural effects. Thus guided waves propagating in cortical bone undergo dispersion due to both material microstructure and bone geometry. However, above 0.8 MHz, ultrasound propagates rather as a dispersive surface Rayleigh wave than a dispersive guided wave because at those frequencies, the corresponding wavelengths are smaller than the thickness of cortical bone. Classical elasticity, although it has been largely used for wave propagation modeling in bones, is not able to support dispersion in bulk and Rayleigh waves. This is possible with the use of Mindlins Form-II gradient elastic theory, which introduces in its equation of motion intrinsic parameters that correlate microstructure with the macrostructure. In this work, the boundary element method in conjunction with the reassigned smoothed pseudo Wigner-Ville transform are employed for the numerical determination of time-frequency diagrams corresponding to the dispersion curves of Rayleigh and guided waves propagating in a cortical bone. A composite material model for the determination of the internal length scale parameters imposed by Mindlins elastic theory is exploited. The obtained results demonstrate the dispersive nature of Rayleigh wave propagating along the complex structure of bone as well as how microstructure affects guided waves.

Evaluation of short-term predictors of glucose concentration in type 1 diabetes combining feature ranking with regression models

Glucose concentration in type 1 diabetes is a function of biological and environmental factors which present high inter-patient variability. The objective of this study is to evaluate a number of features, which are extracted from medical and lifestyle self-monitoring data, with respect to their ability to predict the short-term subcutaneous (s.c.) glucose concentration of an individual. Random forests (RF) and RReliefF algorithms are first employed to rank the candidate feature set. Then, a forward selection procedure follows to build a glucose predictive model, where features are sequentially added to it in decreasing order of importance. Predictions are performed using support vector regression or Gaussian processes. The proposed method is validated on a dataset of 15 type diabetics in real-life conditions. The s.c. glucose profile along with time of the day and plasma insulin concentration are systematically highly ranked, while the effect of food intake and physical activity varies considerably among patients. Moreover, the average prediction error converges in less than d/2 iterations (d is the number of features). Our results suggest that RF and RReliefF can find the most informative features and can be successfully used to customize the input of glucose models.

EFFECT OF TRANSOSSEOUS APPLICATION OF LOW-INTENSITY ULTRASOUND AT THE TENDON GRAFT-BONE INTERFACE HEALING: GENE EXPRESSION AND HISTOLOGICAL ANALYSIS IN RABBITS

The present study investigates the effect of transosseous low-intensity pulsed ultrasound (LiUS) on the healing at tendon graft-bone interface, in molecular and histological level. The anterior cruciate ligament (ACL) in both knees of 52 New Zealand White rabbits was excised and replaced with the long digital extensor. A custom-made ultrasound transducer was implanted onto the medial tibial condyle, adjacent to the surface of the bone tunnel at both knees of the rabbits. The LiUS-treated right knees received 200-mus bursts of 1 MHz sine waves at a pulse repetition rate of 1 kHz and with 30 mW/cm(2) spatial-average temporal-average intensity for 20 min daily (study group), while the left knee received no LiUS (control group). Thirty-six rabbits were used to perform semiquantitative reverse transcription-polymerase chain reaction (RT-PCR) analysis from both study and control groups for transforming growth factor-beta1 (TGF-beta1), biglycan and collagen I. RT-PCR products showed statistically significant upregulation of biglycan and collagen I gene expression in the study group, while TGF-beta1 gene expression exhibited a bimodal profile. Histological examination performed in 16 rabbits from both groups supported the findings of the molecular analysis, indicating a faster healing rate and a more efficient ligamentization process after ultrasound treatment. These findings suggest that transosseous application of LiUS enhances the healing rate of the tendon graft-bone interface, possibly by affecting the expression levels of genes significant for the tendon to bone healing process.