Cubical Mass-Spring Model design based on a tensile deformation test and nonlinear material model

Lattice Models: Non-Conventional simulation methods for mechanobiology

Computational methods represent a powerful tool to explore biophysical phenomena occurring at small scales and hence difficult to observe through experimental setups. In detail, they can provide a support to mechanobiology, with the aim of understanding the behavior of living cells interacting with the surrounding environment. To this end, lattice models can provide a simulation framework that is highly reliable and easy to implement, even for simulations involving large deformations and topological changes during time evolution. In this review article, elastic network models for studying biological molecules are described, several lattice spring models for investigating cell behaviors are discussed, and the adoption of lattice beam models for biomimetic structures design is presented. The lattice modelling approaches could be regarded as a valuable option to conduct in-silico experiments and consolidate the emergent mechanobiology research field.

Real-time simulation for multi-component biomechanical analysis using localized tissue constraint progressive transfer learning

In virtual surgical training, it is crucial to achieve real-time, high-fidelity simulation of the tissue deformation. The anisotropic and nonlinear characteristics of the organ with multi-component make accurate real-time deformation simulation difficult. A localized tissue constraint progressive transfer learning method is proposed in this paper, where the base-compensated dual-output transfer learning strategy and the localized tissue constraint progressive learning architecture are developed. The proposed strategy enriches the multi-component biomechanical dataset to fully represent complex force-displacement with minimal high-quality data. Meanwhile, the proposed architecture adopts focused and progressive model to accurately describe tissues with varied biomechanical properties rather than singular homogeneous model. We made comparison with 4 state-of-the-art (SOTA) methods in simulating multi-component biomechanical deformations of organs with 100 pairs of testing data. Results show that the accuracy of our method is 50% higher than other methods in different validation matrix. And our method can stably simulate the deformations in 0.005 s per frame, which largely improves the computing efficiency.

Multiphysics and multiscale modeling of uterine contractions: integrating electrical dynamics and soft tissue deformation with fiber orientation

The development of a comprehensive uterine model that seamlessly integrates the intricate interactions between the electrical and mechanical aspects of uterine activity could potentially facilitate the prediction and management of labor complications. Such a model has the potential to enhance our understanding of the initiation and synchronization mechanisms involved in uterine contractions, providing a more profound comprehension of the factors associated with labor complications, including preterm labor. Consequently, it has the capacity to assist in more effective preparation and intervention strategies for managing such complications. In this study, we present a computational model that effectively integrates the electrical and mechanical components of uterine contractions. By combining a state-of-the-art electrical model with the Hyperelastic Mass-Spring Model (HyperMSM), we adopt a multiphysics and multiscale approach to capture the electrical and mechanical activities within the uterus. The electrical model incorporates the generation and propagation of action potentials, while the HyperMSM simulates the mechanical behavior and deformations of the uterine tissue. Notably, our model takes into account the orientation of muscle fibers, ensuring that the simulated contractions align with their inherent directional characteristics. One noteworthy aspect of our contraction model is its novel approach to scaling the rest state of the mesh elements, as opposed to the conventional method of applying mechanical loads. By doing so, we eliminate artificial strain energy resulting from the resistance of soft tissues' elastic properties during contractions. We validated our proposed model through test simulations, demonstrating its feasibility and its ability to reproduce expected contraction patterns across different mesh resolutions and configurations. Moving forward, future research efforts should prioritize the validation of our model using robust clinical data. Additionally, it is crucial to refine the model by incorporating a more realistic uterus model derived from medical imaging. Furthermore, applying the model to simulate the entire childbirth process holds immense potential for gaining deeper insights into the intricate dynamics of labor.

Three-dimensional wound flattening method for mapping skin mechanical properties based on finite element method

Clinically, skin flap transplantation was often used to repair skin wounds. However, the flap design process with sample cloth is rough and easy to cause infection and necrosis. So an accurate and individual shape design of preoperative flap should be solved. Therefore, a 3D wound flattening method for mapping skin mechanical properties based on finite element method was proposed. Firstly, the 3D point cloud of skin wound was obtained by 3D scanner, and the hierarchical structure of wound model was established. Then a geometric flattening method of wound surface was proposed based on the existing surface flattening theory. The concept of deformed point was introduced according to the special shape of wound surface, and the corresponding modification was given to the original flattening process. Secondly, the mechanical properties of pig skin samples with different orientations were measured by static tensile test. Finally, based on the morphological flattening of wound model and the mechanical parameters of pig skin, a unit material model based on material deformation energy was established. The unit deformation was attributed to the equivalent load acting on the node, and a finite element optimization method of wound unfolding shape based on material deformation energy was proposed. In order to optimize the overall deformation energy, the flap shape was optimized and adjusted to achieve the preoperative design. Clinical examples were selected for verification and analysis. The results show that the proposed method can provide a reasonable and reliable preliminary guide for preoperative flap shape design in clinical wound repair.

Maximum likelihood-based extended Kalman filter for soft tissue modelling

Realistic modelling of human soft tissue is very important in medical applications. This paper proposes a novel method by dynamically incorporating soft tissue characterisation in the process of soft tissue modelling to increase the modelling fidelity. This method defines nonlinear tissue deformation with unknown mechanical properties as a problem of nonlinear filtering identification to dynamically identify mechanical properties and further estimate nonlinear deformation behaviour of soft tissue. It combines maximum likelihood theory, nonlinear filtering and nonlinear finite element method (NFEM) for modelling of nonlinear tissue deformation behaviour based on dynamic identification of homogeneous tissue properties. On the basis of hyperelasticity, a nonlinear state-space equation is established by discretizing tissue deformation through NFEM for dynamic filtering. A maximum likelihood algorithm is also established to dynamically identify tissue mechanical properties during the deformation process. Upon above, a maximum likelihood-based extended Kalman filter is further developed for dynamically estimating tissue nonlinear deformation based on dynamic identification of tissue mechanical properties. Simulation and experimental analyses reveal that the proposed method not only overcomes the NFEM limitation of expensive computations, but also absorbs the NFEM merit of high accuracy for modelling of homogeneous tissue deformation. Further, the proposed method also effectively identifies tissue mechanical properties during the deformation modelling process.

HyperMSM: A new MSM variant for efficient simulation of dynamic soft-tissue deformations

BACKGROUND AND OBJECTIVE

Fast, accurate, and stable simulation of soft tissue deformation is a challenging task. Mass-Spring Model (MSM) is one of the popular methods used for this purpose for its simple implementation and potential to provide fast dynamic simulations. However, accurately simulating a non-linear material within the mass-spring framework is still challenging. The objective of the present study is to develop and evaluate a new efficient hyperelastic Mass-Spring Model formulation to simulate the Neo-Hookean deformable material, called HyperMSM.

METHODS

Our novel HyperMSM formulation is applicable for both tetrahedral and hexahedral mesh configurations and is compatible with the original projective dynamics solver. In particular, the proposed MSM variant includes springs with variable rest-lengths and a volume conservation constraint. Two applications (transtibial residual limb and the skeletal muscle) were conducted.

RESULTS

Compared to finite element simulations, obtained results show RMSE ranges of [2.8%-5.2%] and [0.46%-5.4%] for stress-strain and volumetric responses respectively for strains ranging from -50% to +100%. The displacement error range in our transtibial residual limb simulation is around [0.01mm-0.7 mm]. The RMSE range of relative nodal displacements for the skeletal psoas muscle model is [0.4%-1.7%].

CONCLUSIONS

Our novel HyperMSM formulation allows hyperelastic behavior of soft tissues to be described accurately and efficiently within the mass-spring framework. As perspectives, our formulation will be enhanced with electric behavior toward a multi-physical soft tissue mass-spring modeling framework. Then, the coupling with an augmented reality environment will be performed.

Soft Tissue Hybrid Model for Real-Time Simulations

In this article, a recent formulation for real-time simulation is developed combining the strain energy density of the Spring Mass Model (SMM) with the equivalent representation of the Strain Energy Density Function (SEDF). The resulting Equivalent Energy Spring Model (EESM) is expected to provide information in real-time about the mechanical response of soft tissue when subjected to uniaxial deformations. The proposed model represents a variation of the SMM and can be used to predict the mechanical behavior of biological tissues not only during loading but also during unloading deformation states. To assess the accuracy achieved by the EESM, experimental data was collected from liver porcine samples via uniaxial loading and unloading tensile tests. Validation of the model through numerical predictions achieved a refresh rate of 31 fps (31.49 ms of computation time for each frame), achieving a coefficient of determination R² from 93.23% to 99.94% when compared to experimental data. The proposed hybrid formulation to characterize soft tissue mechanical behavior is fast enough for real-time simulation and captures the soft material nonlinear virgin and stress-softened effects with high accuracy.

Design and Evaluation of Personalized Percutaneous Coronary Intervention Surgery Simulation System

In recent years, medical simulators have been widely applied to a broad range of surgery training tasks. However, most of the existing surgery simulators can only provide limited immersive environments with a few pre-processed organ models, while ignoring the instant modeling of various personalized clinical cases, which brings substantive differences between training experiences and real surgery situations. To this end, we present a virtual reality (VR) based surgery simulation system for personalized percutaneous coronary intervention (PCI). The simulation system can directly take patient-specific clinical data as input and generate virtual 3D intervention scenarios. Specially, we introduce a fiber-based patient-specific cardiac dynamic model to simulate the nonlinear deformation among the multiple layers of the cardiac structure, which can well respect and correlate the atriums, ventricles and vessels, and thus gives rise to more effective visualization and interaction. Meanwhile, we design a tracking and haptic feedback hardware, which can enable users to manipulate physical intervention instruments and interact with virtual scenarios. We conduct quantitative analysis on deformation precision and modeling efficiency, and evaluate the simulation system based on the user studies from 16 cardiologists and 20 intervention trainees, comparing it to traditional desktop intervention simulators. The results confirm that our simulation system can provide a better user experience, and is a suitable platform for PCI surgery training and rehearsal.

Real-time deformation of human soft tissues: A radial basis meshless 3D model based on Marquardt's algorithm

BACKGROUND

When the meshless method is used to establish the mathematical-mechanical model of human soft tissues, it is necessary to define the space occupied by human tissues as the problem domain and the boundary of the domain as the surface of those tissues. Nodes should be distributed in both the problem domain and on the boundaries. Under external force, the displacement of the node is computed by the meshless method to represent the deformation of biological soft tissues. However, computation by the meshless method consumes too much time, which will affect the simulation of real-time deformation of human tissues in virtual surgery.

METHODS

In this article, the Marquardt's Algorithm is proposed to fit the nodal displacement at the problem domain's boundary and obtain the relationship between surface deformation and force. When different external forces are applied, the deformation of soft tissues can be quickly obtained based on this relationship.

RESULTS AND CONCLUSIONS

The analysis and discussion show that the improved model equations with Marquardt's Algorithm not only can simulate the deformation in real-time but also preserve the authenticity of the deformation model's physical properties.

A New Deformation Model of Biological Tissue for Surgery Simulation

A novel meshless deformation model of biological soft tissue, which is mainly based on the radial basis function point interpolation, is presented for interactive simulation applications such as virtual surgery simulators. Compared with conventional mesh models, the proposed model is particularly suitable for simulating large deformation, sucking and cutting tasks since there is no need to maintain grid information. Kelvin viscoelasticity, which represents relaxation, creep, and hysteresis of soft tissue, is integrated into the proposed model, making the simulation much more realistic than many existing meshless models. To verify the validity of the proposed model, a biomechanical test was performed on real-life biological tissue and the results show that the maximum relative error between the forces from the biomechanical test and those obtained from the model is less than 5.8%. The proposed model was also implemented on a neurosurgery simulator, which showed that the deformation of the brain tumor can be simulated in a high degree of accuracy with real-time performance. In particular, the error and distortion from the remeshing process inherited in conventional mesh models when deformation is large are avoided.

A new deformation simulation algorithm for elastic-plastic objects based on splat primitives

To achieve high computational efficiency and realistic visual effects, a new simulation algorithm for soft tissue deformation, which is based on a shape-matching scheme using splat primitives, is presented for interactive real-time applications, such as surgery simulation and video games. The most important novelty of the proposed approach lies in the fact that surface splats instead of points are employed in the computation of the deformation and fracturing of an elastic-plastic object. By controlling the sampling density and automatically adjusting the size of the circular splats, the surface of the simulated object can be seamlessly covered with a much small number of splats than points. Splats are then divided into clusters using the K-Means clustering algorithm. As a result, the elastic-plastic deformation of these clusters can be simulated using a shape-matching strategy, allowing more degrees of freedom (DOFs) in the simulation. Experimental results demonstrate that the proposed algorithm enormously reduces memory space and greatly improves computational efficiency (approximately twice in simulating plastic deformations compared with classical shape-matching methods), making it more suitable for interactive and real-time applications.

Personalized heterogeneous deformable model for fast volumetric registration

BACKGROUND

Biomechanical deformable volumetric registration can help improve safety of surgical interventions by ensuring the operations are extremely precise. However, this technique has been limited by the accuracy and the computational efficiency of patient-specific modeling.

METHODS

This study presents a tissue-tissue coupling strategy based on penalty method to model the heterogeneous behavior of deformable body, and estimate the personalized tissue-tissue coupling parameters in a data-driven way. Moreover, considering that the computational efficiency of biomechanical model is highly dependent on the mechanical resolution, a practical coarse-to-fine scheme is proposed to increase runtime efficiency. Particularly, a detail enrichment database is established in an offline fashion to represent the mapping relationship between the deformation results of high-resolution hexahedral mesh extracted from the raw medical data and a newly constructed low-resolution hexahedral mesh. At runtime, the mechanical behavior of human organ under interactions is simulated with this low-resolution hexahedral mesh, then the microstructures are synthesized in virtue of the detail enrichment database.

RESULTS

The proposed method is validated by volumetric registration in an abdominal phantom compression experiments. Our personalized heterogeneous deformable model can well describe the coupling effects between different tissues of the phantom. Compared with high-resolution heterogeneous deformable model, the low-resolution deformable model with our detail enrichment database can achieve 9.4× faster, and the average target registration error is 3.42 mm, which demonstrates that the proposed method shows better volumetric registration performance than state-of-the-art.

CONCLUSIONS

Our framework can well balance the precision and efficiency, and has great potential to be adopted in the practical augmented reality image-guided robotic systems.

Local deformation for soft tissue simulation

This paper presents a new methodology to localize the deformation range to improve the computational efficiency for soft tissue simulation. This methodology identifies the local deformation range from the stress distribution in soft tissues due to an external force. A stress estimation method is used based on elastic theory to estimate the stress in soft tissues according to a depth from the contact surface. The proposed methodology can be used with both mass-spring and finite element modeling approaches for soft tissue deformation. Experimental results show that the proposed methodology can improve the computational efficiency while maintaining the modeling realism.

Synchronous simulation for deformation of liver and gallbladder with stretch and compression compensation

One challenge in surgical simulation is to design stable deformable models to simulate the dynamics of organs synchronously. In this paper, we develop a novel mass-spring model on the tetrahedral meshes for soft organs such as the liver and gallbladder, which can stably deform with large time steps. We model the contact forces between the organs as a kind of forces generated by the tensions of repulsive springs connecting in between the organs. The simulation system couples a pair of constraints on the length of springs with an implicit integration method. Based on the novel constraints, our simulator can efficiently preserve the volumes and geometric properties of the liver and gallbladder during the simulation. The numerical examples demonstrate that the proposed simulation system can provide realistic and stable deformable results.