Mathematical modeling and computer simulation of needle insertion into soft tissue

Personalised in silico biomechanical modelling towards the optimisation of high dose-rate brachytherapy planning and treatment against prostate cancer

High dose-rate brachytherapy presents a promising therapeutic avenue for prostate cancer management, involving the temporary implantation of catheters which deliver radioactive sources to the cancerous site. However, as catheters puncture and penetrate the prostate, tissue deformation is evident which may affect the accuracy and efficiency of the treatment. In this work, a data-driven in silico modelling procedure is proposed to simulate brachytherapy while accounting for prostate biomechanics. Comprehensive magnetic resonance and transrectal ultrasound images acquired prior, during and post brachytherapy are employed for model personalisation, while the therapeutic procedure is simulated via sequential insertion of multiple catheters in the prostate gland. The medical imaging data are also employed for model evaluation, thus, demonstrating the potential of the proposed in silico procedure to be utilised pre- and intra-operatively in the clinical setting.

A comprehensive review on modeling aspects of infusion-based drug delivery in the brain

Brain disorders represent an ever-increasing health challenge worldwide. While conventional drug therapies are less effective due to the presence of the blood-brain barrier, infusion-based methods of drug delivery to the brain represent a promising option. Since these methods are mechanically controlled and involve multiple physical phases ranging from the neural and molecular scales to the brain scale, highly efficient and precise delivery procedures can significantly benefit from a comprehensive understanding of drug-brain and device-brain interactions. Behind these interactions are principles of biophysics and biomechanics that can be described and captured using mathematical models. Although biomechanics and biophysics have received considerable attention, a comprehensive mechanistic model for modeling infusion-based drug delivery in the brain has yet to be developed. Therefore, this article reviews the state-of-the-art mechanistic studies that can support the development of next-generation models for infusion-based brain drug delivery from the perspective of fluid mechanics, solid mechanics, and mathematical modeling. The supporting techniques and database are also summarized to provide further insights. Finally, the challenges are highlighted and perspectives on future research directions are provided. STATEMENT OF SIGNIFICANCE: Despite the immense potential of infusion-based drug delivery methods for bypassing the blood-brain barrier and efficiently delivering drugs to the brain, achieving optimal drug distribution remains a significant challenge. This is primarily due to our limited understanding of the complex interactions between drugs and the brain that are governed by principles of biophysics and biomechanics, and can be described using mathematical models. This article provides a comprehensive review of state-of-the-art mechanistic studies that can help to unravel the mechanism of drug transport in the brain across the scales, which underpins the development of next-generation models for infusion-based brain drug delivery. More broadly, this review will serve as a starting point for developing more effective treatments for brain diseases and mechanistic models that can be used to study other soft tissue and biomaterials.

A method for predicting needle insertion deflection in soft tissue based on cutting force identification

The deflection modeling during the insertion of bevel-tipped flexible needles into soft tissues is crucial for robot-assisted flexible needle insertion into specific target locations within the human body during percutaneous biopsy surgery. This paper proposes a mechanical model based on cutting force identification to predict the deflection of flexible needles in soft tissues. Unlike other models, this method does not require measuring Young's modulus (E ) and Poisson's ratio (ν ) of tissues, which require complex hardware to obtain. In the model, the needle puncture process is discretized into a series of uniform-depth puncture steps. The needle is simplified as a cantilever beam supported by a series of virtual springs, and the influence of tissue stiffness on needle deformation is represented by the spring stiffness coefficient of the virtual spring. By theoretical modeling and experimental parameter identification of cutting force, the spring stiffness coefficients are obtained, thereby modeling the deflection of the needle. To verify the accuracy of the proposed model, the predicted model results were compared with the deflection of the puncture experiment in polyvinyl alcohol (PVA) gel samples, and the average maximum error range predicted by the model was between 0.606 ± 0.167 mm and 1.005 ± 0.174 mm, which showed that the model can successfully predict the deflection of the needle. This work will contribute to the design of automatic control strategies for needles.

Impact of Injection-Based Delivery Parameters on Local Distribution Volume of Ethyl-Cellulose Ethanol Gel in Tissue and Tissue Mimicking Phantoms

OBJECTIVE

Local drug delivery aims to minimize systemic toxicity by preventing off-target effects; however, injection parameters influencing depot formation of injectable gels have yet to be thoroughly studied. We explored the effects of needle characteristics, injection depth, rate, volume, and polymer concentration on gel ethanol distribution in both tissue and phantoms.

METHODS

The polymer ethyl cellulose (EC) was added to ethanol to form an injectable gel to ablate cervical precancer and cancer. Tissue mimicking phantoms composed of 1% agarose dissolved in deionized water were used to establish overall trends between various injection parameters and the resulting gel distribution. Additional experiments were performed in excised swine cervices with a CT-imageable injectate formulation, which enabled visualization of the distribution without tissue sectioning.

RESULTS

Needle type and injection rate had minimal impact on gel distribution, while needle depths ≥13 mm yielded significantly larger distributions. Needle gauge and EC concentration impacted injection pressure with maximum gel distribution achieved when the pressure was 70-250 kPa. Injection volumes ≤3 mL of 6% EC-ethanol minimized fluid leakage away from the injection site. Results guided the development of a speculum-compatible hand-held injector to deliver gel ethanol into the cervix.

CONCLUSION

Needle depth, gauge, and polymer concentration are critical to consider when delivering injectable gels.

SIGNIFICANCE

This study addressed key questions related to the impact of injection-based parameters on gel distribution at a scale relevant to human applications including: 1) how best to deliver EC-ethanol into the cervix and 2) general insights about injection protocols relevant to the delivery of injectable gels in tissue.

Toward FBG-Sensorized Needle Shape Prediction in Tissue Insertions

Complex needle shape prediction remains an issue for planning of surgical interventions of flexible needles. In this paper, we validate a theoretical method for flexible needle shape prediction allowing for non-uniform curvatures, extending upon a previous sensor-based model which combines curvature measurements from fiber Bragg grating (FBG) sensors and the mechanics of an inextensible elastic rod to determine and predict the 3D needle shape during insertion. We evaluate the model's effectiveness in single-layer isotropic tissue for shape sensing and shape prediction capabilities. Experiments on a four-active area, FBG-sensorized needle were performed in varying single-layer isotropic tissues under stereo vision to provide 3D ground truth of the needle shape. The results validate a viable 3D needle shape prediction model accounting for non-uniform curvatures in flexible needles with mean needle shape sensing and prediction root-mean-square errors of 0.479 mm and 0.892 mm, respectively.

Patient-specific solution of the electrocorticography forward problem in deforming brain

Invasive intracranial electroencephalography (iEEG), or electrocorticography (ECoG), measures electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery. Combined with numerical modeling it can further improve accuracy of epilepsy surgery planning. Accurate solution of the iEEG forward problem, which is a crucial prerequisite for solving the iEEG inverse problemin epilepsy seizure onset zone localization, requires accurate representation of the patient's brain geometry and tissue electrical conductivity after implantation of electrodes. However, implantation of subdural grid electrodes causes the brain to deform, which invalidates preoperatively acquired image data. Moreover, postoperative magnetic resonance imaging (MRI) is incompatible with implanted electrodes and computed tomography (CT) has insufficient range of soft tissue contrast, which precludes both MRI and CT from being used to obtain the deformed postoperative geometry. In this paper, we present a biomechanics-based image warping procedure using preoperative MRI for tissue classification and postoperative CT for locating implanted electrodes to perform non-rigid registration of the preoperative image data to the postoperative configuration. We solve the iEEG forward problem on the predicted postoperative geometry using the finite element method (FEM) which accounts for patient-specific inhomogeneity and anisotropy of tissue conductivity. Results for the simulation of a current source in the brain show large differences in electric potential predicted by the models based on the original images and the deformed images corresponding to the brain geometry deformed by placement of invasive electrodes. Computation of the lead field matrix (useful for solution of the iEEG inverse problem) also showed significant differences between the different models. The results suggest that rapid and accurate solution of the forward problem in a deformed brain for a given patient is achievable.

Automatic framework for patient-specific modelling of tumour resection-induced brain shift

Our motivation is to enable non-biomechanical engineering specialists to use sophisticated biomechanical models in the clinic to predict tumour resection-induced brain shift, and subsequently know the location of the residual tumour and its boundary. To achieve this goal, we developed a framework for automatically generating and solving patient-specific biomechanical models of the brain. This framework automatically determines patient-specific brain geometry from MRI data, generates patient-specific computational grid, assigns material properties, defines boundary conditions, applies external loads to the anatomical structures, and solves differential equations of nonlinear elasticity using Meshless Total Lagrangian Explicit Dynamics (MTLED) algorithm. We demonstrated the effectiveness and appropriateness of our framework on real clinical cases of tumour resection-induced brain shift.

Effective Viscoplastic-Softening Model Suitable for Brain Impact Modelling

In this paper, we address the numerical aspects and implementation of a nonlinear viscoplastic model of the mechanical behaviour of brain tissue to simulate the dynamic responses related to impact loads which may cause traumatic injury. Among the various viscoelastic models available, we deliberately considered modifying the Norton–Hoff model in order to introduce non-typical viscoplastic softening behaviour that imitates a brain’s response just several milliseconds after a rapid impact. We describe the discretisation and three dimensional implementation of the model, with the aim of obtaining accurate numerical results in a reasonable computational time. Due to the large scale and complexity of the problem, a parallel computation technique, using a space–time finite element method, was used to facilitate the computation boost. It is proven that, after calibrating, the introduced viscoplastic-softening model is better suited for modelling brain tissue behaviour for the specific case of rapid impact loading rather than the commonly used viscoelastic models.