Surface deformation and reaction force estimation of liver tissue based on a novel nonlinear mass-spring-damper viscoelastic model

Kirchhoff's law-based velocity-controlled motion models to predict real-time cutting forces in minimally invasive surgeries

A theoretical framework, united by a "system effect" is formulated to model the cutting/haptic force evolution at the cutting edge of a surgical cutting instrument during its penetration into soft biological tissue in minimally invasive surgery. Other cutting process responses, including tissue fracture force, friction force, and damping, are predicted by the model as well. The model is based on a velocity-controlled formulation of the corresponding equations of motion, derived for a surgical cutting instrument and tissue based on Kirchhoff's fundamental energy conservation law. It provides nearly zero residues (absolute errors) in the equations of motion balances. In addition, concurrent closing relationships for the fracture force, friction coefficient, friction force, process damping, strain rate function (a constitutive tissue model), and their implementation within the proposed theoretical framework are established. The advantage of the method is its ability to make precise real-time predictions of the aperiodic fluctuating evolutions of the cutting forces and the other process responses. It allows for the robust modeling of the interactions between a medical instrument and a nonlinear viscoelastic tissue under any physically feasible working conditions. The cutting process model was partially qualitatively verified through numerical simulations and by comparing the computed cutting forces with experimentally measured values during robotic uniaxial biopsy needle constant velocity insertion into artificial gel tissue, obtained from previous experimental research. The comparison has shown a qualitatively similar adequate trend in the evolution of the experimentally measured and numerically predicted cutting forces during insertion of the needle.

Quantifying the Impact of Cancer on the Viscoelastic Properties of the Prostate Gland using a Quasi-Linear Viscoelastic Model

Pathological disorders can alter the mechanical properties of biological tissues, and studying such changes can help to better understand the disease progression. The prostate gland is no exception, as previous studies have shown that cancer can affect its mechanical properties. However, most of these studies have focused on the elastic properties of the tissue and have overlooked the impact of cancer on its viscous response. To address this gap, we used a quasi-linear viscoelastic model to investigate the impact of cancer on both the elastic and viscous characteristics of the prostate gland. By comparing the viscoelastic properties of segments influenced by cancer and those unaffected by cancer in 49 fresh prostates, removed within two hours after prostatectomy surgery, we were able to determine the influence of cancer grade and tumor volume on the tissue. Our findings suggest that tumor volume significantly affects both the elastic modulus and viscosity of the prostate (p-value less than 2%). Specifically, we showed that cancer increases Young's modulus and shear relaxation modulus by 20%. These results have implications for using mechanical properties of the prostate as a potential biomarker for cancer. However, developing an in vivo apparatus to measure these properties remains a challenge that needs to be addressed in future research. STATEMENT OF SIGNIFICANCE: This study is the first to explore how cancer impacts the mechanical properties of prostate tissues using a quasi-linear viscoelastic model. We examined 49 fresh prostate samples collected immediately after surgery and correlated their properties with cancer presence identified in pathology reports. Our results demonstrate a 20% change in the viscoelastic properties of the prostate due to cancer. We initially validated our approach using tissue-mimicking phantoms and then applied it to differentiate between cancerous and normal prostate tissues. These findings offer potential for early cancer detection by assessing these properties. However, conducting these tests in vivo remains a challenge for future research.

Quasi-Linear Viscoelastic Characterization of Soft Tissue-Mimicking Materials

We present a novel method based on the quasi-linear viscoelastic (QLV) theory to describe the time-dependent behavior of soft materials. Unlike previous methods for deriving QLV parameters, we characterize the elastic and viscous behavior of materials separately by using two different sets of experiments. To model the nonlinear elastic behavior, we fit the elastic stress response with a one-term Ogden model. Then, we model the relaxation behavior with a Prony series to compare the stress relaxation of the material at different timescales. This new method allows us to characterize materials with narrow confidence intervals (high accuracy), independently from the loading conditions. We validate our model using samples made of phantom materials that mimic normal and cancerous prostate tissues in terms of Young's modulus. Our model is shown to distinguish materials with similar elastic (viscous) properties but different viscous (elastic) properties. Drawing a precise distinction between the phantoms, this method could be useful for prostate cancer (PCa) diagnosis; but significant clinical studies will be needed in the future.

A Novel Nonlinear Parameter Estimation Method of Soft Tissues

The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine (WCFM_SVM). Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young's modulus and Poisson's ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg-Marquardt (LM) algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.

Deformation of facial model for complete denture prosthesis using ARAP group method and elastic properties

With the development of 3D printing and computer graphics technology, mouth rehabilitation has increasingly adopted digital methods. This research proposes a new method to transform the appearance of facial model after complete denture prosthesis. A feature template with few feature points is first constructed according to the facial muscle anatomy and facial deformation after complete denture prosthesis. Next, the traditional as-rigid-as-possible (ARAP) method is optimised by clustering based on facial muscles. The optimised ARAP method is then used for real-time and interactive simulations. Finally, by classifying the degrees of elasticity in the model with additional weights, the simulation can be customised to the skin of individual patients. Different degrees of elastic deformation and post-operative models are superimposed for match analysis. Compared with our previous study, the error is reduced by 24.05%. Results show that our method can deform facial models accurately and efficiently.