Evaluation of the impedance technique for cryosurgery in a theoretical model of the head

Impedance and conductivity of bovine myocardium during freezing and thawing at slow rates - implications for cardiac cryo-ablation

Increasing impedance during freezing might be a valuable marker for guiding cardiac cryo-ablation. We provide model based insights on how decreasing temperature below the freezing point of tissue relates to the percentage of frozen water. Furthermore, we provide experimental data for comparing this percentage with the increase in impedance. Measurements were performed on a bovine tissue sample at frequencies between 5 and 80 kHz. Slow cooling and heating rates were applied to minimize temperature gradients in the myocardial sample and to allow accurate assessment of the freezing point. Computer simulation was applied to link impedance with temperature dependent conductivities. The osmotic virial equation was used to estimate the percentage of frozen water. Measurements identified the freezing point at -0.6 ^∘C. At -5 ^∘C, impedance rose by more than a factor of ten compared to that at the freezing point and the percentage of frozen water was estimated as being 89%. At -49 ^∘C impedance had increased by up to three orders of magnitude and ice formation was most pronounced in the extracellular space. Progressive ice formation in tissue is reflected by a large increase in impedance, and impedance increases monotonically with the percentage of frozen water. Its analysis allows for experimental assessment of factors relevant to cell death. Solid ice contributes to the rupture of the micro-vasculature, while phase shifts reflect concentration differences between extra- and intracellular space driving osmotic water transfer across cell membranes.

Characteristics of Ice Impedance Recorded From a Ring Electrode Placed at the Anterior Surface of the Cryoballoon: Novel Approach to Define Ice Formation and Pulmonary Vein Isolation

BACKGROUND

The success of cryoablation of the pulmonary vein isolation (PVI) is dependent on transmural and circumferential ice formation. We hypothesize that rising impedance recorded from a ring electrode placed 2 mm from the cryoballoon signifies ice formation covering the balloon surface and indicates ice expansion. The impedance level enables titration of the cryoapplication time to avoid extracardiac damage while ensuring PVI.

METHODS AND RESULTS

In 12 canines, a total of 57 pulmonary veins were targeted for isolation. Two cryoapplications were delivered per vein with a minimum of 90 and maximum of 180-second duration. Cryoapplication was terminated on reaching a 500 Ω change from baseline. Animals recovered 38±6 days post-procedure, and veins were assessed electrically for isolation. Heart tissue was histologically analyzed. Extracardiac structures were examined for damage. PVI was achieved in 100% of the veins if the impedance reached 500 Ω in <90 seconds with freeze time of 90 seconds. When 500 Ω was reached >90 to 180 seconds (142.60±29.3 seconds), 90% PVI was achieved. When the final impedance was between 200 and 500 Ω with 180 seconds of freeze time, PVI was achieved in 86.8%. For impedance of <200 Ω, PVI was achieved in 14%. No extracardiac damage was recorded.

CONCLUSIONS

Impedance rise of 500 Ω at <90 seconds with freeze time of 90 seconds resulted in 100% PVI. Impedance measurements from the nose of the balloon is a direct measure of ice formation on the balloon. It provides real-time feedback on the quality of the ablation and defines the cryoapplication termination time based on ice formation, limiting ice expansion to extracardiac tissues.

Determination of single cryoablation outcome within 30 to 60 seconds of freezing based on ice impedance

Background

A direct indicator of effective pulmonary vein isolation (PVI) based on early ice formation is presently lacking.

Objective

The initial impedance rise within 30 to 60 seconds (sec) of single cryoablation relating to ice on the distal surface of the cryoballoon could; predict effective PVI with early termination, the need for prolonging the cryoablation, or failure to achieve effective ablation.

Methods

Impedance measurements were taken between two ring electrodes, at the anterior balloon surface and at the shaft behind the balloon. Ice covering the anterior ring leads to impedance rise. Single cryoablation (eight animals, 37 veins) was applied for 90 to 180 sec. Cryoapplication was terminated if the impedance reached ≥500 Ω. Impedance levels at ≤60 sec of cryoablation were divided into three groups based on the characteristics of the impedance rise. PVI was confirmed acutely and at 45 ± 9 days recovery by electrophysiology mapping and histopathology.

Results

At 60 sec of freezing, an impedance rise of 34.1 ± 15.2 Ω (13‐50 Ω) and slope of the impedance rise (measured during 15‐30 sec of cryoapplication) less than 1 Ω/sec resulted in failed PVI. An impedance rise of 104.4 ± 31.5 Ω (76‐159 Ω) and slope of 2 Ω/sec resulted in 100% PVIs. An impedance rise of 130.9 ± 137.8 Ω (40‐590 Ω) and slope of 10 Ω/sec resulted in 100% PVIs with early termination at 90 sec.

Conclusion

The efficacy of single cryoablation can be defined within 30 to 60 sec based on ice impedance. Three unique impedance profiles described in this investigation are associated with the uniformity and thickness of the ice buildup on the anterior surface of the balloon. One cryoablation with an adequate impedance rise is needed for successful outcomes.

Bioimpedance technique for monitoring cerebral artery stenosis in a 3D numerical model of the head

Insufficient blood supply to the brain causes a transient ischemic attack (TIA) or a stroke. One of the causes to insufficient blood supply is cerebral artery stenosis. In this study, the feasibility of bioimpedance for monitoring such stenosis was analyzed. Simulations were conducted on a realistic numerical model of the head, focusing on the left middle cerebral artery (LMCA). Tissues were assumed to act as linear isotropic volume conductors, and the quasi-static approximation was applied. Electrical potentials were calculated by solving Poisson's equation, using the finite volume method (FVM) and the successive over relaxation (SOR) method. The best sensitivity found was 0.471 μV/% stenosis, using this electrode configuration: one injector near the left eye and the other injector near the right ear, one measurement position near the left eye and the other one in the right ear, keeping a distance of at least 2.5 cm between measurement and injection positions. The maximal sensitivity achieved in the numerical model under the applied assumptions supports the feasibility of bioimpedance technique for monitoring cerebral artery stenosis. However, according to sensitivity [1/m(4)] maps, calculated for the preferable electrode configurations, the measurements' specificity to the stenosis degree might be inadequate and should be further studied.

Frequency-division multiplexing for electrical impedance tomography in biomedical applications

Electrical impedance tomography (EIT) produces an image of the electrical impedance distribution of tissues in the body, using electrodes that are placed on the periphery of the imaged area. These electrodes inject currents and measure voltages and from these data, the impedance can be computed. Traditional EIT systems usually inject current patterns in a serial manner which means that the impedance is computed from data collected at slightly different times. It is usually also a time-consuming process. In this paper, we propose a method for collecting data concurrently from all of the current patterns in biomedical applications of EIT. This is achieved by injecting current through all of the current injecting electrodes simultaneously, and measuring all of the resulting voltages at once. The signals from various current injecting electrodes are separated by injecting different frequencies through each electrode. This is called frequency-division multiplexing (FDM). At the voltage measurement electrodes, the voltage related to each current injecting electrode is isolated by using Fourier decomposition. In biomedical applications, using different frequencies has important implications due to dispersions as the tissue's electrical properties change with frequency. Another significant issue arises when we are recording data in a dynamic environment where the properties change very fast. This method allows simultaneous measurements of all the current patterns, which may be important in applications where the tissue changes occur in the same time scale as the measurement. We discuss the FDM EIT method from the biomedical point of view and show results obtained with a simple experimental system.

Finite-element analysis of ex vivo and in vivo hepatic cryoablation

Cryoablation is a widely used method for the treatment of nonresectable primary and metastatic liver tumors. A model that can accurately predict the size of a cryolesion may allow more effective treatment of tumor, while sparing normal liver tissue. We generated a computer model of tissue cryoablation using the finite-element method (FEM). In our model, we considered the heat transfer mechanism inside the cryoprobe and also cryoprobe surfaces so our model could incorporate the effect of heat transfer along the cryoprobe from the environment at room temperature. The modeling of the phase shift from liquid to solid was a key factor in the accurate development of this model. The model was verified initially in an ex vivo liver model. Temperature history at three locations around one cryoprobe and between two cryoprobes was measured. The comparison between the ex vivo result and the FEM modeling result at each location showed a good match, where the maximum difference was within the error range acquired in the experiment (< 5 degrees C). The FEM model prediction of the lesion size was within 0.7 mm of experimental results. We then validated our FEM in an in vivo experimental porcine model. We considered blood perfusion in conjunction with blood viscosity depending on temperature. The in vivo iceball size was smaller than the ex vivo iceball size due to blood perfusion as predicted in our model. The FEM results predicted this size within 0.1-mm error. The FEM model we report can accurately predict the extent of cryoablation in the liver.

A narrow-band level set method applied to EIT in brain for cryosurgery monitoring

In this paper, we investigate the feasibility of applying a novel level set reconstruction technique to electrical imaging of the human brain. We focus particularly on the potential application of electrical impedance tomography (EIT) to cryosurgery monitoring. In this application, cancerous tissue is treated by a local freezing technique using a small needle-like cryosurgery probe. The interface between frozen and nonfrozen tissue can be expected to have a relatively high contrast in conductivity and we treat the inverse problem of locating and monitoring this interface during the treatment. A level set method is used as a powerful and flexible tool for tracking the propagating interfaces during the monitoring process. For calculating sensitivities and the Jacobian when deforming the interfaces we employ an adjoint formula rather than a direct differentiation technique. In particular, we are using a narrow-band technique for this procedure. This combination of an adjoint technique and a narrow-band technique for calculating Jacobians results in a computationally efficient and extremely fast method for solving the inverse problem. Moreover, due to the reduced number of unknowns in each step of the narrow-band approach compared to a pixel- or voxel-based technique, our reconstruction scheme tends to be much more stable. We demonstrate that our new method also outperforms its pixel-/voxel-based counterparts in terms of image quality in this application.

A portable bio-impedance system for monitoring lung resistivity

The principles of a hybrid bio-impedance technique are implemented in a novel, lung resistivity monitoring system ("CardioInspect" Tel-Aviv University, Israel). The system is to be utilized in the clinic or at home, for daily monitoring of patients suffering from pulmonary edema. The developed system consists of an eight-electrode belt worn around the thorax, an electronic unit containing analog and digital boards, and a stand-alone DSP based system with a designated software to analyze the data. A Newton-Raphson algorithm based on the finite-volume method is employed for the optimization of the left and right lung resistivity values, making use of the voltage measurements retrieved from opposite current injections. In this preliminary study, 33 healthy volunteers were measured with the system during tidal respiration, yielding symmetric mean left and right lung resistivity values of (1205+/-163, 1200+/-165) (Omega cm). The system reproducibility was better than 2% for both within and between tests measurements, and no dependency between the reconstructed values and various anthropometric parameters was found.

Induced current bio-impedance technique for monitoring cryosurgery procedure in a two-dimensional head model using generalized coordinate systems

In the noninvasive bio-impedance technique, small amplitude currents are applied to the body and the developing potentials on its surface are measured. This noninvasive technique is used to monitor physiological and pathological processes, which alter the values or the spatial distribution of the electrical impedance inside the human body. A possible application of the bio-impedance technique is monitoring brain cryosurgery procedure--a surgical technique that employs freezing to destroy undesirable tissues. A numerical solver was developed to evaluate the ability of an induced-current bio-impedance system to monitor the growth of the frozen tissue inside the head in simulation. The forward-problem bio-impedance solver, which is based on the finite volume method in generalized two-dimensional (2-D) coordinate systems, was validated by a comparison to a known analytical solution for body-fitted and Cartesian meshing grids. The sensitivity of the developed surface potential to the ice-ball area was examined using a 2-D head model geometry, and was found to range between 0.8 x 10(-2) and 1.68 x 10(-2) (relative potential difference/mm2), depending on the relative positioning of the excitation coil and the head. The maximal sensitivity was achieved when the coil was located at the geometrical center of the model.

Contactless bio-impedance monitoring technique for brain cryosurgery in a 3D head model

A contactless induced-current bio-impedance system for monitoring brain cryosurgery procedure was modeled and numerically simulated, where the excitation coil was also performing as the measuring, or pick-up coil. A segmented three-dimensional (3D) MRI database was used for building the volume conductor geometry, and the numerical finite-volume method was employed for solving the forward problem for calculating the scalar potential distribution and the second-order voltage change on the pick-up coil. Several coil configurations were considered, varying in their relative positioning to the 3D head model. For each case, the sensitivity of the measured voltage change on the excitation coil to the volume of a frozen lesion was calculated. The highest sensitivity (1.1 x 10(-5) relative voltage change per mm3 of frozen tissue) was obtained for a coil arrangement where its closest segment to the volume conductor is at the maximum distance away from the frozen region position. The simulated system signal-to-carrier ratio was O(10(-8)).

Front-tracking image reconstruction algorithm for EIT-monitored cryosurgery using the boundary element method

The effectiveness of cryosurgery, treatment of tumors by freezing, is highly dependent on knowledge of transient freezing extent, and therefore relies heavily on real-time imaging techniques for monitoring. Electrical impedance tomography (EIT) holds much promise for this application. In cryosurgery there is a three order of magnitude change in impedance across the freezing boundary and there is a priori knowledge of the freezing origin. Furthermore, an EIT image of the tissue can be done prior to the cryosurgery. In this study, we have developed an EIT front tracking reconstruction algorithm which takes advantage of these particular attributes of cryosurgery. The method tracks the freezing interface rather than the impedance distribution in the freezing tissue. In addition to drastically reducing the number of parameters needed to define the image, the computational complexity is further reduced by using the more appropriate boundary element method (BEM) for solution to the forward problem. The front-tracking method was found to converge rapidly and accurately to a variety of simulated phantom images.

Improving the forward solver for the complete electrode model in EIT using algebraic multigrid

Image reconstruction in electrical impedance tomography is an ill-posed nonlinear inverse problem. Linearization techniques are widely used and require the repeated solution of a linear forward problem. To account correctly for the presence of electrodes and contact impedances, the so-called complete electrode model is applied. Implementing a standard finite element method for this particular forward problem yields a linear system that is symmetric and positive definite and solvable via the conjugate gradient method. However, preconditioners are essential for efficient convergence. Preconditioners based on incomplete factorization methods are commonly used but their performance depends on user-tuned parameters. To avoid this deficiency, we apply black-box algebraic multigrid, using standard commercial and freely available software. The suggested solution scheme dramatically reduces the time cost of solving the forward problem. Numerical results are presented using an anatomically detailed model of the human head.

Parametric analysis of intercellular ice propagation during cryosurgery, simulated using monte carlo techniques

A microscale theoretical model of intracellular ice formation (IIF) in a heterogeneous tissue volume comprising a tumor mass and surrounding normal tissue is presented. Intracellular ice was assumed to form either by intercellular ice propagation or by processes that are not affected by the presence of ice in neighboring cells (e.g., nucleation or mechanical rupture). The effects of cryosurgery on a 2D tissue consisting of 10(4) cells were simulated using a lattice Monte Carlo technique. A parametric analysis was performed to assess the specificity of IIF-related cell damage and to identify criteria for minimization of collateral damage to the healthy tissue peripheral to the tumor. Among the parameters investigated were the rates of interaction-independent IIF and intercellular ice propagation in the tumor and in the normal tissue, as well as the characteristic length scale of thermal gradients in the vicinity of the cryosurgical probe. Model predictions suggest gap junctional intercellular communication as a potential new target for adjuvant therapies complementing the cryosurgical procedure.

Distributed network imaging and electrical impedance tomography of minimally invasive surgery

Minimally invasive surgery has become highly dependent on imaging. For instance, the effectiveness of cryosurgery in treating cancer is dependent on knowledge of freezing extent, and relies on real-time imaging techniques for monitoring. However, medical imaging is often very expensive and therefore not available to most of the world population. Here we propose the concept of distributed network imaging (DNI) which could make medical imaging and minimally invasive surgery available to all who need these advanced medical modalities. We demonstrate the concept through electrical impedance tomography (EIT) of cryosurgery. The central idea is to develop an inexpensive measurend (data collection hardware) at a remote site and then to connect the measurend apparatus to an advanced image reconstruction server, which can serve a large number of distributed measurends at remote sites, using existing communication conduits (Ethernet, telephone, satellite, etc.). These conduits transfer the raw data from the measurend to the server and the reconstructed image from the server to the measurend. Electrical impedance tomography (EIT) is an imaging modality which utilizes tissue impedance variation to construct an image. The EIT measurend which consists of electrodes, a power supply, and means to measure voltage is inexpensive, and therefore suitable for DNI. EIT is also very well-suited to imaging cryosurgery since frozen tissue impedance is much higher than that of unfrozen tissue. In this study, we first develop numerical models to illustrate the theoretical ability of EIT to image cryosurgery. We begin with a simplified two dimensional model, and then extend the study to the more appropriate three dimensional model. Our simulated finite element phantoms and pixel-based Newton-Raphson reconstruction algorithms were able to produce easily identifiable images of frozen regions within tissue. Then, we demonstrate the feasibility of the DNI concept though a case study using EIT to image an in vitro liver cryosurgery procedure through a modem. We find that the acquired raw data packets are less than 5KB per image and the images, using compression, do not exceed 50KB per image.

Using multiple-electrode impedance measurements to monitor cryosurgery

We outfitted cryoprobes with electrodes and used them in conjunction with a multiple channel electrical impedance tomography (EIT) system to record data during freezing experiments in a shallow saline tank. We made measurements using electrodes mounted on the probes and the tank's periphery. Reconstructed images based on both sets of electrodes indicate a significant improvement in the appearance of the ice ball over using tank electrodes alone. The size of the ice balls was varied by deliberately altering the cooling rate. We found a positive correlation between the measured size of the ice ball and the sizes of isocontour lines in the reconstructed impedance maps. Similarly, the shape of the ice balls was altered by circulating the saline about the probe. Two-dimensional reconstructed impedance contours indicated a deformation in agreement with the shape of the ice ball during the experiments. These findings suggest that using multielectrode impedance sensing may constitute a means for monitoring cryosurgery.

Cryosurgery

Cryosurgery is a surgical technique that employs freezing to destroy undesirable tissue. Developed first in the middle of the nineteenth century it has recently incorporated new imaging technologies and is a fast growing minimally invasive surgical technique. A historical review of the field of cryosurgery is presented, showing how technological advances have affected the development of the field. This is followed by a more in-depth survey of two important topics in cryosurgery: (a) the biochemical and biophysical mechanisms of tissue destruction during cryosurgery and (b) monitoring and imaging techniques for cryosurgery.