An explainable machine learning-based probabilistic framework for the design of scaffolds in bone tissue engineering.

Recently, 3D-printed biodegradable scaffolds have shown great potential for bone repair in critical-size fractures. The differentiation of the cells on a scaffold is impacted among other factors by the surface deformation of the scaffold due to mechanical loading and the wall shear stresses imposed by the interstitial fluid flow. These factors are in turn significantly affected by the material properties, the geometry of the scaffold, as well as the loading and flow conditions. In this work, a numerical framework is proposed to study the influence of these factors on the expected osteochondral cell differentiation. The considered scaffold is rectangular with a 0/90 lay-down pattern and a four-layered strut made of polylactic acid with a 5% steel particle content. The distribution of the different types of cells on the scaffold surface is estimated through a scalar stimulus, calculated by using a mechanobioregulatory model. To reduce the simulation time for the computation of the stimulus, a probabilistic machine learning (ML)-based reduced-order model (ROM) is proposed. Then, a sensitivity analysis is performed using the Shapley additive explanations to examine the contribution of the various parameters to the framework stimulus predictions. In a final step, a multiobjective optimization procedure is implemented using genetic algorithms and the ROM, aiming to identify the material parameters and loading conditions that maximize the percentage of surface area populated by bone cells while minimizing the area corresponding to the other types of cells and the resorption condition. The results of the performed analysis highlight the potential of using ROMs for the scaffold design, by dramatically reducing the simulation time while enabling the efficient implementation of sensitivity analysis and optimization procedures.

Gradient 3D Printed PLA Scaffolds on Biomedical Titanium: Mechanical Evaluation and Biocompatibility.

The goal of the present investigation was to find a solution to crucial engineering aspects related to the elaboration of multi-layered tissue-biomimicking composites. 3D printing technology was used to manufacture single-layered and gradient multi-layered 3D porous scaffolds made of poly-lactic acid (PLA). The scaffolds manufacturing process was optimized after adjusting key printing parameters. The scaffolds with 60 µm side length (square-shaped pores) showed increased stiffness values comparing to the other specimens. A silicone adhesive has been further used to join biomedical titanium plates, and the PLA scaffolds; in addition, titania nanotubes (TNTs were produced on the titanium for improved adhesion. The titanium-PLA scaffold single lap joints were evaluated in micro-tensile testing. The electrochemical processing of the titanium surface resulted in a 248% increase of the ultimate strength in the overlap area for dry specimens and 40% increase for specimens immersed in simulated body fluid. Finally, the biocompatibility of the produced scaffolds was evaluated with primary cell populations obtained after isolation from bone residual tissue. The manufactured scaffolds present promising features for applications in orthopedic implantology and are worth further.

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.

Concrete wave dispersion interpretation through Mindlin's strain gradient elastic theory.

Classical elastic wave features like pulse velocity and attenuation have been used for decades for concrete condition characterization. Relatively recently the effect of frequency has been studied showing no doubt over the dispersive behavior of the material. Despite the experimental evidence, there is no unified theory to model the material and explain this phase velocity change at frequencies below 200 kHz. Herein, the Mindlin's strain gradient elastic theory including the additional micro-stiffness and micro-inertia parameters is considered as an alternative of multiple scattering theory. Experimental results are produced from material with dictated microstructure using a specific diameter of glass beads in cement paste. Results show that Mindlin's theory provides conclusions on the microstructure of the material and is suitable for describing the observed dispersion in different length scales (from millimeters in the case of mortar to several centimeters in the case of concrete).

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.

Non-linear dynamic modeling of glucose in type 1 diabetes with kernel adaptive filters.

We propose a non-linear recursive solution to the problem of short-term prediction of glucose in type 1 diabetes. The Fixed Budget Quantized Kernel Least Mean Square (QKLMS-FB) algorithm is employed to construct a univariate model of subcutaneous glucose concentration, which: (i) handles nonlinearities by transforming the input space into a high-dimensional Reproducing Kernel Hilbert Space and, (ii) finds a sparse solution by retaining a representative subset of the training input vectors. The dataset comes from the continuous multi-day recordings of 15 type 1 patients in free-living conditions. QKLMS-FB produces an average root mean squared error of 18.66±3.19 mg/dl for a prediction horizon of 30 min with 82.04% of hypoglycemic readings and 93.30% of hyperglycemic ones being classified as clinically accurate or with benign errors. The effect of the prediction horizon is more evident in the hypoglycemic range.

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.

Fracture of human femur tissue monitored by acoustic emission sensors.

The study describes the acoustic emission (AE) activity during human femur tissue fracture. The specimens were fractured in a bending-torsion loading pattern with concurrent monitoring by two AE sensors. The number of recorded signals correlates well with the applied load providing the onset of micro-fracture at approximately one sixth of the maximum load. Furthermore, waveform frequency content and rise time are related to the different modes of fracture (bending of femur neck or torsion of diaphysis). The importance of the study lies mainly in two disciplines. One is that, although femurs are typically subjects of surgical repair in humans, detailed monitoring of the fracture with AE will enrich the understanding of the process in ways that cannot be achieved using only the mechanical data. Additionally, from the point of view of monitoring techniques, applying sensors used for engineering materials and interpreting the obtained data pose additional difficulties due to the uniqueness of the bone structure.

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.

Online prediction of glucose concentration in type 1 diabetes using extreme learning machines.

We propose an online machine-learning solution to the problem of nonlinear glucose time series prediction in type 1 diabetes. Recently, extreme learning machine (ELM) has been proposed for training single hidden layer feed-forward neural networks. The high accuracy and fast learning speed of ELM drive us to investigate its applicability to the glucose prediction problem. Given that diabetes self-monitoring data are received sequentially, we focus on online sequential ELM (OS-ELM) and online sequential ELM kernels (KOS-ELM). A multivariate feature set is utilized concerning subcutaneous glucose, insulin therapy, carbohydrates intake and physical activity. The dataset comes from the continuous multi-day recordings of 15 type 1 patients in free-living conditions. Assuming stationarity and evaluating the performance of the proposed method by 10-fold cross- validation, KOS-ELM were found to perform better than OS-ELM in terms of prediction error, temporal gain and regularity of predictions for a 30-min prediction horizon.

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.

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.

Wave dispersion and attenuation on human femur tissue.

Cortical bone is a highly heterogeneous material at the microscale and has one of the most complex structures among materials. Application of elastic wave techniques to this material is thus very challenging. In such media the initial excitation energy goes into the formation of elastic waves of different modes. Due to "dispersion", these modes tend to separate according to the velocities of the frequency components. This work demonstrates elastic wave measurements on human femur specimens. The aim of the study is to measure parameters like wave velocity, dispersion and attenuation by using broadband acoustic emission sensors. First, four sensors were placed at small intervals on the surface of the bone to record the response after pencil lead break excitations. Next, the results were compared to measurements on a bulk steel block which does not exhibit heterogeneity at the same wave lengths. It can be concluded that the microstructure of the tissue imposes a dispersive behavior for frequencies below 1 MHz and care should be taken for interpretation of the signals. Of particular interest are waveform parameters like the duration, rise time and average frequency, since in the next stage of research the bone specimens will be fractured with concurrent monitoring of acoustic emission.

A study on Rayleigh wave dispersion in bone according to Mindlin's Form II gradient elasticity.

The classical elasticity cannot effectively describe bone's mechanical behavior since only homogeneous media and local stresses are assumed. Additionally, it cannot predict the dispersive nature of the Rayleigh wave which has been reported in experimental studies and was also demonstrated in a previous computational study by adopting Mindlin's Form II gradient elasticity. In this work Mindlin's theory is employed to analytically determine the dispersion of Rayleigh waves in a strain gradient elastic half-space. An isotropic semi-infinite space is considered with properties equal to those of bone and dynamic behavior suffering from microstructural effects. Microstructural effects are considered by incorporating four intrinsic parameters in the stress analysis. The results are presented in the form of group and phase velocity dispersion curves and compared with existing computational results and semi-analytical curves calculated for a simpler case of Rayleigh waves in dipolar gradient elastic half-spaces. Comparisons are also performed with the velocity of the first-order antisymmetric mode propagating in a dipolar plate so as to observe the Rayleigh asymptotic behavior. It is shown that Mindlin's Form II gradient elasticity can effectively describe the dispersive nature of Rayleigh waves. This study could be regarded as a step toward the ultrasonic characterization of bone.

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.

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

In the process of fracture healing, several phases of recovery are observed as the mechanical stability, continuity and normal load carrying capacity are gradually restored. The ultrasonic monitoring and discrimination of different healing stages is a complex process due to the significant microstructure and porous nature of osseous and callus tissues. In this study, we investigate the influence of the callus pores' size and concentration on ultrasound propagation in a long bone at a late healing stage. Different excitation frequencies are applied in the range of 300 kHz-1 MHz. A 2D geometry is developed and axial transmission calculations are performed based on a Finite Element Method. The velocity of the first arriving signal (FAS) and the propagation of guided waves are used as the estimated parameters. It was shown that the FAS velocity can reflect callus porosity changes, while the propagation of guided waves is sensitive to pores' distribution for higher frequencies.