Dynamic Data-Driven Finite Element Models for Laser Treatment of Cancer

Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States

The rapid spread of the numerous outbreaks of the coronavirus disease 2019 (COVID-19) pandemic has fueled interest in mathematical models designed to understand and predict infectious disease spread, with the ultimate goal of contributing to the decision making of public health authorities. Here, we propose a computational pipeline that dynamically parameterizes a modified SEIRD (susceptible-exposed-infected-recovered-deceased) model using standard daily series of COVID-19 cases and deaths, along with isolated estimates of population-level seroprevalence. We test our pipeline in five heavily impacted states of the US (New York, California, Florida, Illinois, and Texas) between March and August 2020, considering two scenarios with different calibration time horizons to assess the update in model performance as new epidemiologic data become available. Our results show a median normalized root mean squared error (NRMSE) of 2.38% and 4.28% in calibrating cumulative cases and deaths in the first scenario, and 2.41% and 2.30% when new data are assimilated in the second scenario, respectively. Then, 2-week (4-week) forecasts of the calibrated model resulted in median NRMSE of cumulative cases and deaths of 5.85% and 4.68% (8.60% and 17.94%) in the first scenario, and 1.86% and 1.93% (2.21% and 1.45%) in the second. Additionally, we show that our method provides significantly more accurate predictions of cases and deaths than a constant parameterization in the second scenario (p < 0.05). Thus, we posit that our methodology is a promising approach to analyze the dynamics of infectious disease outbreaks, and that our forecasts could contribute to designing effective pandemic-arresting public health policies.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00366-023-01816-9.

Modeling neuron growth using isogeometric collocation based phase field method

We present a new computational framework of neuron growth based on the phase field method and develop an open-source software package called “NeuronGrowth_IGAcollocation”. Neurons consist of a cell body, dendrites, and axons. Axons and dendrites are long processes extending from the cell body and enabling information transfer to and from other neurons. There is high variation in neuron morphology based on their location and function, thus increasing the complexity in mathematical modeling of neuron growth. In this paper, we propose a novel phase field model with isogeometric collocation to simulate different stages of neuron growth by considering the effect of tubulin. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation, and dendrite formation considering the effect of intracellular transport of tubulin on neurite outgrowth. Through comparison with experimental observations, we can demonstrate qualitatively and quantitatively similar reproduction of neuron morphologies at different stages of growth and allow extension towards the formation of neurite networks.

Model-Based Thermometry for Laser Ablation Procedure Using Kalman Filters and Sparse Temperature Measurements

In this work, we implement a data-assimilation Bayesian framework for the reconstruction of the spatiotemporal profile of the tissue temperature during laser irradiation. The predictions of a physical model simulating the heat transfer in the tissue are associated with sparse temperature measurements, using an Unscented Kalman Filter. We compare a standard state-estimation filtering procedure with a joint-estimation (state and parameters) approach: whereas in the state-estimation only the temperature is evaluated, in the joint-estimation the filter corrects also uncertain model parameters (i.e., the medium thermal diffusivity, and laser beam properties). We have tested the method on synthetic temperature data, and on the temperature measured on agar-gel phantom and porcine liver with fiber optic sensors. The joint-estimation allows retrieving an accurate estimate of the temperature distribution with a maximal error < 1.5 C in both synthetic and liver 1D data, and < 2 C in phantom 2D data. Our approach allows also suggesting a strategy for optimizing the temperature estimation based on the positions of the sensors. Under the constraint of using only two sensors, optimal temperature estimations are obtained when one sensor is placed in proximity of the source, and the other one is in a non-symmetrical position.

Interstitial ultrasound ablation of vertebral and paraspinal tumours: parametric and patient-specific simulations

PURPOSE

Theoretical parametric and patient-specific models are applied to assess the feasibility of interstitial ultrasound ablation of tumours in and near the spine and to identify potential treatment delivery strategies.

METHODS

3D patient-specific finite element models (n = 11) of interstitial ultrasound ablation of tumours associated with the spine were generated. Gaseous nerve insulation and various applicator configurations, frequencies (3 and 7 MHz), placement trajectories, and tumour locations were simulated. Parametric studies with multilayered models investigated the impacts of tumour attenuation, tumour dimension, and the thickness of bone insulating critical structures. Temperature and thermal dose were calculated to define ablation (>240 equivalent minutes at 43 °C (EM43 °C)) and safety margins (<45 °C and <6 EM43 °C), and to determine performance and required delivery parameters.

RESULTS

Osteolytic tumours (≤44 mm) encapsulated by bone could be successfully ablated with 7 MHz interstitial ultrasound (8.1-16.6 W/cm(2), 120-5900 J, 0.4-15 min). Ablation of tumours (94.6-100% volumetric) 0-14.5 mm from the spinal canal was achieved within 3-15 min without damaging critical nerves. 3 MHz devices provided faster ablation (390 versus 930 s) of an 18 mm diameter osteoblastic (high bone content) volume than 7 MHz devices. Critical anatomy in proximity to the tumour could be protected by selection of appropriate applicator configurations, active sectors, and applied power schemas, and through gaseous insulation. Preferential ultrasound absorption at bone surfaces facilitated faster, more effective ablations in osteolytic tumours and provided isolation of ablative energies and temperatures.

CONCLUSIONS

Parametric and patient-specific studies demonstrated the feasibility and potential advantages of interstitial ultrasound ablation treatment of paraspinal and osteolytic vertebral tumours.

Thermally induced apoptosis, necrosis, and heat shock protein expression in 3D culture

This study was conducted to compare the heat shock responses of cells grown in 2D and 3D culture environments as indicated by the level of heat shock protein 70 expression and the incidence of apoptosis and necrosis of prostate cancer cell lines in response to graded hyperthermia. PC3 cells were stably transduced with a dual reporter system composed of two tandem expression cassettes-a conditional heat shock protein promoter driving the expression of green fluorescent protein (HSPp-GFP) and a cytomegalovirus (CMV) promoter controlling the constitutive expression of a "beacon" red fluorescent protein (CMVp-RFP). Two-dimensional and three-dimensional cultures of PC3 prostate cancer cells were grown in 96-well plates for evaluation of their time-dependent response to supraphysiological temperature. To induce controlled hyperthermia, culture plates were placed on a flat copper surface of a circulating water manifold that maintained the specimens within ±0.1°C of a target temperature. Hyperthermia protocols included various combinations of temperature, ranging from 37°C to 57°C, and exposure times of up to 2 h. The majority of protocols were focused on temperature and time permutations, where the response gradient was greatest. Post-treatment analysis by flow cytometry analysis was used to measure the incidences of apoptosis (annexin V-FITC stain), necrosis (propidium iodide (PI) stain), and HSP70 transcription (GFP expression). Cells grown in 3D compared with 2D culture showed reduced incidence of apoptosis and necrosis and a higher level of HSP70 expression in response to heat shock at the temperatures tested. Cells responded differently to hyperthermia when grown in 2D and 3D cultures. Three-dimensional culture appears to enhance survival plausibly by activating protective processes related to enhanced-HSP70 expression. These differences highlight the importance of selecting physiologically relevant 3D models in assessing cellular responses to hyperthermia in experimental settings.

Kalman filtered MR temperature imaging for laser induced thermal therapies

The feasibility of using a stochastic form of Pennes bioheat model within a 3-D finite element based Kalman filter (KF) algorithm is critically evaluated for the ability to provide temperature field estimates in the event of magnetic resonance temperature imaging (MRTI) data loss during laser induced thermal therapy (LITT). The ability to recover missing MRTI data was analyzed by systematically removing spatiotemporal information from a clinical MR-guided LITT procedure in human brain and comparing predictions in these regions to the original measurements. Performance was quantitatively evaluated in terms of a dimensionless L(2) (RMS) norm of the temperature error weighted by acquisition uncertainty. During periods of no data corruption, observed error histories demonstrate that the Kalman algorithm does not alter the high quality temperature measurement provided by MR thermal imaging. The KF-MRTI implementation considered is seen to predict the bioheat transfer with RMS error < 4 for a short period of time, ∆t < 10 s, until the data corruption subsides. In its present form, the KF-MRTI method currently fails to compensate for consecutive for consecutive time periods of data loss ∆t > 10 sec.

Model-based planning and real-time predictive control for laser-induced thermal therapy

In this article, the major idea and mathematical aspects of model-based planning and real-time predictive control for laser-induced thermal therapy (LITT) are presented. In particular, a computational framework and its major components developed by authors in recent years are reviewed. The framework provides the backbone for not only treatment planning but also real-time surgical monitoring and control with a focus on MR thermometry enabled predictive control and applications to image-guided LITT, or MRgLITT. Although this computational framework is designed for LITT in treating prostate cancer, it is further applicable to other thermal therapies in focal lesions induced by radio-frequency (RF), microwave and high-intensity-focused ultrasound (HIFU). Moreover, the model-based dynamic closed-loop predictive control algorithms in the framework, facilitated by the coupling of mathematical modelling and computer simulation with real-time imaging feedback, has great potential to enable a novel methodology in thermal medicine. Such technology could dramatically increase treatment efficacy and reduce morbidity.

Adaptive real-time bioheat transfer models for computer-driven MR-guided laser induced thermal therapy

The treatment times of laser induced thermal therapies (LITT) guided by computational prediction are determined by the convergence behavior of partial differential equation (PDE)-constrained optimization problems. In this paper, we investigate the convergence behavior of a bioheat transfer constrained calibration problem to assess the feasibility of applying to real-time patient specific data. The calibration techniques utilize multiplanar thermal images obtained from the nondestructive in vivo heating of canine prostate. The calibration techniques attempt to adaptively recover the biothermal heterogeneities within the tissue on a patient-specific level and results in a formidable PDE constrained optimization problem to be solved in real time. A comprehensive calibration study is performed with both homogeneous and spatially heterogeneous biothermal model parameters with and without constitutive nonlinearities. Initial results presented here indicate that the calibration problems involving the inverse solution of thousands of model parameters can converge to a solution within three minutes and decrease the [see text for symbol](L) (2) (2) ((0, T; L) (2) ((Omega))) norm of the difference between computational prediction and the measured temperature values to a patient-specific regime.

Computational modeling and real-time control of patient-specific laser treatment of cancer

An adaptive feedback control system is presented which employs a computational model of bioheat transfer in living tissue to guide, in real-time, laser treatments of prostate cancer monitored by magnetic resonance thermal imaging. The system is built on what can be referred to as cyberinfrastructure-a complex structure of high-speed network, large-scale parallel computing devices, laser optics, imaging, visualizations, inverse-analysis algorithms, mesh generation, and control systems that guide laser therapy to optimally control the ablation of cancerous tissue. The computational system has been successfully tested on in vivo, canine prostate. Over the course of an 18 min laser-induced thermal therapy performed at M.D. Anderson Cancer Center (MDACC) in Houston, Texas, the computational models were calibrated to intra-operative real-time thermal imaging treatment data and the calibrated models controlled the bioheat transfer to within 5 degrees C of the predetermined treatment plan. The computational arena is in Austin, Texas and managed at the Institute for Computational Engineering and Sciences (ICES). The system is designed to control the bioheat transfer remotely while simultaneously providing real-time remote visualization of the on-going treatment. Post-operative histology of the canine prostate reveal that the damage region was within the targeted 1.2 cm diameter treatment objective.

The laser driven heating balloon catheter: vessel dilatation characteristics

We studied on the dilatation characteristics of our new angioplasty, photo-thermo dynamic balloon (PTDB) angioplasty, which provides short-term heating (15s, 50-70 degrees C) dilatation by the combination of laser heat generator and fluid perfusion. In this study, we employed the ex vivo experiments to demonstrate the feasibility of our PTDB angioplasty with extracted porcine carotid artery. Balloon temperature and heating duration were easily controlled with the laser power and irradiation duration. Arterial dilatation was performed with the prototype PTDB catheter (3mm in diameter) ex vivo, sufficient dilation was attained with low dilatation pressure (2atm) that is lower than the limit pressure of elastic region (8atm in this case). The principal of our PTDB angioplasty that was based on the experimental results was dilatation in elastic region, while traditional POBA was accompanied with plastic deformation of artery. It is predicted that successful way of PTDB dilatation was attributed to collagen softening. Collagen coagulation and/or restructure after the heating dilatation might suspend the dilated arterial lumen. We demonstrated the feasibility of our PTDB angioplasty. We think collagen denaturation degree may be the important factor in this methodology.

Optimization and real-time control for laser treatment of heterogeneous soft tissues

Predicting the outcome of thermotherapies in cancer treatment requires an accurate characterization of the bioheat transfer processes in soft tissues. Due to the biological and structural complexity of tumor (soft tissue) composition and vasculature, it is often very difficult to obtain reliable tissue properties that is one of the key factors for the accurate treatment outcome prediction. Efficient algorithms employing in vivo thermal measurements to determine heterogeneous thermal tissues properties in conjunction with a detailed sensitivity analysis can produce essential information for model development and optimal control. The goals of this paper are to present a general formulation of the bioheat transfer equation for heterogeneous soft tissues, review models and algorithms developed for cell damage, heat shock proteins, and soft tissues with nanoparticle inclusion, and demonstrate an overall computational strategy for developing a laser treatment framework with the ability to perform real-time robust calibrations and optimal control. This computational strategy can be applied to other thermotherapies using the heat source such as radio frequency or high intensity focused ultrasound.

Nanoshell-mediated laser surgery simulation for prostate cancer treatment

Laser surgery, or laser-induced thermal therapy, is a minimally invasive alternative or adjuvant to surgical resection in treating tumors embedded in vital organs with poorly defined boundaries. Its use, however, is limited due to the lack of precise control of heating and slow rate of thermal diffusion in the tissue. Nanoparticles, such as nanoshells, can act as intense heat absorbers when they are injected into tumors. These nanoshells can enhance thermal energy deposition into target regions to improve the ability for destroying larger cancerous tissue volumes with lower thermal doses. The goal of this paper is to present an integrated computer model using a so-called nested-block optimization algorithm to simulate laser surgery and provide transient temperature field predictions. In particular, this algorithm aims to capture changes in optical and thermal properties due to nanoshell inclusion and tissue property variation during laser surgery. Numerical results show that this model is able to characterize variation of tissue properties for laser surgical procedures and predict transient temperature fields comparable to those measured by in vivo magnetic resonance temperature imaging techniques. Note that the computational approach presented in the study is quite general and can be applied to other types of nanoparticle inclusions.