Material Design of Porous Hydroxyapatite Ceramics via Inverse Analysis of an Estimation Model for Bone-Forming Ability Based on Machine Learning and Experimental Validation of Biological Hard Tissue Responses.

Hydroxyapatite and ß-tricalcium phosphate have been clinically applied as artificial bone materials due to their high biocompatibility. The development of artificial bones requires the verification of safety and efficacy through animal experiments; however, from the viewpoint of animal welfare, it is necessary to reduce the number of animal experiments. In this study, we utilized machine learning to construct a model that estimates the bone-forming ability of bioceramics from material fabrication conditions, material properties, and in vivo experimental conditions. We succeeded in constructing two models: 'Model 1', which predicts material properties from their fabrication conditions, and 'Model 2', which predicts the bone-formation rate from material properties and in vivo experimental conditions. The inclusion of full width at half maximum (FWHM) in the feature of Model 2 showed an improvement in accuracy. Furthermore, the results of the feature importance showed that the FWHMs were the most important. By an inverse analysis of the two models, we proposed candidates for material fabrication conditions to achieve target values of the bone-formation rate. Under the proposed conditions, the material properties of the fabricated material were consistent with the estimated material properties. Furthermore, a comparison between bone-formation rates after 12 weeks of implantation in the porcine tibia and the estimated bone-formation rate. This result showed that the actual bone-formation rates existed within the error range of the estimated bone-formation rates, indicating that machine learning consistently predicts the results of animal experiments using material fabrication conditions. We believe that these findings will lead to the establishment of alternative animal experiments to replace animal experiments in the development of artificial bones.

An inverse analysis procedure for characterizing the homogeneous skull model used for predicting blast-induced brain response.

Based upon the homogeneous skull model, the skull/brain assembly can be simplified as a homogeneous-shell (HMS)/core structure, in which the exterior shell and interior core represent the skull and brain, respectively. From the blast responses of the spherical shell/core structures calculated via finite element modeling, it is found that the existing homogeneous skull model developed by the well-accepted approach based upon three-point bending tests cannot properly describe the blast response of the skull, modeled as a three-layered sandwich (TLS) shell in the present work, e.g. the average error in the calculated core (brain) pressure is up to ∼30%. Moreover, an innovative approach based upon inverse analysis procedure is then proposed to develop a modified homogeneous skull model, which can give a proper description of the blast response of the skull (a TLS shell), e.g. the average error in the calculated core (brain) pressure is reduced to ∼7%. It is concluded that the well-accepted three-point bending approach cannot develop an effective HMS skull model for studying the blast response of the skull/brain assembly, upon which the model parameter will be overestimated by ∼60%; instead, the innovative approach based upon inverse analysis procedure should be adopted.

On the Material Constitutive Behavior of the Aortic Root in Patients with Transcatheter Aortic Valve Implantation.

BACKGROUND: Transcatheter aortic valve implantation (TAVI) is a minimally invasive procedure used to treat patients with severe aortic valve stenosis. However, there is limited knowledge on the material properties of the aortic root in TAVI patients, and this can impact the credibility of computer simulations. This study aimed to develop a non-invasive inverse approach for estimating reliable material constituents for the aortic root and calcified valve leaflets in patients undergoing TAVI. METHODS: The identification of material parameters is based on the simultaneous minimization of two cost functions, which define the difference between model predictions and cardiac-gated CT measurements of the aortic wall and valve orifice area. Validation of the inverse analysis output was performed comparing the numerical predictions with actual CT shapes and post-TAVI measures of implanted device diameter. RESULTS: A good agreement of the peak systolic shape of the aortic wall was found between simulations and imaging, with similarity index in the range in the range of 83.7% to 91.5% for n.20 patients. Not any statistical difference was observed between predictions and CT measures of orifice area for the stenotic aortic valve. After TAVI simulations, the measurements of SAPIEN 3 Ultra (S3) device diameter were in agreement with those from post-TAVI angio-CT imaging. A sensitivity analysis demonstrated a modest impact on the S3 diameters when altering the elastic material property of the aortic wall in the range of inverse analysis solution. CONCLUSIONS: Overall, this study demonstrates the feasibility and potential benefits of using non-invasive imaging techniques and computational modeling to estimate material properties in patients undergoing TAVI.

Computer-Aided Structural Diagnosis of Bridges Using Combinations of Static and Dynamic Tests: A Preliminary Investigation.

Reinforced concrete bridges deteriorate over time, therefore displaying a regular need for structural assessment and diagnosis. The reasons for their deterioration are often the following: (a) intensive use, (b) very dynamic loads acting for long periods of time, (c) and sometimes chemical processes that damage the concrete or lead to corrosion of the reinforcement. Assuming the hypothesis that both the stiffness of the material and its density change over time, these parameters shall be identified, preferably in a non-destructive way, in different locations of the investigated structure. Such task is expected to be possibly exerted by means of one or more tests, which must not be laborious or cause the bridge to be out of service for a long time. In this paper, an attempt is made to prepare a procedure based on dynamic tests supplemented with several static measurements, in order to identify the largest number of parameters in the shortest possible time, within an inverse analysis methodology. The proposed procedure employs a popular algorithm for minimizing the objective function, i.e., trust region in the least square framework, as part of the inverse analysis, where the difference between measurements made in situ and those calculated numerically is minimized. As a result of the work performed, optimal sets of measurements and test configurations are proposed, allowing the searched parameters to be found in a reliable manner, with the greatest possible precision.

Method for Evaluating Cortical Bone Young's Modulus: Numerical Twin Reconstruction, Finite Element Calculation, and Microstructure Analysis.

The determination of bone mechanical properties remains crucial, especially to feed up numerical models. An original methodology of inverse analysis has been developed to determine the longitudinal elastic modulus of femoral cortical bone. The method is based on a numerical twin of a specific three-point bending test. It has been designed to be reproducible on each test result. In addition, the biofidelity of the geometric acquisition method has been quantified. As the assessment is performed at the scale of a bone shaft segment, the Young's modulus values obtained (between 9518.29 MPa and 14181.15 MPa) are considered average values for the whole tissue, highlighting some intersubject variability. The material microstructure has also been studied through histological analysis, and bone-to-bone comparisons highlighted discrepancies in quadrants microstructures. Furthermore, significant intrasubject variability exists since differences between the bone's medial-lateral and anterior-posterior quadrants have been observed. Thus, the study of microstructures can largely explain the differences between the elastic modulus values obtained. However, a more in-depth study of bone mineral density would also be necessary and would provide some additional information. This study is currently being setup, alongside an investigation of the local variations of the elastic modulus.

Numerical investigation on circular and elliptical bulge tests for inverse soft tissue characterization.

The acquisition of insights concerning the mechanobiology of aneurysmatic aortic tissues is an important field of investigation. The complete characterization of aneurysm mechanical behaviour can be carried out by biaxial experimental tests on ex vivo specimens. In literature, several works proposed bulge inflation tests as a valid method to analyse aneurysmatic tissue. Bulge test data processing requires the adoption of digital image correlation and inverse analysis approaches to estimate strain and stress distributions, respectively. In this context, however, the accuracy of inverse analysis method has not been evaluated yet. This aspect appears particularly interesting given the anisotropic behaviour of the soft tissue and the possibility to adopt different die geometries. The goal of this study is to provide an accuracy characterization of the inverse analysis applied to the bulge test technique using a numerical approach. In particular, different cases of bulge inflation were simulated in a finite element environment as a reference. To investigate the effect of tissue anisotropic degree and bulge die geometries (circular and elliptical), different input parameters were considered to obtain multiple test cases. The specimen deformed shapes, resulting from the reference finite element simulations, were then analysed through an inverse analysis approach to produce an estimation of stress distributions. The estimated stresses were, at last, compared with the values from the reference finite element simulations. The results demonstrated that the circular die geometry produces a satisfactory estimation accuracy only under certain conditions of material quasi-isotropy. On the other hand, the choice of an elliptical bulge die was proven to be more suitable for the analysis of anisotropic tissues.

Mechanical Properties of GFRP Bolts and Its Application in Tunnel Face Reinforcement.

As a new type of pre-reinforcement material for tunnel faces, glass fiber-reinforced polymer (GFRP) bolts can effectively and safely improve the stability of tunnel faces in soft surrounding rocks and speed up excavation. Therefore, in this paper, systematic research is carried out on the bond strength of GFRP bolts in tunnel faces and their relative pre-reinforcement parameters. Firstly, the effects of rebar diameter, anchorage length, and mortar strength on the bonding properties of GFRP bars were studied by indoor pull-out tests. The bond strength-slip curves under different working conditions were obtained, and the curves showed that the ultimate bond strength between GFRP bars and mortar was negatively correlated with the diameter of GFRP bars but positively correlated with the strength of the mortar. In addition, the increase in anchorage length led to a reduction in bonding strength. Secondly, inverse analysis was used to analyse the mechanical parameters of the bond performance of the anchor bars by the finite difference software FLAC3D, and the results indicated that 1/5 of the compressive strength of the GFRP bar grouting body can be taken as the ultimate bond strength to calculate the cohesive strength of the grout. Additionally, the formula of GFRP bar grouting body stiffness was revised. Finally, based on the results of laboratory tests and the inverse analysis, the numerical simulation analysis results showed that the optimal reinforcement configuration for a shallow buried tunnel face surrounded by weak rock is to use GFRP bars with a length of 17 m arranged in the center circle of the tunnel face with a reasonable reinforcement density of 1.0 bolt/m2. The calculation formula of the stiffness and cohesion strength of the GFRP bar grouting body and the reinforcement scheme proposed in this paper can provide a reference for the construction of shallowly buried rock tunnels in soft surrounding rock.

Use of mathematical modeling and its inverse analysis for precise assessment of pesticide dissipation in a paddy environment.

The extrapolability of the lysimeter test as a dissipation simulator in an actual paddy field was evaluated using mathematical models and their inverse analyses for predicting pesticide fate and transport processes in paddy test systems. As a source of experimental data, a four-year comparative experiment in lysimeters and paddy fields was conducted using various paddy pesticides. First, the dissipations for various active ingredients in granule pesticides under submerged applications were statistically compared using simple kinetic modeling. Second, the dissipation pathways, unobserved experimental components, and effect of the experimental setting were evaluated using a higher tier mathematical model with a novel inverse analysis protocol. Finally, owing to experimental constraints, the unobtainable parameters were extracted from the laboratory container test before being transferred to compare the outdoor experimental data under different formulation types.

A Consolidation Curve Reproduction Based on Sigmoid Model: Evaluation and Statistical Assessment.

In the present study, various shapes of laboratory consolidation curves were numerically reproduced using a four-parametric sigmoid function. Sixteen consolidation curves were selected based on one-dimensional oedometer tests to statistically evaluate the sigmoid model and to determine the appropriate deviation statistics. Comparisons between observed and predicted data were performed using the following statistical metrics: mean error (E), root mean square error (RMSE), mean absolute error (MAE), weighted error (WE), revised Nash-Sutcliffe efficiency index (CE1) and refined index of model performance (dr). The weighted error (WE) was chosen as the optimization target in a first-order iterative optimization algorithm to determine a local minimum of a differentiable function. Comparing the simulated and observed settlements showed close correspondence in the values of CE1 and dr in terms of model performance. Based on statistical assessment, the maximum values of RMSE and MAE for the average degree of consolidation were 0.029 (-) and 0.021 (-), respectively. In turn the settlement data RMSE and MAE were 0.039 mm and 0.025 mm, respectively. These results indicated that the sigmoid expression effectively reproduced the shape of the consolidation curve.

The Application of a Hybrid Method for the Identification of Elastic-Plastic Material Parameters.

The indentation test is a popular method for the investigation of the mechanical properties of materials. The technique, which combines traditional indentation tests with mapping the shape of the imprint, provides more data describing the material parameters. In this paper, such methodology is employed for estimating the selected material parameters described by Ramberg-Osgood's law, i.e., Young's modulus, the yield point, and the material hardening exponent. Two combined identification methods were used: the P-A procedure, in which the material parameters are identified on the basis of the coordinates of the indentation curves, and the P-C procedure, which uses the coordinates describing the imprint profile. The inverse problem was solved by neural networks. The results of numerical indentation tests-pairs of coordinates describing the indentation curves and imprint profiles-were used as input data for the networks. In order to reduce the size of the input vector, a simple and effective method of approximating the branches of the curves was proposed. In the Results Section, we show the performance of the approximation as a data reduction mechanism on a synthetic dataset. The sparse model generated by the presented approach is also shown to efficiently reconstruct the data while minimizing error in the prediction of the mentioned material parameters. Our approach appeared to consistently provide better performance on the testing datasets with considerably easier computation than the principal component analysis compression results available in the literature.

Nonlinear Inverse Analysis for Predicting the Tensile Properties of Strain-Softening and Strain-Hardening UHPFRC.

The tensile stress-strain response is considered to be the most important and fundamental mechanical property of ultra-high-performance fiber-reinforced concrete (UHPFRC). Nevertheless, it is still a challenging matter for researchers to determine the tensile properties of UHPFRC. As a simpler alternative to the direct tensile test, bending tests are widely performed to characterize the tensile behavior of UHPFRC, but require further consideration and a sophisticated inverse analysis procedure. In order to efficiently predict the tensile properties of UHPFRC, a nonlinear inverse method based on notched three-point bending tests (3PBT) was proposed in this paper. A total of fifteen UHPFRC beams were fabricated and tested to evaluate the sensitivity of the predicted tensile behavior to variations in fiber volume fraction. A segmented stress-strain model was used, which is capable of describing the various tensile properties of UHPFRC, including strain softening and strain hardening. A more approximate formulation was adopted to simulate the load-deflection response of UHPFRC beam specimens. The closed-form analytical solutions were validated by tensile test results and existing methods in literature. Finally, parametric studies were also conducted to investigate the robustness of the proposed method. The load-deflection responses obtained from notched 3PBT could be easily converted into tensile properties with this inverse method.

Physical and Numerical Simulations for Predicting Distribution of Microstructural Features during Thermomechanical Processing of Steels.

The design of modern construction materials with heterogeneous microstructures requires a numerical model that can predict the distribution of microstructural features instead of average values. The accuracy and reliability of such models depend on the proper identification of the coefficients for a particular material. This work was motivated by the need for advanced experimental data to identify stochastic material models. Extensive experiments were performed to supply data to identify a model of austenite microstructure evolution in steels during hot deformation and during the interpass times between deformations. Two sets of tests were performed. The first set involved hot compressions with a nominal strain of 1. The second set involved hot compressions with lower nominal strains, followed by holding at the deformation temperature for different times. Histograms of austenite grain size after each test were measured and used in the identification procedure. The stochastic model, which was developed elsewhere, was identified. Inverse analysis with the objective function based on the distance between the measured and calculated histograms was applied. Validation of the model was performed for the experiments, which were not used in the identification. The distance between the measured and calculated histograms was determined for each test using the Bhattacharyya metric and very low values were obtained. As a case study, the model with the optimal coefficients was applied to the simulation of the selected industrial hot-forming process.

Cure Kinetics and Inverse Analysis of Epoxy-Amine Based Adhesive Used for Fastening Systems.

Thermosetting polymers are used in building materials, for example adhesives in fastening systems. They harden in environmental conditions with a daily temperature depending on the season and location. This curing process takes hours or even days effected by the relatively low ambient temperature necessary for a fast and complete curing. As material properties depend on the degree of cure, its accurate estimation is of paramount interest and the main objective in this work. Thus, we develop an approach for modeling the curing process for epoxy based thermosetting polymers. Specifically, we perform experiments and demonstrate an inverse analysis for determining parameters in the curing model. By using calorimetry measurements and implementing an inverse analysis algorithm by using open-source packages, we obtain 10 material parameters describing the curing process. We present the methodology for two commercial, epoxy based products, where a statistical analysis provides independence of material parameters leading to the conclusion that the material equation is adequately describing the material response.

Calibration of Drucker-Prager Cap Constitutive Model for Ceramic Powder Compaction through Inverse Analysis.

Phenomenological plasticity models that relate relative density to plastic strain are frequently used to simulate ceramic powder compaction. With respect to the form implemented in finite element codes, they need to be modified in order to define governing parameters as functions of relative densities. Such a modification increases the number of constitutive parameters and makes their calibration a demanding task that involves a large number of experiments. The novel calibration procedure investigated in this paper is based on inverse analysis methodology, centered on the minimization of a discrepancy function that quantifies the difference between experimentally measured and numerically computed quantities. In order to capture the influence of sought parameters on measured quantities, three different geometries of die and punches are proposed, resulting from a sensitivity analysis performed using numerical simulations of the test. The formulated calibration protocol requires only data that can be collected during the compaction test and, thus, involves a relatively smaller number of experiments. The developed procedure is tested on an alumina powder mixture, used for refractory products, by making a reference to the modified Drucker-Prager Cap model. The assessed parameters are compared to reference values, obtained through more laborious destructive tests performed on green bodies, and are further used to simulate the compaction test with arbitrary geometries. Both comparisons evidenced excellent agreement.

Visco-Hyperelastic Characterization of the Equine Immature Zona Pellucida.

This article presents a very detailed study on the mechanical characterization of a highly nonlinear material, the immature equine zona pellucida (ZP) membrane. The ZP is modeled as a visco-hyperelastic soft matter. The Arruda-Boyce constitutive equation and the two-term Prony series are identified as the most suitable models for describing the hyperelastic and viscous components, respectively, of the ZP's mechanical response. Material properties are identified via inverse analysis based on nonlinear optimization which fits nanoindentation curves recorded at different rates. The suitability of the proposed approach is fully demonstrated by the very good agreement between AFM data and numerically reconstructed force-indentation curves. A critical comparison of mechanical behavior of two immature ZP membranes (i.e., equine and porcine ZPs) is also carried out considering the information on the structure of these materials available from electron microscopy investigations documented in the literature.

Thermophysical Properties of Temperature-Sensitive Paint.

The complex thermophysical property of temperature-sensitive paint (TSP) research is discussed. TSP is used for visualization of the surface temperature distribution in wind tunnel aerodynamic tests. The purpose of this research was to provide reliable, experimental, thermophysical data of the paint applied as a coating. As TSP is applied as thin surface layers, investigation of its final properties is challenging and demands the application of non-standard procedures. At present, most measurements were performed on composite specimens of TSP deposed onto a thin metallic film substrate or on TSP combined with a cellulose sheet support. The studies involved gravimetric,, thermogravimetric, and microcalorimetric analyses, transversal thermal diffusivity estimation from laser flash data and in-plane effective thermal diffusivity measurements done by the temperature oscillation technique. These results were complemented with scanning electron microcopy analysis, surface characterization and the results of dilatometric measurements performed on the TSP bulk specimens obtained from liquid substrate by casting. Complex analysis of the obtained results indicated an isotropic characteristic of the thermal diffusivity of the TSP layer and provided reliable data on all measured thermophysical parameters-they were revealed to be typical for insulators. Further to presenting these data, the paper, in brief, presents the applied investigation procedures.

A biphasic multilayer computational model of human skin.

The present study investigates the layer-specific mechanical behavior of human skin. Motivated by skin's histology, a biphasic model is proposed which differentiates between epidermis, papillary and reticular dermis, and hypodermis. Inverse analysis of ex vivo tensile and in vivo suction experiments yields mechanical parameters for each layer and predicts a stiff reticular dermis and successively softer papillary dermis, epidermis and hypodermis. Layer-specific analysis of simulations underlines the dominating role of the reticular dermis in tensile loading. Furthermore, it shows that the observed out-of-plane deflection in ex vivo tensile tests is a direct consequence of the layered structure of skin. In in vivo suction experiments, the softer upper layers strongly influence the mechanical response, whose dissipative part is determined by interstitial fluid redistribution within the tissue. Magnetic resonance imaging-based visualization of skin deformation in suction experiments confirms the deformation pattern predicted by the multilayer model, showing a consistent decrease in dermal thickness for large probe opening diameters.

Line source estimation of environmental pollutants using super-Gaussian geometry model and bayesian inference.

A line is a common geometry for pollution sources, e.g., outdoor traffic pollution, and is thus useful for developing a suitable source term estimation (STE) method. Most existing methods regard the source as a single point that only includes location and strength parameters; however, limited attention has been paid to the geometric information of the source. This negligence may cause errors, or even failure, in the STE. Therefore, this paper proposes a line source estimation method that combines Bayesian inference with the super-Gaussian function. This function can approximate the shape of sources with several intuitive coefficients, which are adjusted to their true value through Bayesian inference. The performance of the proposed method was evaluated through estimation of a line source in two cases: an ideal urban boundary layer, via simulation, and a complex urban square, via a wind tunnel experiment. The results demonstrate that this method is capable of identifying the source information without any prior geometric information regarding the source. Moreover, it was confirmed that the conventional point-based assumption method leads to failure in estimating the line source, which implies that geometry estimation is necessary for STE.

The identification of the unloaded configuration of breast tissue with unknown non-homogenous stiffness parameters using surface measured data in deformed configuration.

Large deformation analysis of the breast is known as a useful approach for locating the tumor and treatment strategies of breast cancer, for which knowing the breast stiffness parameters and unloaded configuration is crucial to obtain reliable results. In this study, an iterative inverse finite element algorithm is developed to identify the unloaded configuration of the breast while its stiffness constants are unknown and its internal structure is assumed to be non-homogeneous. The position vector of surface points in the deformed configuration of the breast is employed to obtain the unknowns of the inverse problem. An objective function based on the difference between the position vector of the calculated and measured deformed configurations is defined. Thereafter, the objective function is minimized using a gradient-based method. The sensitivity analysis for material parameters is performed using an analytic direct differentiation approach. Through several numerical examples, the effectiveness of the proposed inverse method for identifying the unloaded configuration of a uniform, a computational breast phantom with a single inclusion as well as a computational breast phantom with randomly distributed stiffness, is demonstrated. The effects of the number of load cases, measurement error, and initial guesses on the results of the inverse problem are investigated, as well. It is observed that the unloaded configuration of the computational breast phantom with a single inclusion or heterogeneous breast tissues can be accurately found by considering an equivalent homogenous material for the tissue.

Towards enabling a cardiovascular digital twin for human systemic circulation using inverse analysis.

An exponential rise in patient data provides an excellent opportunity to improve the existing health care infrastructure. In the present work, a method to enable cardiovascular digital twin is proposed using inverse analysis. Conventionally, accurate analytical solutions for inverse analysis in linear problems have been proposed and used. However, these methods fail or are not efficient for nonlinear systems, such as blood flow in the cardiovascular system (systemic circulation) that involves high degree of nonlinearity. To address this, a methodology for inverse analysis using recurrent neural network for the cardiovascular system is proposed in this work, using a virtual patient database. Blood pressure waveforms in various vessels of the body are inversely calculated with the help of long short-term memory (LSTM) cells by inputting pressure waveforms from three non-invasively accessible blood vessels (carotid, femoral and brachial arteries). The inverse analysis system built this way is applied to the detection of abdominal aortic aneurysm (AAA) and its severity using neural networks.