Magnetic resonance temperature imaging validation of a bioheat transfer model for laser-induced thermal therapy

Treatment Modelling of a 3D Tumour in Brain by Laser-Induced Interstitial Thermotherapy

Introduction: There are some ways to examine heat transfer in tumor tissue, which is an important issue in bioengineering. One of these ways uses the bioheat equation, proposed by Pennes, in a continuous medium. Another one uses a porous medium to model heat transfer in living tissues. The objective of this paper was to study an approach to modelling the temperature distribution and tumour ablation in brain tissue and compare results to Pennes' approach. Methods: This approach presents and uses a porous medium as the tissue instead of a continuous medium. In addition, the two approaches (simulation in continuous and porous medium) are compared in terms of temperature simulation and amount of cell ablation. The density, heat conduction factor, and blood perfusion rate are considered functions of temperature. Results: In these approaches, after an 85-second treatment, the temperature increases to about 90°C. The temperature increase of the porous medium is relatively the same as that of the continuous medium and for this reason, the amount of cancerous cells that are ablated in a porous medium is approximately the same as that in a continuous medium. The volume of cell ablation is about 6500 mm3 for two ideas. In addition, the degree of damage, computed from the Arrhenius integral method, and the ablated volume of the tumour endorse equality at the end of treatment. According to the results, similar to the continuous approach, the porous approach predicts the temperature and amount of volume of damaged cells. Conclusion: Therefore, it is possible to use the porous approach instead of the Pennes approach for tumour treatment.

Experimental assessment of microwave ablation computational modeling with MR thermometry

PURPOSE

Computational models are widely used during the design and characterization of microwave ablation (MWA) devices, and have been proposed for pretreatment planning. Our objective was to assess three-dimensional (3D) transient temperature and ablation profiles predicted by MWA computational models with temperature profiles measured experimentally using magnetic resonance (MR) thermometry in ex vivo bovine liver.

MATERIALS AND METHODS

We performed MWA in ex vivo tissue under MR guidance using a custom, 2.45 GHz water-cooled applicator. MR thermometry data were acquired for 2 min prior to heating, during 5-10 min microwave exposures, and for 3 min following heating. Fiber-optic temperature sensors were used to validate the accuracy of MR temperature measurements. A total of 13 ablation experiments were conducted using 30-50 W applied power at the applicator input. MWA computational models were implemented using the finite element method, and incorporated temperature-dependent changes in tissue physical properties. Model-predicted ablation zone extents were compared against MRI-derived Arrhenius thermal damage maps using the Dice similarity coefficient (DSC).

RESULTS

Prior to heating, the observed standard deviation of MR temperature data was in the range of 0.3-0.7°C. Mean absolute error between MR temperature measurements and fiber-optic temperature probes during heating was in the range of 0.5-2.8°C. The mean DSC between model-predicted ablation zones and MRI-derived Arrhenius thermal damage maps for 13 experimental set-ups was 0.95. When comparing simulated and experimentally (i.e. using MRI) measured temperatures, the mean absolute error (MAE %) relative to maximum temperature change was in the range 5%-8.5%.

CONCLUSION

We developed a system for characterizing 3D transient temperature and ablation profiles with MR thermometry during MWA in ex vivo liver tissue, and applied the system for experimental validation of MWA computational models.

Mathematical modeling of mass and energy transport for thermoembolization

Background: Thermoembolization presents a unique treatment alternative for patients diagnosed with hepatocellular carcinoma. The approach delivers a reagent that undergoes an exothermic chemical reaction and combines the benefits of embolic as well as thermal- and chemical-ablative therapy modalities. The target tissue and vascular bed are subjected to simultaneous hyperthermia, ischemia, and chemical denaturation in a single procedure. To guide optimal delivery, we developed a mathematical model for understanding the competing diffusive and convective effects observed in thermoembolization delivery protocols.Methods: A mixture theory formulation was used to mathematically model thermoembolization as chemically reacting transport of an electrophile, dichloroacetyl chloride (DCACl), within porous living tissue. Mass and energy transport of each relevant constituent are considered. Specifically, DCACl is injected into the vessels and exothermically reacts with water in the blood or tissue to form dichloroacetic acid and hydrochloric acid. Neutralization reactions are assumed instantaneous in this approach. We validated the mathematical model predictions of temperature using MR thermometry of the thermoembolization procedure performed in ex vivo kidney.Results: Mathematical modeling predictions of tissue death were highly dependent on the vascular geometry, injection pressure, and intrinsic amount of exothermic energy released from the chemical species, and were able to recapitulate the temperature distributions observed in MR thermometry.Conclusion: These efforts present a first step toward formalizing a mathematical model for thermoembolization and are promising for providing insight for delivery protocol optimization. While our approach captured the observed experimental temperature measurements, larger-scale experimental validation is needed to prioritize additional model complexity and fidelity.

Improved MR thermometry for laser interstitial thermotherapy

OBJECTIVES

To develop, test and evaluate improved 2D and 3D protocols for proton resonance frequency shift magnetic resonance temperature imaging (MRTI) of laser interstitial thermal therapy (LITT). The objective was to develop improved MRTI protocols in terms of temperature measurement precision and volume coverage compared to the 2D MRTI protocol currently used with a commercially available LITT system.

METHODS

Four different 2D protocols and four different 3D protocols were investigated. The 2D protocols used multi-echo readouts to prolong the total MR sampling time and hence the MRTI precision, without prolonging the total acquisition time. The 3D protocols provided volumetric thermometry by acquiring a slab of 12 contiguous slices in the same acquisition time as the 2D protocols. The study only considered readily available pulse sequences (Cartesian 2D and 3D gradient recalled echo and echo planar imaging [EPI]) and methods (partial Fourier and parallel imaging) to ensure wide availability and rapid clinical implementation across vendors and field strengths. In vivo volunteer studies were performed to investigate and compare MRTI precision and image quality. Phantom experiments with LITT heating were performed to investigate and compare MRTI precision and accuracy. Different coil setups were used in the in vivo studies to assess precision differences between using local (such as flex and head coils) and non-local (i.e., body coil) receive coils. Studies were performed at both 1.5 T and 3 T.

RESULTS

The improved 2D protocols provide up to a factor of two improvement in the MRTI precision in the same acquisition time, compared to the currently used clinical protocol. The 3D echo planar imaging protocols provide comparable precision as the currently used 2D clinical protocol, but over a substantially larger field of view, without increasing the acquisition time. As expected, local receive coils perform substantially better than the body coil, and 3 T provides better MRTI accuracy and precision than 1.5 T. 3D data can be zero-filled interpolated in all three dimensions (as opposed to just two dimensions for 2D data), reducing partial volume effects and measuring higher maximum temperature rises.

CONCLUSIONS

With the presented protocols substantially improved MRTI precision (for 2D imaging) or greatly improved field of view coverage (for 3D imaging) can be achieved in the same acquisition time as the currently used protocol. Only widely available pulse sequences and acquisition methods were investigated, which should ensure quick translation to the clinic. Lasers Surg. Med. 51:286-300, 2019. © 2019 Wiley Periodicals, Inc.

Fast MR thermometry using an echo-shifted sequence with simultaneous multi-slice imaging

PURPOSE

Real-time monitoring is important for the safety and effectiveness of high-intensity focused ultrasound (HIFU) therapy. Magnetic resonance imaging is the preferred imaging modality for HIFU monitoring, with its unique capability of temperature imaging. For real-time temperature imaging, higher temporal resolution and larger spatial coverage are needed. In this study, a sequence based on the echo-shifted RF-spoiled gradient echo (GRE) with simultaneous multi-slice (SMS) imaging was designed for fast temperature imaging.

METHODS

A phantom experiment was conducted to evaluate the accuracy of the echo-shifted sequence using a fluorescent fiber thermometer as reference. The temperature uncertainty of the echo-shifted sequence was compared with the traditional GRE sequence at room temperature through the ex vivo porcine muscle. Finally, the ex vivo porcine liver tissue experiment using HIFU heating was performed to demonstrate that the spatial coverage was increased without decreasing temporal resolution.

RESULTS

The echo-shifted sequence had a better temperature uncertainty performance compared with the traditional GRE sequence with the same temporal resolution. The ex vivo heating experiment confirmed that by combining the SMS technique and echo-shifted sequence, the spatial coverage was increased without decreasing the temporal resolution while maintaining high temperature measurement precision.

CONCLUSION

The proposed technique was validated as an effective real-time method for monitoring HIFU therapy.

Accelerated magnetic resonance thermometry in the presence of uncertainties

A model-based information theoretic approach is presented to perform the task of magnetic resonance (MR) thermal image reconstruction from a limited number of observed samples on k-space. The key idea of the proposed approach is to optimally detect samples of k-space that are information-rich with respect to a model of the thermal data acquisition. These highly informative k-space samples can then be used to refine the mathematical model and efficiently reconstruct the image. The information theoretic reconstruction was demonstrated retrospectively in data acquired during MR-guided laser induced thermal therapy (MRgLITT) procedures. The approach demonstrates that locations with high-information content with respect to a model-based reconstruction of MR thermometry may be quantitatively identified. These information-rich k-space locations are demonstrated to be useful as a guide for k-space undersampling techniques. The effect of interactively increasing the predicted number of data points used in the subsampled model-based reconstruction was quantified using the L2-norm of the distance between the subsampled and fully sampled reconstruction. Performance of the proposed approach was also compared with uniform rectilinear subsampling and variable-density Poisson disk subsampling techniques. The proposed subsampling scheme resulted in accurate reconstructions using a small fraction of k-space points, suggesting that the reconstruction technique may be useful in improving the efficiency of thermometry data temporal resolution.

Precision Nanomedicine Using Dual PET and MR Temperature Imaging-Guided Photothermal Therapy

Imaging-based techniques have enabled the direct integration of noninvasive imaging with minimally invasive interventions such as photothermal therapy (PTT) to improve the precision of treatment.

METHODS

We investigated the feasibility of PTT for ovarian cancer under the guidance of PET and MR temperature imaging using copper sulfide nanoparticles (CuS NPs). The tumor distribution of the CuS NPs after systemic administration was assessed using highly sensitive, quantifiable PET imaging. Two wavelengths of near-infrared (NIR) lasers-808 and 980 nm-were tested for PTT using noninvasive MR temperature imaging real-time monitoring.

RESULTS

The in vivo studies revealed that the 980-nm NIR laser had better photothermal effects than the 808-nm NIR laser. These results were in accord with the histologic findings. In vivo PTT using CuS NPs combined with 980-nm laser irradiation achieved significant tumor ablation compared with no treatment control in both subcutaneous (P = 0.007) and orthotopic (P < 0.001) models of ovarian cancer with regard to the percentage of necrotic damage.

CONCLUSION

Our results indicate that real-time monitoring of the accuracy of PTT is a promising approach for future clinical translation of this emerging thermal ablation technique.

A model evaluation study for treatment planning of laser-induced thermal therapy

A cross-validation analysis evaluating computer model prediction accuracy for a priori planning magnetic resonance-guided laser-induced thermal therapy (MRgLITT) procedures in treating focal diseased brain tissue is presented. Two mathematical models are considered. (1) A spectral element discretisation of the transient Pennes bioheat transfer equation is implemented to predict the laser-induced heating in perfused tissue. (2) A closed-form algorithm for predicting the steady-state heat transfer from a linear superposition of analytic point source heating functions is also considered. Prediction accuracy is retrospectively evaluated via leave-one-out cross-validation (LOOCV). Modelling predictions are quantitatively evaluated in terms of a Dice similarity coefficient (DSC) between the simulated thermal dose and thermal dose information contained within N = 22 MR thermometry datasets. During LOOCV analysis, the transient model's DSC mean and median are 0.7323 and 0.8001 respectively, with 15 of 22 DSC values exceeding the success criterion of DSC ≥ 0.7. The steady-state model's DSC mean and median are 0.6431 and 0.6770 respectively, with 10 of 22 passing. A one-sample, one-sided Wilcoxon signed-rank test indicates that the transient finite element method model achieves the prediction success criteria, DSC ≥ 0.7, at a statistically significant level.

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

MRI-guided monitoring of thermal dose and targeted drug delivery for cancer therapy

Application of localized hyperthermia treatment for solid tumor therapy is under active clinical investigation. The success of this treatment methodology, whether for tumor ablation or drug delivery, requires accurate target localization and real-time temperature mapping of the targeted region. Magnetic Resonance Imaging (MRI) can monitor temperature elevations in tissues in real-time during tumor therapy. MRI can also be applied in concert with methods such as High Intensity Focused Ultrasound (HIFU) to enable image-guided drug delivery (IGDD) from temperature sensitive nanocarriers, by exploiting not only its anatomic resolution, but its ability to detect and measure drug release using markers co-loaded with drugs within the nanocarriers. We review this rapidly emerging technology, providing an overview of MRI-guided tissue thermal dose monitoring for HIFU and Laser therapy, its role in targeted drug delivery and its future potential for clinical translation.

Generalised polynomial chaos-based uncertainty quantification for planning MRgLITT procedures

PURPOSE

A generalised polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided laser-induced thermal therapies (MRgLITT).

METHODS

The Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n = 4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms.

RESULTS

Optical parameters provided the highest variance in the model output (peak standard deviation: anisotropy 3.51 °C, absorption 2.94 °C, scattering 1.84 °C, conductivity 1.43 °C, and perfusion 0.94 °C). Further, within the statistical sense considered, a non-linear model of the temperature and damage-dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data.

CONCLUSIONS

Given parameter uncertainties and mathematical modelling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning.

An inverse problem approach to recovery of in vivo nanoparticle concentrations from thermal image monitoring of MR-guided laser induced thermal therapy

Quantification of local variations in the optical properties of tumor tissue introduced by the presence of gold-silica nanoparticles (NP) presents significant opportunities in monitoring and control of NP-mediated laser induced thermal therapy (LITT) procedures. Finite element methods of inverse parameter recovery constrained by a Pennes bioheat transfer model were applied to estimate the optical parameters. Magnetic resonance temperature imaging (MRTI) acquired during a NP-mediated LITT of a canine transmissible venereal tumor in brain was used in the presented statistical inverse problem formulation. The maximum likelihood (ML) value of the optical parameters illustrated a marked change in the periphery of the tumor corresponding with the expected location of NP and area of selective heating observed on MRTI. Parameter recovery information became increasingly difficult to infer in distal regions of tissue where photon fluence had been significantly attenuated. Finite element temperature predictions using the ML parameter values obtained from the solution of the inverse problem are able to reproduce the NP selective heating within 5 °C of measured MRTI estimations along selected temperature profiles. Results indicate the ML solution found is able to sufficiently reproduce the selectivity of the NP mediated laser induced heating and therefore the ML solution is likely to return useful optical parameters within the region of significant laser fluence.

Focal laser ablation of prostate cancer: definition, needs, and future

Current challenges and innovations in prostate cancer management concern the development of focal therapies that allow the treatment of only the cancer areas sparing the rest of the gland to minimize the potential morbidity. Among these techniques, focal laser ablation (FLA) appears as a potential candidate to reach the goal of focusing energy delivery on the identified targets. The aim of this study is to perform an up-to-date review of this new therapeutic modality. Relevant literature was identified using MEDLINE database with no language restrictions (entries: focal therapy, laser interstitial thermotherapy, prostate cancer, FLA) and by cross-referencing from previously identified studies. Precision, real-time monitoring, MRI compatibility, and low cost of integrated system are principal advantages of FLA. Feasibility and safety of this technique have been reported in phase I assays. FLA might eventually prove to be a middle ground between active surveillance and radical treatment. In conclusion, FLA may have found a role in the management of prostate cancer. However, further trials are required to demonstrate the oncologic effectiveness in the long term.

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.

Computational modeling of temperature elevation and thermoregulatory response in the brains of anesthetized rats locally exposed at 1.5 GHz

The dominant effect of human exposures to microwaves is caused by temperature elevation ('thermal effect'). In the safety guidelines/standards, the specific absorption rate averaged over a specific volume is used as a metric for human protection from localized exposure. Further investigation on the use of this metric is required, especially in terms of thermophysiology. The World Health Organization (2006 RF research agenda) has given high priority to research into the extent and consequences of microwave-induced temperature elevation in children. In this study, an electromagnetic-thermal computational code was developed to model electromagnetic power absorption and resulting temperature elevation leading to changes in active blood flow in response to localized 1.457 GHz exposure in rat heads. Both juvenile (4 week old) and young adult (8 week old) rats were considered. The computational code was validated against measurements for 4 and 8 week old rats. Our computational results suggest that the blood flow rate depends on both brain and core temperature elevations. No significant difference was observed between thermophysiological responses in 4 and 8 week old rats under these exposure conditions. The computational model developed herein is thus applicable to set exposure conditions for rats in laboratory investigations, as well as in planning treatment protocols in the thermal therapy.

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.