Anterior vs. posterior position of dispersive patch during radiofrequency catheter ablation: insights from in silico modelling.

AIMS: To test the hypothesis that the dispersive patch (DP) location does not significantly affect the current distribution around the catheter tip during radiofrequency catheter ablation (RFCA) but may affect lesions size through differences in impedance due to factors far from the catheter tip. METHODS: An in silico model of RFCA in the posterior left atrium and anterior right ventricle was created using anatomic measurements from patient thoracic computed tomography scans and tested the effect of anterior vs. posterior DP locations on baseline impedance, myocardial power delivery, radiofrequency current path, and predicted lesion size. RESULTS: For posterior left atrium ablation, the baseline impedance, total current delivered, current distribution, and proportion of power delivered to the myocardium were all similar with both anterior and posterior DP locations, resulting in similar RFCA lesion sizes (< 0.2 mm difference). For anterior right ventricular (RV) ablation, an anterior DP location resulted in slightly higher proportion of power delivered to the myocardium and lower baseline impedance leading to slightly larger RFCA lesions (0.6 mm deeper and 0.8 mm wider). CONCLUSIONS: An anterior vs. posterior DP location will not meaningfully affect RFCA for posterior left atrial ablation, and the slightly larger lesions predicted with anterior DP location for anterior RV ablation are of unclear clinical significance.

Comparison of two radiofrequency-based hemostatic devices: saline-linked bipolar vs. cooled-electrode monopolar.

PURPOSE: To characterize the coagulation zones created by two radiofrequency (RF)-based hemostatic devices: one comprised an internally cooled monopolar electrode and the other comprised externally irrigated bipolar electrodes (saline-linked). MATERIALS AND METHODS: RF-induced coagulation zones were created on ex vivo and in vivo porcine models. Computer modeling was used to determine the RF power distribution in the saline-linked device. RESULTS: Both external (irrigation) and internal cooling effectively prevented tissue sticking. Under ex vivo conditions in 'painting' application mode, coagulation depth increased with the applied power: 2.8 - 5.6 mm with the 3-mm monopolar electrode, 1.6 - 6.0 mm with the 5-mm monopolar electrode and 0.6 - 3.2 mm with the saline-linked bipolar electrodes. Under in vivo conditions and using spot applications, the 3-mm monopolar electrode created coagulation zones of similar depth to the saline-linked bipolar electrodes (around 3 mm), while the 5-mm monopolar electrode created deeper coagulations (4.5 - 6 mm) with less incidence of popping. The presence of saline around the saline-linked bipolar electrodes meant that a significant percentage of RF power (50 - 80%) was dissipated by heating in the saline layer. Coagulation zones were histologically similar for all the tested devices. CONCLUSIONS: Both external (irrigation) and internal cooling in hemostatic RF devices effectively prevent tissue sticking and create similar coagulation zones from a histological point of view. Overall, saline-linked bipolar electrodes tend to create shallower coagulations than those created with an internally cooled monopolar electrode.

Limitations of Baseline Impedance, Impedance Drop and Current for Radiofrequency Catheter Ablation Monitoring: Insights from In silico Modeling.

Background: Baseline impedance, radiofrequency current, and impedance drop during radiofrequency catheter ablation are thought to predict effective lesion formation. However, quantifying the contributions of local versus remote impedances provides insights into the limitations of indices using those parameters. Methods: An in silico model of left atrial radiofrequency catheter ablation was used based on human thoracic measurements and solved for (1) initial impedance (Z), (2) percentage of radiofrequency power delivered to the myocardium and blood (3) total radiofrequency current, (4) impedance drop during heating, and (5) lesion size after a 25 W−30 s ablation. Remote impedance was modeled by varying the mixing ratio between skeletal muscle and fat. Local impedance was modeled by varying insertion depth of the electrode (ID). Results: Increasing the remote impedance led to increased baseline impedance, lower system current delivery, and reduced lesion size. For ID = 0.5 mm, Z ranged from 115 to 132 Ω when fat percentage varied from 20 to 80%, resulting in a decrease in the RF current from 472 to 347 mA and a slight decrease in lesion size from 5.6 to 5.1 mm in depth, and from 9.2 to 8.0 mm in maximum width. In contrast, increasing the local impedance led to lower system current but larger lesions. For a 50% fat−muscle mixture, Z ranged from 118 to 138 Ω when ID varied from 0.3 to 1.9 mm, resulting in a decrease in the RF current from 463 to 443 mA and an increase in lesion size, from 5.2 up to 7.5 mm in depth, and from 8.4 up to 11.6 mm in maximum width. In cases of nearly identical Z but different contributions of local and remote impedance, markedly different lesions sizes were observed despite only small differences in RF current. Impedance drop better predicted lesion size (R2 > 0.93) than RF current (R2 < 0.1). Conclusions: Identical baseline impedances and observed RF currents can lead to markedly different lesion sizes with different relative contributions of local and remote impedances to the electrical circuit. These results provide mechanistic insights into the advantage of measuring local impedance and identifies potential limitations of indices incorporating baseline impedance or current to predict lesion quality.

Full torso and limited-domain computer models for epicardial pulsed electric field ablation.

BACKGROUND AND OBJECTIVES: Pulsed Electric Field (PEF) ablation has been proposed as a non-thermal energy to treat atrial fibrillation (AF) by ablation of ganglionated plexi using the epicardial approach. The electric field distribution at the target site (heart) and its surroundings has not yet been assessed previously, using epicardial ablation technique. Our objective was to develop computational models, incorporating the real anatomy of the heart and the patient's torso, to assess the electric field distribution when applying epicardial monopolar PEF. METHODS: A novel 3D realistic full torso model was built with the multi-electrode ablation device placed on the epicardium and a dispersive pad on the patient's back to evaluate the electric field distribution. The 400 V/cm isoline was used to estimate the 'PEF-zone'. A 3D limited-domain model was also built including only the region of interest around the ablation device to assess its validity in comparison with the full torso model. RESULTS: The electrical field is mainly limited to the target site (PEF-zone with lengths of 25.79 to 29.00 mm, depths of 5.98-7.02 mm and maximum widths of 8.75-10.57 mm) and is practically negligible in adjacent organs (<30 V/cm and <36 V/cm in oesophagus and lungs, respectively). The electrical currents ranged from 3.67 A to 7.44 A. The 3D limited-domain model provided a similar electric field distribution to those obtained from the 3D full torso models (differences < 0.5 mm in PEF-zone depth). CONCLUSIONS: Computational results suggest that PEF-zone is very focused around the ablation catheter. Limited-domain models offer similar results in terms of PEF-zone size, reducing the complexity of the modelling.

Radiofrequency ablation using a novel insulated-tip ablation catheter can create uniform lesions comparable in size to conventional irrigated ablation catheters while using a fraction of the energy and irrigation.

INTRODUCTION: During radiofrequency ablation (RFA) using conventional RFA catheters (RFC), ~90% of the energy dissipates into the bloodstream/surrounding tissue. We hypothesized that a novel insulated-tip ablation catheter (SMT) capable of blocking the radiofrequency path may focus most of the energy into the targeted tissue while utilizing reduced power and irrigation. METHODS: This study evaluated the outcomes of RFA using SMT versus an RFC in silico, ex vivo, and in vivo. Radiofrequency applications were delivered over porcine myocardium (ex vivo) and porcine thigh muscle preparations superfused with heparinized blood (in vivo). Altogether, 274 radiofrequency applications were delivered using SMT (4-15 W, 2 or 20 ml/min) and 74 applications using RFC (30 W, 30 ml/min). RESULTS: RFA using SMT proved capable of directing 66.8% of the radiofrequency energy into the targeted tissue. Accordingly, low power-low irrigation RFA using SMT (8-12 W, 2 ml/min) yielded lesion sizes comparable with RFC, whereas high power-high irrigation (15 W, 20 ml/min) RFA with SMT yielded lesions larger than RFC (p < .05). Although SMT was associated with greater impedance drops ex vivo and in vivo, ablation using RFC was associated with increased charring/steam pop/tissue cavitation (p < .05). Lastly, lesions created with SMT were more homogeneous than RFC (p < .001). CONCLUSION: Low power-low irrigation (8-12 W, 2 ml/min) RFA using the novel SMT ablation catheter can create more uniform, but comparable-sized lesions as RFC with reduced charring/steam pop/tissue cavitation. High power-high irrigation (15 W, 20 ml/min) RFA with SMT yields lesions larger than RFC.

Computer modeling of radiofrequency cardiac ablation: 30 years of bioengineering research.

This review begins with a rationale of the importance of theoretical, mathematical and computational models for radiofrequency (RF) catheter ablation (RFCA). We then describe the historical context in which each model was developed, its contribution to the knowledge of the physics of RFCA and its implications for clinical practice. Next, we review the computer modeling studies intended to improve our knowledge of the biophysics of RFCA and those intended to explore new technologies. We describe the most important technical details of the implementation of mathematical models, including governing equations, tissue properties, boundary conditions, etc. We discuss the utility of lumped element models, which despite their simplicity are widely used by clinical researchers to provide a physical explanation of how RF power is absorbed in different tissues. Computer model verification and validation are also discussed in the context of RFCA. The article ends with a section on the current limitations, i.e. aspects not yet included in state-of-the-art RFCA computer modeling and on future work aimed at covering the current gaps.

Effect of the relative position of electrode and stellate ganglion during thermal radiofrequency ablation: a simulation study.

PURPOSE: Stellate ganglion (SG) block by thermal radiofrequency ablation (RFA) is frequently conducted as a therapeutic intervention for sympathetic-maintained and neuropathic pain syndromes. RFA's partial lack of effectiveness could be partly due to the ablation zone (AZ) not completely covering the SG section and therefore preventing the 'cutting' of the afferent pathways. Our objective was to build a theoretical model to conduct computer simulations to assess the effect of the electrode position relative to the SG. METHODS: A three-dimensional model was built including the SG and adjacent tissues (vertebrae C7-T1-T2, trachea, carotid artery and vertebral artery). RFA (90-s, 80 °C) was simulated considering a 22 G-5 mm electrode. The AZ was computed using the 50 °C isotherm. RESULTS: An electrode displacement of 2 mm in any direction from the optimal position (centered on the SG) meant that the AZ did not fully cover the SG section. Likewise, SG size considerably affected the RFA effectiveness since the AZ fully covered the section of small but not large SGs. CONCLUSIONS: The findings suggest that the currently used SG RFA settings (i.e., 22 G-5 mm electrode, 90-s, 80 °C) may not be appropriate due to their inability to achieve an AZ that fully covers the SG cross section under certain circumstances, such as a large SG and non-optimal positioning of the RF electrode with respect to the SG center.

Differences in applied electrical power between full thorax models and limited-domain models for RF cardiac ablation.

Purpose: Most modeling studies on radiofrequency cardiac ablation (RFCA) are based on limited-domain models, which means the computational domain is restricted to a few centimeters of myocardium and blood around the active electrode. When mimicking constant power RFCA procedures (e.g., atrial fibrillation ablation) it is important to know how much power is absorbed around the active electrode and how much in the rest of the tissues before reaching the dispersive electrode.Methods: 3D thorax full models were built by progressively incorporating different organs and tissues with simplified geometries (cardiac chamber, cardiac wall, subcutaneous tissue and skin, spine, lungs and aorta). Other 2D limited-domain models were also built based on fragments of myocardium and blood. The electrical problem was solved for each model to estimate the spatial power distribution around the active electrode.Results: From 79 to 82% of the power was absorbed in a 4 cm-radius sphere around the active electrode in the full thorax model at active electrode insertion depths of between 0.5 and 2.5 mm, while the impedance values ranged from 104 to 118 Ω, which were consistent with those found (from 83 to 103 Ω) in a 4 cm radius cylindrical limited domain model.Conclusion: The applied power in limited-domain RFCA models is approximately 80% of that applied in full thorax models, which is equivalent to the power programed in a clinical setting.

Effect of the trabecular bone microstructure on measuring its thermal conductivity: A computer modeling-based study.

The objective of this work is to quantify the relation between the value of the effective thermal conductivity of trabecular bone and its microstructure and marrow content. The thermal conductivity of twenty bovine trabecular bone samples was measured prior to and after defatting at 37, 47, and 57 °C. Computer models were built including the microstructure geometry and the gap between the tissue and measurement probe. The thermal conductivity (k) measured was 0.39 ±â€¯0.06 W m-1 K-1 at 37 °C, with a temperature dependence of + 0.2%°C-1. Replacing marrow by phosphate-buffered saline (defatting) increased both the computer simulations and measurement results by 0.04 W m-1 K-1. The computer simulations showed that k increases by 0.02-0.04 W m-1 K-1 when the model includes a gap filled by phosphate-buffered saline between the tissue and measurement probe. In the presence of microstructure and fatty red marrow, k varies by ±â€¯0.01 W m-1 K-1 compared with the case considering matrix only, which suggests that there are no significant differences between cortical and trabecular bone in terms of k. The computer results showed that the presence of a gap filled by phosphate-buffered saline around the energy applicator changes maximum temperature by < 0.7 °C, while including the bone microstructure involved a variation of < 0.2 mm in the isotherm location. Future experimental studies on measuring the value of k involving the insertion of a probe into the bone through a drill hole should consider the bias found in the simulations. Thermal models based on a homogeneous geometry (i.e. ignoring the microstructure) could provide sufficient accuracy.

Thermal latency adds to lesion depth after application of high-power short-duration radiofrequency energy: Results of a computer-modeling study.

INTRODUCTION: The use of ultra-short RF pulses could achieve greater lesion depth immediately after the application of the pulse due to thermal latency. METHODS AND RESULTS: A computer model of irrigated-catheter RF ablation was built to study the impact of thermal latency on the lesion depth. The results showed that the shorter the RF pulse duration (keeping energy constant), the greater the lesion depth during the cooling phase. For instance, after a 10-second pulse, lesion depth grew from 2.05 mm at the end of the pulse to 2.39 mm (17%), while after an ultra-short RF pulse of only 1 second the extra growth was 37% (from 2.22 to 3.05 mm). Importantly, short applications resulted in deeper lesions than long applications (3.05 mm vs. 2.39 mm, for 1- and 10-second pulse, respectively). While shortening the pulse duration produced deeper lesions, the associated increase in applied voltage caused overheating in the tissue: temperatures around 100 °C were reached at a depth of 1 mm in the case of 1- and 5-second pulses. However, since the lesion depth increased during the cooling period, lower values of applied voltage could be applied in short durations in order to obtain lesion depths similar to those in longer durations while avoiding overheating. CONCLUSION: The thermal latency phenomenon seems to be the cause of significantly greater lesion depth after short-duration high-power RF pulses. Balancing the applied total energy when the voltage and duration are changed is not the optimal strategy since short pulses can also cause overheating.

How coagulation zone size is underestimated in computer modeling of RF ablation by ignoring the cooling phase just after RF power is switched off.

All the numerical models developed for radiofrequency ablation so far have ignored the possible effect of the cooling phase (just after radiofrequency power is switched off) on the dimensions of the coagulation zone. Our objective was thus to quantify the differences in the minor radius of the coagulation zone computed by including and ignoring the cooling phase. We built models of RF tumor ablation with 2 needle-like electrodes: a dry electrode (5 mm long and 17G in diameter) with a constant temperature protocol (70°C) and a cooled electrode (30 mm long and 17G in diameter) with a protocol of impedance control. We observed that the computed coagulation zone dimensions were always underestimated when the cooling phase was ignored. The mean values of the differences computed along the electrode axis were always lower than 0.15 mm for the dry electrode and 1.5 mm for the cooled electrode, which implied a value lower than 5% of the minor radius of the coagulation zone (which was 3 mm for the dry electrode and 30 mm for the cooled electrode). The underestimation was found to be dependent on the tissue characteristics: being more marked for higher values of specific heat and blood perfusion and less marked for higher values of thermal conductivity.

Chirality in a quaternionic representation of the genetic code.

A quaternionic representation of the genetic code, previously reported by the authors (BioSystems 141 (10-19), 2016), is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation associates with each nucleotide base a prime integer quaternion of norm 7 and involves a function that assigns to each codon, represented by three of these quaternions, another integer quaternion (amino acid type quaternion). The assignation is such that the essentials of the standard genetic code (particularly its degeneration) are preserved. To show the advantages of such a quaternionic representation we have designed an algorithm to go from the primary to the tertiary structure of the protein. The algorithm uses, besides of the type quaternions, a second kind of quaternions with real components that we additionally associate with the amino acids according to their order along the proteins (order quaternions). In this context, we incorporate chirality in our representation by observing that the set of eight integer quaternions of norm 7 can be partitioned into a pair of subsets of cardinality four each with their elements mutually conjugate and by putting them into correspondence one to one with the two sets of enantiomers (D and L) of the four nucleotide bases adenine, cytosine, guanine and uracil, respectively. We then propose two diagrams in order to describe the hypothetical evolution of the genetic codes corresponding to both of the chiral systems of affinities: D-nucleotide bases/L-amino acids and L-nucleotide bases/D-amino acids at reading frames 5'→3' and 3'→5', respectively. Guided by these diagrams we define functions that in each case assign to the triplets of D- (L-) bases a L- (D-) amino acid type integer quaternion. Specifically, the integer quaternion associated with a given D-amino acid is the conjugate of that one corresponding to the enantiomer L. The chiral type quaternions obtained for the amino acids are used, together with a common set of order quaternions, to describe the folding of the two classes, L and D, of homochiral proteins.

Computer modelling of RF ablation in cortical osteoid osteoma: Assessment of the insulating effect of the reactive zone.

PURPOSE: The aim was to study by computer simulations the insulating role of the reactive zone surrounding a cortical osteoid osteoma (OO) in terms of electrical and thermal performance during radiofrequency ablation (RFA). MATERIAL AND METHODS: We modelled a cortical OO consisting of a nidus (10 mm diameter) enclosed by a reactive zone. The OO was near a layer of cortical bone 1.5 mm thick. Trabecular bone partially surrounds the OO and there was muscle around the cortical bone layer. We modelled RF ablations with a non-cooled-tip 17-gauge needle electrode (300 s duration and 90 °C target temperature). Sensitivity analyses were conducted assuming a reactive zone electrical conductivity value (σrz) within the limits of the cortical and trabecular bone, i.e. 0.02 S/m and 0.087 S/m, respectively. In this way we were really modelling the different degrees of osteosclerosis associated with the reactive zone. RESULTS: The presence of the reactive zone drastically reduced the maximum temperature reached outside it. The temperature drop was proportional to the thickness of the reactive zone: from 68 °C when it was absent to 44 °C when it is 7.5 mm thick. Higher nidus conductivity values (σn) implied higher temperatures, while lower temperatures meant higher σrz values. Changing σrz from 0.02 S/m to 0.087 S/m reduced lesion diameters from 2.4 cm to 1.8 cm. CONCLUSIONS: The computer results suggest that the reactive zone plays the role of insulator in terms of reducing the temperature in the surrounding area.

Quaternionic representation of the genetic code.

A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearance of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.

Mathematical modeling of uniaxial mechanical properties of collagen gel scaffolds for vascular tissue engineering.

Small diameter tissue-engineered arteries improve their mechanical and functional properties when they are mechanically stimulated. Applying a suitable stress and/or strain with or without a cycle to the scaffolds and cells during the culturing process resides in our ability to generate a suitable mechanical model. Collagen gel is one of the most used scaffolds in vascular tissue engineering, mainly because it is the principal constituent of the extracellular matrix for vascular cells in human. The mechanical modeling of such a material is not a trivial task, mainly for its viscoelastic nature. Computational and experimental methods for developing a suitable model for collagen gels are of primary importance for the field. In this research, we focused on mechanical properties of collagen gels under unconfined compression. First, mechanical viscoelastic models are discussed and framed in the control system theory. Second, models are fitted using system identification. Several models are evaluated and two nonlinear models are proposed: Mooney-Rivlin inspired and Hammerstein models. The results suggest that Mooney-Rivlin and Hammerstein models succeed in describing the mechanical behavior of collagen gels for cyclic tests on scaffolds (with best fitting parameters 58.3% and 75.8%, resp.). When Akaike criterion is used, the best is the Mooney-Rivlin inspired model.

Modeling of the dielectric properties of trabecular bone samples at microwave frequency.

In this paper, the dielectric properties of human trabecular bone are evaluated under physiological condition in the microwave range. Assuming a two components medium, simulation and experimental data are presented and discussed. A special experimental setup is developed in order to deal with inhomogeneous samples. Simulation data are obtained using finite difference time domain from a realistic sample. The bone mineral density of the samples are also measured. The simulation and experimental results of the present study suggest that there is a negative relation between bone volume fraction (BV/TV) and permittivity/conductivity: the higher the BV/TV, the lower the permittivity/conductivity. This is in agreement with the recently published in vivo data.

Mechanisms of interaction between Candida albicans and Streptococcus mutans: an experimental and mathematical modelling study.

OBJECTIVE: To evaluate the mechanisms of microbial interaction between the oral pathogens Candida albicans and Streptococcus mutans. MATERIALS AND METHODS: Growth kinetics for the two micro-organisms, cultured individually or together, were followed experimentally for 36 h. The different growth curves were analysed by means of mathematical modelling. RESULTS: Under the experimental conditions, S. mutans final concentration, when grown individually, was 5-times that of C. albicans. Contrarily, when both micro-organisms grew together, this ratio was inversed and C. albicans final concentration was even higher than that of S. mutans. When both micro-organisms share the niche, a model including linear competition among one another was best suited to reproduce the experimental observations. The results of this model show that the initial growth rates of both species are positively influenced by their mutual interaction. However, at longer incubation times, C. albicans prevents bacterial growth and achieves concentrations 4-times higher than when grown individually. CONCLUSIONS: The results suggest that C. albicans biofilm formation could be potentiated by the presence of S. mutans by two mechanisms: synergically at short times and by competition at longer periods.