Material Stiffness Parameters Research Articles

Assessment of the Corneal Biomechanical Features of Sturge-Weber Syndrome Using Dynamic Ultrahigh-speed Scheimpflug Imaging.

To evaluate the corneal biomechanical characteristics of eyes with Sturge-Weber syndrome (SWS) secondary glaucoma (SSG) by analyzing corneal biomechanical parameters obtained using the Corneal Visualization Scheimpflug Technology instrument (Corvis ST). In patients with SWS, eyes affected by SSG were designated as the SSG group while the contralateral eyes were designated as the SWS contralateral group (SC group). Patients from the myopia clinic served as the control group. Dynamic corneal response parameters (DCRs) including the stress-strain index (SSI)-a critical material stiffness parameter that excludes interference from IOP and central corneal thickness (CCT)-were analyzed. For CCT, no significant difference was observed between the SSG and SC groups. However, significant differences were found between the SSG and control groups and between the SC and control groups. Parameters such as HC Time, A1 Deformation Amp., A2 Deformation Amp., length of Whole Eye Movement (WEM), DA Ratio Max (2 mm), PachySlope, DA Ratio Max (1 mm), and ARTh showed significant differences between the SSG group and control group. In the SSG group, 4 of night eyes had an SSI of less than 0.85. Some DCRs indicated a stiffer cornea in the SSG group, possibly due to a thicker cornea in this group. On analyzing SSI, it was found that corneal material properties change, becoming less stiff in some of the patients with SSG. In conclusion, our study provides a preliminary exploration of the biomechanical properties of SWS secondary glaucoma.

Load history dependency of stiffness properties of PTFE-coated glass fibre membranes

The aim of this contribution is to investigate whether the order of load ratios applied to a textile structure impacts the biaxial stiffness behaviour of the structural textile itself. These investigations are performed based on biaxial tests on an architectural woven glass fibre fabric, a representative of such membranes. The first part of the paper investigates the existence and extent of load history dependency in the material response. Biaxial test results show that effects of a previous load history on the weave geometry cannot be eliminated by further load cycling in all biaxial stress ratios. Moderate to strong effects are recognized in two stress ratios, although not in both weave directions.The second part of the paper examines how these effects influence material stiffness parameters and structural calculations. Two boundary value problems are investigated: a pressure chamber test and a roof structure. Parameters obtained by fitting biaxial tests with or without history are considered. By incorporating an adaptive load-ratio dependent scheme, highly predictive numerical results are obtained, showing that while the effect of load history may appear small in the biaxial tests and pressure chamber test, it can be significant in complex structural problems like roof structures.

Effect of central corneal curvature on corneal material stiffness parameter acquired by dynamic corneal responses.

The stress-strain index (SSI) is a measure of corneal material stiffness, which is obtained using the Corvis ST algorithm based on dynamic corneal response parameters. The reduced SSI corresponds to the longer axial length (AL). In a previous study, we found SSI increases as the corneal curvature flattens, whereas a flatter corneal curvature indicates a longer AL (emmetropia or myopia). Therefore, in this cross-sectional study, we aimed to address these contradictory findings. First, we characterized the features of SSI, curvature radius of the anterior corneal surface (CR), and AL and analyzed their correlation with advanced myopia. Next, we compared the relationship between AL and SSI after adjusting for the effect of CR. We found a significant positive correlation between SSI and CR, which contradicts the developmental law of axial myopia. Furthermore, after accounting for the effect of CR, we observed a stronger correlation between SSI and AL than that in the unadjusted model. In conclusion, CR is an independent influencing factor for SSI in addition to AL, which masked the decrease in SSI caused by prolonged AL in axial myopia.

Mechanical Properties of Uncured Thermoset Tow Prepreg: Experiment and Finite Element Analysis

This paper presents an experimental analysis of the tensile behavior of unidirectional carbon/epoxy prepreg, focusing on the nonlinearity observed at the beginning of the stress–strain curve. Due to the material’s high viscosity, securely holding specimens during testing was challenging, prompting modifications in the gripping method to ensure reliable data. By using a longer gauge length, the slippage impact on elastic modulus measurement was minimized, resulting in good repeatability among the test samples. Experimental findings highlighted the significant interaction between fiber waviness and the viscous matrix, leading to stiffness reduction. The linear stiffness of the samples closely matched that of the fibers and remained unaffected by temperature variations. However, at higher temperatures, the epoxy matrix’s decreased viscosity caused an upward shift in the stiffness plot within the non-linear region. To support the experimental findings, a micromechanical model of prepreg tow with fiber waviness was proposed. An RVE model of periodically distributed unidirectional waved cylindrical fibers embedded within the matrix was developed to predict effective material stiffness parameters. The simulation outcomes aligned well with the uniaxial tensile test of the prepreg tow, demonstrating the proposed RVE model’s capability to accurately predict elastic properties, considering factors like fiber arrangement, waviness, and temperature.

Performance-Based Expressway Asphalt Pavement Structural Surface Layer Modulus Matching Mode Research

The current asphalt pavement design theory is a traditional line elastic theory. The voltage resistance recovery modulus is used as the material stiffness parameter in the design, which does not fully consider the significant differences between the road material pull-up modulus. Therefore, to improve the overall stress of the pavement structure, this article started from the perspective of the volume of the structure layer, analyzed the development characteristics of reflected cracks in terms of the modular volume of different surface layers, and studied the size of each layer. It is proposed to match the asphalt pavement layer modulus with the crack development level. Based on structural computing and simulation, the application of different modular matching modes was verified, and support was provided for the design of the pavement structure. The results showed that with the increase of the surface modulus, the stress intensity factor determined by a semi-analytical method showed a nonlinear decrease trend, and the change of stress intensity factor was not obvious when the modulus was greater than 10,000; the surface layer compression mode ratio increased, and the vertical deformation of the road surface and the top surface pressure of the road base slowly increased, especially when the volume of the pressure pull-up ratio was greater than 1.5. In addition, the impact of the constraint between the surface layer on the vertical deformation of the road table decreased with the decrease in the volume of the surface layer.

Effect of corneal stiffness decrease on axial length elongation in myopia determined based on a mathematical estimation model.

Purpose: To investigate the relationship between the corneal material stiffness parameter stress-strain index (SSI) and axial length (AL) elongation with varying severities of myopia, based on a mathematical estimation model. Methods: This single-center, cross-sectional study included data from healthy subjects and patients preparing for refractive surgery in the Qingdao Eye Hospital of Shandong First Medical University. Data were collected from July 2021 to April 2022. First, we performed and tested an estimated AL model ( ) based on the mathematical equation proposed by Morgan. Second, we proposed an axial increment model ( ) corresponding to spherical equivalent error (SER) based on ( at SER = 0) and subject's real AL. Finally, we evaluated the variations of with SSI changes based on the mathematical estimation model. Results: We found that AL was closely associated with (r = 0.91, t = 33.8, p < 0.001) with good consistency and SER was negatively associated with (r = -0.89, t = -30.7, p < 0.001). The association of SSI with AL, , and can be summarized using the following equations: , , and . In adjusted models, SSI was negatively associated with AL (Model 1: β = -2.01, p < 0.001) and (Model 3: β = -2.49, p < 0.001) but positively associated with (Model 2: β = 0.48, p < 0.05). In addition, SSI was negatively associated with among subjects with AL ≥ 26mm (β = -1.36, p = 0.02). Conclusion: AL increased with decreasing SSI in myopia.

Changes in Corneal Biomechanical Properties in PRK Followed by Two Accelerated CXL Energy Doses in Rabbit Eyes.

To evaluate whether photorefractive keratectomy (PRK) combined with the two commonly delivered energy doses in accelerated corneal cross-linking (A-CXL) could help the cornea maintain its preoperative stiffness level. A total of 72 corneas of 36 healthy white Japanese rabbits were randomly divided into four equal groups. The groups included an untreated control group and three that had undergone PRK. After tissue ablation, one of the latter three groups (PRK group) was left untreated, whereas the other two were exposed to riboflavin (0.22% concentration by volume) and ultraviolet-A (370 nm) with the same irradiation (30 mW/cm2) but different CXL energy doses of 1.8 J/cm2 (PXL group) and 2.7 J/cm2 (PXH group). Dynamic Scheimpflug analyzer (Corvis ST; Oculus Optikgeräte GmbH) measurements of stiffness parameter at first applanation (SP-A1), Stress-Strain Index (SSI), and other dynamic corneal response parameters were taken 3 days preoperatively and 1 month postoperatively. Subsequently, ex vivo inflation testing was performed and the tangent modulus of each specimen was estimated using an inverse analysis process. In comparison to the control group, the tangent modulus at a stress of 10 kPa decreased by 8.9% in the PRK group and increased by 10.6% and 22.4% in the PXL and PXH groups, respectively. SP-A1 decreased postoperatively in the PRK group (P < .05), indicating an overall stiffness reduction of -7.4, -3.5, and -5.3 mm Hg/mm in PRK, PXL, and PXH groups, respectively. The material stiffness parameter SSI remained almost unchanged in the PRK group (P = .989), increased slightly in the PXL group (8.3%, P = .077), and increased significantly in the PXH group (11.1%) (P < .05). Biomechanical deterioration following PRK was significant and could not be fully compensated for by ACXL with either 1.8 or 2.7 J/cm2 doses. The increased value of corneal overall stiffness was higher in A-CXL with 2.7 J/cm2 energy than with 1.8 J/cm2 energy. [J Refract Surg. 2021;37(12):853-860.].

Fluid-Structure Interaction Based Algorithms for IOP and Corneal Material Behavior.

Purpose: This paper presents and clinically validates two algorithms for estimating intraocular pressure (IOP) and corneal material behavior using numerical models that consider the fluid-structure interaction between the cornea and the air-puff used in non-contact tonometry.Methods: A novel multi-physics fluid-structure interaction model of the air-puff test was employed in a parametric numerical study simulating human eyes under air-puff pressure with a wide range of central corneal thickness (CCT = 445–645 μm), curvature (R = 7.4–8.4 mm), material stiffness and IOP (10–25 mmHg). Models were internally loaded with IOP using a fluid cavity, then externally with air-puff loading simulated using a turbulent computational fluid dynamics model. Corneal dynamic response parameters were extracted and used in development of two algorithms for IOP and corneal material behavior; fIOP and fSSI, respectively. The two algorithms were validated against clinical corneal dynamic response parameters for 476 healthy participants. The predictions of IOP and corneal material behavior were tested on how they varied with CCT, R, and age.Results: The present study produced a biomechanically corrected estimation of intraocular pressure (fIOP) and a corneal material stiffness parameter or Stress-Strain Index (fSSI), both of which showed no significant correlation with R (p > 0.05) and CCT (p > 0.05). Further, fIOP had no significant correlation with age (p > 0.05), while fSSI was significantly correlated with age (p = 0.001), which was found earlier to be strongly correlated with material stiffness.Conclusion: The present study introduced two novel algorithms for estimating IOP and biomechanical material behavior of healthy corneas in-vivo. Consideration of the fluid structure interaction between the cornea and the air puff of non-contact tonometry in developing these algorithms led to improvements in performance compared with bIOP and SSI.

МОДЕЛИРОВАНИЕ И БИФУРКАЦИОННЫЙ АНАЛИЗ УСТОЙЧИВОСТИ ГЕОТЕХНИЧЕСКОЙ СИСТЕМЫ В УСЛОВИЯХ ВОЗДЕЙСТВИЯ ВИБРАЦИОННЫХ ФАКТОРОВ

The automation of control processes for the stability of geotechnical systems is a great challenge involving the development of methods for multivariate analyzing and forecasting the stability with the subject to the nonlinearity of material stiffness parameters. The aim of the study is to improve the efficiency of automated control systems for geotechnical stability by developing an approach to detect negative changes in bifurcation diagrams of vibration displacement parameters of object structures. The authors present a mathematical model of the dynamic behavior of structural elements of an object as an elementary unit of a geotechnical system that describes a response to an external vibration action. An algorithm of bifurcation analysis is presented, which allows authors to determine the initial transition stage of the object structure to an unstable state by the acceleration values of forced oscillations exceeding the model parameters. A bifurcation diagram of stability changes in the structure of object at the displacement resulting from the load increase under vibration action has been constructed. This diagram, which type of codimension-one bifurcations is merging, enabled to determine the critical load values resulting in an unstable state transition of a system due to the influence of a combination of vibration factors. The efficiency evaluation of the proposed approach was carried out by the comparison with the results of construction stability calculations obtained by the use of the dynamic coefficient. The difference between the values of the maximum object displacement without loss of the stability under vibration action, obtained by the standard calculation method and using the developed model, is 32.5%, and it is significant in the theory of structure stability. When exogenous vibration noise is used as a source of a sounding signal, the application of the developed approach in automated control systems for geotechnical stability enable to change the permissible stability thresholds of objects being exploited depending on the level and combination of influencing factors.

Determination of Corneal Biomechanical Behavior in-vivo for Healthy Eyes Using CorVis ST Tonometry: Stress-Strain Index.

Purpose: This study aims to introduce and clinically validate a new algorithm that can determine the biomechanical properties of the human cornea in vivo.Methods: A parametric study was conducted involving representative finite element models of human ocular globes with wide ranges of geometries and material biomechanical behavior. The models were subjected to different levels of intraocular pressure (IOP) and the action of external air puff produced by a non-contact tonometer. Predictions of dynamic corneal response under air pressure were analyzed to develop an algorithm that can predict the cornea's material behavior. The algorithm was assessed using clinical data obtained from 480 healthy participants where its predictions of material behavior were tested against variations in central corneal thickness (CCT), IOP and age, and compared against those obtained in earlier studies on ex-vivo human ocular tissue.Results: The algorithm produced a material stiffness parameter (Stress-Strain Index or SSI) that showed no significant correlation with both CCT (p > 0.05) and IOP (p > 0.05), but was significantly correlated with age (p < 0.01). The stiffness estimates and their variation with age were also significantly correlated (p < 0.01) with stiffness estimates obtained earlier in studies on ex-vivo human tissue.Conclusions: The study introduced and validated a new method for estimating the in vivo biomechanical behavior of healthy corneal tissue. The method can aid optimization of procedures that interfere mechanically with the cornea such as refractive surgeries and introduction of corneal implants.

Echo-Based FSI Models to Simulate Ventricular Electrical Signal Conduction in Pig Pacemaker Models

Cardiac pacing has been an effective treatment in the management of patients with arrhythmia. Different pacemaker location may have different impact on pacemaker effectiveness. A novel image-based ventricle animal modeling approach was proposed to integrate echocardiography images, propagating dynamic electric potential on ventricle surface to perform myocardial function assessment. The models will be used to simulate ventricular electrical signal conduction and optimize pacemaker location for better cardiac outcome. One health female adult pig weight 42.5kg was used to make pacing animal model with different ventricle pacing locations. Pig health status was assessed before undergoing experimental procedures. Ventricle surface electric signal, blood pressure and echo image were acquired 15 minutes after the pacemaker was implanted. Echo-based left ventricle (LV) fluid-structure interaction (FSI) models were constructed to perform ventricle function analysis and investigate impact of pacemaker location on cardiac outcome. The nonlinear Mooney-Rivlin model was used for ventricle tissue material model. With the measured electric signal map from the pig associated with the actual pacemaker site, electric potential conduction of myocardium was modeled by material stiffening and softening in our model, with stiffening simulating contraction and softening simulating relaxation. Material stiffness parameters were adjusted in a cardiac cycle to match Echo-measured LV deformation and volume variations. Mapping between material stiffness and ventricle electric signal was quantified using data measured from the animal with different pacemaker locations. Ventricle model without pacemaker and three ventricle models with the following pacemaker locations were simulated: right ventricular apex (RVA), posterior interventricular septum (PIVS) and right ventricular outflow tract (RVOT). Data for ventricle volume change, ejection fraction, stress and strain, flow velocity and shear stress data were collected for comparisons. Our results demonstrating that PIVS pacing model had higher peak flow velocity and stress/strain. It indicated that PIVS pacemaker site may be the best location. This modeling approach could be used as “virtual surgery” to try various pacemaker locations and avoid risky and dangerous surgical experiments on real patients.

Relative identifiability of anisotropic properties from magnetic resonance elastography.

Although magnetic resonance elastography (MRE) has been used to estimate isotropic stiffness in the heart, myocardium is known to have anisotropic properties. This study investigated the determinability of global transversely isotropic material parameters using MRE and finite-element modeling (FEM). A FEM-based material parameter identification method, using a displacement-matching objective function, was evaluated in a gel phantom and simulations of a left ventricular (LV) geometry with a histology-derived fiber field. Material parameter estimation was performed in the presence of Gaussian noise. Parameter sweeps were analyzed and characteristics of the Hessian matrix at the optimal solution were used to evaluate the determinability of each constitutive parameter. Four out of five material stiffness parameters (Young's modulii E1 and E3 , shear modulus G13 and damping coefficient s), which describe a transversely isotropic linear elastic material, were well determined from the MRE displacement field using an iterative FEM inversion method. However, the remaining parameter, Poisson's ratio, was less identifiable. In conclusion, Young's modulii, shear modulii and damping can theoretically be well determined from MRE data, but Poisson's ratio is not as well determined and could be set to a reasonable value for biological tissue (close to 0.5).

Effect of sugar beet fiber concentrations on rheological properties of meat emulsions and their correlation with texture profile analysis

The effect of sugar beet fiber (SBF) concentration on the rheological properties of meat emulsions was determined. In addition, texture profile analysis (TPA) of cooked meat emulsions was carried out to find a possible relationship between the dynamic rheological data and TPA parameters. All studied emulsions exhibited non-Newtonian, pseudoplastic behavior since apparent viscosity decreased with increasing shear rate. The Ostwald–de Waele model was successfully used to describe the flow properties of meat emulsions (R2>0.913). Emulsion systems were characterized as weak gel-like macromolecular dispersions with storage modulus (G′) much greater than loss modulus (G″). A modified Cox–Merz rule was applied by multiplying angular frequency with shift factors (αSF). Material stiffness parameter (Aα) calculated from complex modulus (G*) increased as SBF concentration increased. Significant correlations among the material stiffness data and TPA parameters were observed. It was concluded that TPA parameters could be predicted by using dynamic shear tests, and hence, this will make possible to save time and cost for meat processors when manufacturing a product with acceptable structural or textural characteristics.

Quantifying in vivo laxity in the anterior cruciate ligament and individual knee joint structures

A custom knee loading apparatus (KLA), when used in conjunction with magnetic resonance imaging, enables in vivo measurement of the gross anterior laxity of the knee joint. A numerical model was applied to the KLA to understand the contribution of the individual joint structures and to estimate the stiffness of the anterior-cruciate ligament (ACL). The model was evaluated with a cadaveric study using an in situ knee loading apparatus and an ElectroForce test system. A constrained optimization solution technique was able to predict the restraining forces within the soft-tissue structures and joint contact. The numerical model presented here allowed in vivo prediction of the material stiffness parameters of the ACL in response to applied anterior loading. Promising results were obtained for in vivo load sharing within the structures. The numerical model overestimated the ACL forces by 27.61–92.71%. This study presents a novel approach to estimate ligament stiffness and provides the basis to develop a robust and accurate measure of in vivo knee joint laxity.

Material stiffness parameters as potential predictors of presence of left ventricle myocardial infarction: 3D echo-based computational modeling study.

BackgroundVentricle material properties are difficult to obtain under in vivo conditions and are not readily available in the current literature. It is also desirable to have an initial determination if a patient had an infarction based on echo data before more expensive examinations are recommended. A noninvasive echo-based modeling approach and a predictive method were introduced to determine left ventricle material parameters and differentiate patients with recent myocardial infarction (MI) from those without.MethodsEcho data were obtained from 10 patients, 5 with MI (Infarct Group) and 5 without (Non-Infarcted Group). Echo-based patient-specific computational left ventricle (LV) models were constructed to quantify LV material properties. All patients were treated equally in the modeling process without using MI information. Systolic and diastolic material parameter values in the Mooney-Rivlin models were adjusted to match echo volume data. The equivalent Young’s modulus (YM) values were obtained for each material stress–strain curve by linear fitting for easy comparison. Predictive logistic regression analysis was used to identify the best parameters for infract prediction.ResultsThe LV end-systole material stiffness (ES-YMf) was the best single predictor among the 12 individual parameters with an area under the receiver operating characteristic (ROC) curve of 0.9841. LV wall thickness (WT), material stiffness in fiber direction at end-systole (ES-YMf) and material stiffness variation (∆YMf) had positive correlations with LV ejection fraction with correlation coefficients r = 0.8125, 0.9495 and 0.9619, respectively. The best combination of parameters WT + ∆YMf was the best over-all predictor with an area under the ROC curve of 0.9951.ConclusionComputational modeling and material stiffness parameters may be used as a potential tool to suggest if a patient had infarction based on echo data. Large-scale clinical studies are needed to validate these preliminary findings.

Towards the design of a new standard for composite stiffness identification

This paper presents a step towards the design of a novel test for simultaneous identification of all the stiffness components of orthotropic composite materials. A simulator was adopted to numerically simulate the whole identification process. Synthetic images were generated and then processed by Digital Image Correlation (DIC) to calculate the strain fields. The Virtual Fields Method (VFM) was used to identify the material stiffness parameters and error functions were finally defined to evaluate the identification error. Two steps of optimization were applied to obtain the best design variables of different specimens and the optimal DIC processing parameters. Four types of test configuration were simulated including short off-axis tensile test, short off-axis open-hole tensile test, off-axis Brazilian disc and off-axis unnotched Iosipescu test and the most promising configuration was identified.

Refined Biaxial Test Procedures for the Determination of Design Elastic Constants of Architectural Fabrics

In today's structural design practice for textile structures, still one of the most challenging aspects is the determination of material stiffness parameters. The only constitutive law used in practice describes orthotropic linear-elastic stress-strain relations in the two principal directions. The elastic constants are “tensile modulus” and “Poisson's ratio”. In contrast, the actual stiffness behaviour of architectural textiles is nonlinear and nonelastic. Moreover, the potential high orthotropy of textiles is often not sufficiently covered by the test and evaluation methods available.This paper presents principles for refined biaxial test procedures that fit to the requirements of structural fabrics. As a result, sets of elastic constants for design purposes can be determined which ensure a very good correlation between measured and calculated strain on a specific stress level for all common PVC-coated polyester fabrics and PTFE-coated glass fibre fabrics. Furthermore, the refined method enables to model the very high transverse strains which are observed especially for glass-PTFE fabrics.

Stiffness Parameters for Architectural Fabrics: An Analysis of Two Determination Procedures

One important and challenging aspect of the design process for tensile membrane structures is the determination of biaxial material stiffness parameters. Coated textiles that are used as architectural fabrics display highly nonlinear and anisotropic stress–strain behaviour under biaxial tensile stresses. Nevertheless, in state-of-the-art structural analyses, the behaviour of these coated textiles is often simplified to a linear-elastic plane stress relationship, where the elastic constants are “tensile stiffness” and “Poisson’ s ratio.” The elastic constants must be determined for each material using biaxial tensile tests. Several different biaxial test procedures to determine the elastic constants exist worldwide, and these procedures yield various sets of elastic constants with a wide spectrum of stiffness parameters. At the same time, design engineers have no guidelines to assess which set of parameters is appropriate for a specific design situation.This paper compares two different methods of determining stiffness parameters using theoretical and experimental analyses. The variation in structural analysis results due to stiffness parameters that were determined using different techniques is demonstrated using three types of PES/PVC materials from two material producers. Furthermore, this paper provides guidance regarding the manner of evaluation of sets of elastic constants and the modification of the evaluation of experimental biaxial tests, if required. Information is also provided concerning the applicability of the investigated procedures.

Numerical Analysis of El-Agrem Concrete Face Rockfill Dam

For concrete face rockfill dams, the behaviour of the concrete slab which provides the watertightness of the dam is a major concern. The deformation of the dam embankment during construction and operation leads to concrete slab deformation. This deformation should be compatible with the structural integrity of the concrete slab. This paper presents the numerical analysis of El-Agrem concrete face rockfill dam during reservoir filling using the finite element code Plaxis 2D-2010. Two models are used in this study, the Mohr Coulomb model and the Hardening Soil model to emphasize the impact of constitutive model on the dam deformation. The material stiffness parameters used in constitutive models were calibrated based on the available measured crest settlement. The analysis results indicate that the face slab deformation can be numerically predicted based on monitoring data at the dam crest and the Hardening Soil model gives a maximum slab deformation less than that obtained using Mohr Coulomb model.

Gradient field based inhomogeneous volumetric mesh deformation for maxillofacial surgery simulation

This paper presents a novel inhomogeneous volumetric mesh deformation approach by gradient field manipulation, and uses it for maxillofacial surgery simulation. The study is inspired by the state-of-the-art surface deformation techniques based on differential representations. Working in the volumetric domain instead of on only the surface can preserve the volumetric details much better, avoid local self-intersections, and achieve better deformation propagation because of the internal mesh connections. By integrating the mesh cell material stiffness parameter into our new discrete volumetric Laplacian operator, it is very convenient to incorporate inhomogeneous materials into the deformation framework. In addition, the system matrix for solving the volumetric harmonic field to handle the local transformation problem is the same used for Poisson reconstruction equation, thus it requires solving essentially only one global linear system. The system is easy to use, and can accept explicit rotational constraints, or only translational constraints to drive the deformation. One typical maxillofacial surgery case was simulated by the new methodology with inhomogeneous material estimated directly from CT data, and compared to the commonly used finite element method (FEM) approach. The results demonstrated that the deformation methodology achieved good accuracy, as well as interactive performance. Therefore, the usage of our volumetric mesh deformation approach is relevant and suitable for daily clinical practice.