Experimental and Numerical Analysis ofLesion Growth during Cardiac

Radiofrequency Ablation

Sytske Foppen

BMTE 09.14, April 2009

.

Supervisorsdr. ir. E.G.A Harks1

dr. ir. P.H.M. Bovendeerd2,

Committeeprof. dr. ir. F.N. van de Vosse2

prof. dr. ir. A.A. van Steenhovendr. ir. P.H.M. Bovendeerddr. D.W.J. van der Schaft

Advisordr. ir. E.G.A. Harks

1) Healthcare Devices and Instrumentation, Philips Research Eindhoven2) Division of Cardiovascular Biomechanics, Department of Biomedical Engineering, Eindhoven Universityof Technology

Abstract

Radiofrequency ablation (RFA) is currently used in clinic as a cure for several cardiac arrhythmia,like Wolff-Parkinson-White and Atrial Fibrillation. These arrhythmia are caused by a disturbance ofthe healthy conduction pattern of the heart. RFA treatment aims for electrical isolation of the locationsthat cause the disturbed conduction. Due to the application of an alternating current to the tissue,the tissue becomes hyperthermic. This induces structural changes in the tissue that block the electricalconductance. Transmurality of the lesions is an important factor for successful treatment. To preventdamage to surrounding tissues however, the lesion formation should be controlled. In this study thedevelopment of lesion depth is studied.

In literature, many determinants of lesion depth are discussed. The most pronounced ones are elec-trode design, the power that is dissipated in the tissue, and the duration of the ablation. Furthermore,uncontrollable determinants like wall thickness and convection are described. Experiments were done onporcine cardiac tissue, to investigate the influence of power settings, ablation duration and wall thickness.Lesions were created with a power of 10, 15 and 20 Watt for durations up to 180 seconds. The lesionswere bisected and stained using a histologic staining (NTB) and lesion depth was measured. Lesion depthwas defined as the maximum transmural damage perpendicular to the ablated surface. A finite elementmodel was created for further investigation of the influence of these variables. This model was based onequations for ohmic heating, heat conduction and convection, and fluid flow. Simulations were designedto mimic the experiments. A transient and a steady state analysis were done. The lesion border wasdefined by the 50C isotherm. In this model the same determinants were studied as in the experiments.Furthermore, the model gave insight in the influence of other factors, like natural convection. The resultsof the experiments and the model were compared for similar ablation powers and durations.

The experiments and the finite element model provides insight in the development of lesion depthduring RFA. An exponential growth in time was found for lesion depth. Steady state was approachedafter one minute of ablation. The final lesion depth was strongly dependent on the power used duringablation in the model. This final lesion depth was limited when the ablated tissue was thin, due to coolingof the tissue by surrounding fluid. In the experiments, no significant difference was found between lesiondepth in tissue of different thickness. No transmural lesions were achieved in both the experiments andthe model.

1

Contents

1 Introduction 4

2 Literature on Characteristics and Development of RFA Lesions 62.1 Lesion Characterics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Protein Denaturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.2 Lesion Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Lesion Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Lesion Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.1 Kinetics of Lesion Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.2 Determinants of Lesion Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Experiments 143.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1 Lesion Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1.2 Performed Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1.3 Data Acquirement and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Finite Element Model 224.1 Physics of Radiofrequency Ablation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.1.1 Electric Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.1.2 Heat Conduction and Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Model Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2.1 Model Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2.3 Mesh Generation and Simulation Protocol . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3.1 Physics of Radiofrequency Ablation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3.2 Lesion Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5 Model versus Experiments 365.1 Combined Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6 Conclusion and Recommendations 41

References 42

A Polarization Microscopy 44A.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44A.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

B Nondimensionalization of the Heat Equation 46

2

C Protocols for Histological Staining 48C.1 General Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48C.2 Staining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

C.2.1 Hematoxylin and Eosin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48C.2.2 Masson’s TriChrome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

D Lesions of Duration Experiments, Session 2 50

3

1 Introduction

The efficient way in which the heart pumps blood depends largely on its electrical conduction system. Thissystem is shown in Figure 1. The heart exists of atrial and ventricular muscle, and specialized excitatory andconductive muscle fibers. The latter are found in the Sinus Node, Atrioventricular (AV) Node, His Bundleand Purkinje fibers. These fibers are responsible for the rhythmical beating of the heart. The Sinus Nodeis the primary pacemaker of the heart. It generates electrical impulses that are directly conducted throughthe atria, which contract in response. Through the atria, the stimuli reach the AV Node. This is the onlyconductive pathway from the atria to the ventricles. From there, the impulse is conducted through thebundle of His to the ventricles which contract in their turn. The AV Node delays the impulse propagationto the ventricles, allowing the atria to empty completely, before contraction of the ventricles. Furthermore,it limits the rate of ventricle contraction by conducting 200 beats per minute maximally [12].

Figure 1: Image of the electric conduction system of the heart. UpToDate Inc, www.uptodate.com

When the generation or conduction of electrical impulses in the heart is disturbed, abnormal contractionpatterns may occur. For example, when an accessory pathway exists between the ventricles and the atria,the rate control of the ventricles by the AV node can be overruled. Besides, impulses can re-enter the atriaand thus disturb normal atrial contraction. This is called Wolf-Parkinson-White (WPW) syndrome, and isschematically represented in Figure 2(a). Another example is Atrial Fibrillation, as shown in Figure 2(b).Many small polarization waves travel in different directions simultaneously. This impedes the atria fromcontracting, and thus lowers the cardiac output. When these conditions are sustained, serious problems canoccur. Destruction of the erroneous loci can solve these problems.Controlled destruction of tissue is called ablation. Radiofrequency ablation (RFA) is currently the mostcommonly used ablation technique, because of the relatively large control on safety and lesion growth [11].In this method, an alternating current of a frequency around 500 Hz is applied to the tissue. This currentelevates the temperature in the tissue. Due to this heating, the cells turn into a necrotic state. In thatway, the regions of abnormal cardiac conduction are destroyed or electrically isolated. As the abnormalregions should be completely destroyed or isolated, lesions should be transmural and continuous. Otherwise,conduction may take place over the remaining tissue. To prevent excess damage to the myocardium andsurrounding tissues however, ablations should be limited to the lowest possible temperatures and durations.

4

(a) WPW syndrome (b) Atrial Fibrillation

Figure 2: Two examples of cardiac arrhythmia. (a) WPW syndrome. The blue zone shows the existence of an acces-sory pathway between the ventricle and the atrium (b) Atrial Fibrillation. The normal conductive pathwayelements are colored yellow, the abnormal are red. MCG Electrophysiology Services, www.epmcg.net

As the transmurality of the lesions is important but hard to determine, this study aims to get more insight inthe development of lesion depth. Lesion depth is defined as the maximum transmural damage, perpendicularto the surface of electrode tip to tissue contact. Determinants on lesion depth include duration and power ofablation, thickness of the tissue, and convection of heat by intracardiac blood flow. These determinants areregarded by experiments on porcine cardiac tissue and by finite element modeling. Furthermore, methodsto visualize lesion depth in both macroscopy and microscopy are used.

5

2 Literature on Characteristics and Development of RFA Lesions

6

2.1 Lesion Characterics

2.1.1 Protein Denaturation

The temperature rise induced in RFA causes necrosis via protein denaturation [20]. Many basic propertiesof cells are dependent on proteins. Integrin proteins on the cell membrane are responsible for functionality ofthe cell. The cytoskeleton, which consists of protein polymers, is largely responsible for the cell’s structure.Also the extracellular matrix (ECM) mainly consists of proteins, namely elastin, collagen and proteoglycans.Upon moderate heating, breakage of hydrogen bonds causes a reversible local unfolding of the proteins.Severe heating increases the amount of broken hydrogen bonds and reduces cross linking, which destroys thenative structure of the protein. [20, 34].

2.1.2 Lesion Characteristics

Figure 3(a) shows a cardiac RFA lesion. The lesion (marked ’Abl’), exists of necrotic cells. Necrosis is foundin roughly two zones, as can be seen in Figure 3(b). The zone that was nearest to the electrode showscoagulation necrosis (marked ’cn’), in which the cell structure is totally disrupted. It can be recognizedby a loss of cell definition, separation of the fibers by edema, extravascular red blood cells, and loss ofnuclei and cross-striations [31]. Around this zone of coagulation necrosis, a border zone with partial necrosisexists (marked ’cb’). In this zone, the cross striations and sarcolemma are partially preserved. This zone issometimes hard to distinguish, but is important to recognize, as recovery of the cells might undo the electricisolation.

(a) Cardiac tissue with RFA Lesion (b) Part of a RFA Lesion

Figure 3: Two examples of cardiac RFA lesions. (a) Ablation lesion in myocardium, Gomorri’s trichrome staining.Lesion looks blue and unaffected tissue is red. Thomas et al [31]. (b) Cardiac RFA lesion, showingthree zones: n = normal myocardium, cb = borderline zone of contraction band necrosis, cn = zone ofcoagulation necrosis. H&E staining, bar is 200 µ. Aupperle et al [17]

2.1.3 Lesion Visualization

Several methods for visualization of lesions are known. These include Nitro-Blue Tetrazolium (NTB) formacroscopy, and histological staining for microscopy.

7

MacroscopyLesions look like pale white regions in the tissue. It is not clear, if the border of such a region is indeed theexact border of the necrotic zone. Tetrazolium salts can be used for distinguishing viable from nonviabletissue in macroscopy. Tetrazolium salts are soluble, but can be transformed into an insoluble formazan byreduction, as shown by Figure 4(a). In the tissue, this reduction is achieved by dehydrogenase. As thisonly occurs in viable cells, the formazan is only formed in viable tissue. With use of Nitro-Tetrazolium Blue(NTB), which has a side chain that causes the formazan to stain the viable tissue dark blue, viable tissuecan be diminished from nonviable tissue. The NTB molecule is shown in Figure 4(b).

(a) Reduction of general tetrazolium to formazan. (b) NTB molecule, as formazan.

Figure 4: (a) Reduction of tetrazolium to formazan (b) The formazan molecule derived from Nitro-Blue Tetrazolium.Kiernan [24]

MicroscopyTo visualize tissue structure on a microscopic level, histological staining is applied. A common used stainingis hematoxylin and eosin (H&E). This colors basophilic structures like nuclei blue, and eosinophilic structureslike cytoplasm and extracellular proteins (e.g. collagen) bright pink. Characteristics of RFA lesions thathave been described include loss of nuclei, rounded, homogenous myocytes, contraction bands and a ”woolyappearance”. All these can be identified using H&E staining, but it is hard to distinguish the border of alesion, as healthy and damaged tissue have the same color. Therefore, a Tri-Chrome staining can be used.An example of this is the Gomorri staining used in shown Figure 3(a).The exact mechanism of this tri-chrome staining method remains unknown, but it exists of three main steps[24]. First, a small dye is used to color the cytoplasm and erythrocytes by diffusion. Then, the tissue isbriefly washed and put into a mixture of acids, which bind strongly to collagen and less so to cytoplasm.Then, the collagen fibers are stained with a larger dye that attaches to the acids. By using dyes of twodifferent colors, the necrotic region can be easily distinguished from healthy tissue.Furthermore, loss of birefringence by the tissue can be used as an indicator for tissue damage. Due to thestrongly anisotropic structure of cardiac tissue, the refractive indices are direction dependent. Thereforepolarized light can be depolarized by the tissue. When the tissue structure is damaged, these birefringentproperties are lost. Appendix A.1 explains how this loss of birefringence can be visualized with polarizationmicroscopy.

8

2.2 Lesion Development

2.2.1 Kinetics of Lesion Growth

The destruction of tissue is caused by a combination of the elevation of temperature and the duration ofthis elevation. The induction of necrosis by a combination of time and temperature in cardiac tissue canbe compared to that of burn injury in skin, described by Henriques in 1947 [18]. He studied the time thatit takes for skin to become necrotic at certain temperatures. His results are shown in Table 1. These datashow, that inducing necrosis in skin takes 5 minutes at a temperature of 50C, but only 90 seconds at 52C.Henriques described the tissue damage as function of time and temperature with use of a temperature

Table 1: Relationship between duration and temperature, for skin to become necrotic Henriques [18].

Temperature [C] 44 46 48 50 52 54 56 60Duration [s] 25 000 5 000 1 100 300 90 35 16 5

dependent reaction rate k = k(T ). This reaction rate is a measure for the speed at which the concentrationof vital cells C decreases, as in equation (1).

dC

dt= −k(T ) (1)

If the rate constant is independent of the concentration of the reactants, the reaction is of the zeroth orderand occurs linear in time. This is assumed for cell destruction during RFA, as the denaturation of proteinsis not slowed down when surrounding cells have already disintegrated [20]. If C(t) is the amount of viablecells at time t, and C(0) the initial amount of viable cells, this reaction can be described by equation (2).

C(t) = C(0)− kt (2)

The reaction rate of any chemical reaction, is strongly related to temperature. The Arrhenius equation is agood predictor of the dependency of the reaction rate on temperature and activation energy. It is given byequation (3), with the universal gas constant R [J/molK], material parameter A [s−1], and the activationenergy Ea [J/mol]. The latter can be determined by the slope of the plot of the natural logarithm of thereaction rate k versus the inverse of the temperature T [20].

k(T ) = A exp(−Ea

RT) (3)

Induction of necrosis is thus dependent on the temperature elevation and its duration. Therefore, the mostprominent determinants of lesion growth during RFA are the energy applied to the tissue and the durationof ablation.

2.2.2 Determinants of Lesion Depth

The focus of this study is on the development of lesion depth. This depth is defined as the transmural size ofthe lesion, perpendicular to the surface of electrode to tissue contact. In other studies however, often lesionwidth is regarded, which is the size of the lesion on the surface of electrode to tissue contact.

TemperatureAs only the tissue is affected, in which the combination of temperature and duration is sufficient, the aimis to get a sufficient temperature and duration combination in the aimed lesion volume. In clinic, ablationduration is often 60 to 90 seconds. For the desired temperature in cardiac tissue, 47 to 50C is often chosenin literature for onset of necrosis in mathematical models [21, 4, 6]. Enough energy should be applied to

9

heat the tissue sufficiently, but care should be taken not to induce tissue pops, which might be caused bytoo high temperatures. Haines investigated the relation of tissue pops with the temperature of the electrodeat the tissue surface. As can be seen in Figure 5, the ratio of tissue pops is elevated when the temperatureexceeds 100C. He subscribed this effect of high temperatures to tissue boiling [15].

Figure 5: Tissue pops occur mostly when temperature exceeds 100 Haines [15].

Power and DurationDuring RFA, a constant power (CP) or temperature controlled (TC) ablation protocol is followed. DuringCP ablation, the alternating current voltage is automatically adjusted to the impedance that is measuredbetween the electrodes. At TC ablation, the voltage is adjusted to maintain a certain maximum temperatureat the electrode tip on the tissue surface. In this study, the focus is on CP ablation.A good example of the time- and power dependency of lesion growth is given by Wittkampf [9]. His resultsare shown in Figure 6. He created endocardial lesions in vivo in canine right ventricle (RV) tissue, using a 6F(i.e. 2 mm) electrode catheter. He performed CP ablations with powers from 0.3 to 9.3 Watt, and ablatedfor durations of 5, 10, 20, 30 and 60 seconds. Then he measured lesion size L, which he defined as the sumof the lesion depth, width and depth divided by three. He found, that in the first 20 seconds of ablation,the lesion size depended on both power and duration. After 20 seconds however, he found that the lesionshad reached a maximum size which only depended on power. Note from Figure 6(b), that a larger powerinduces a larger lesion. The time constant τ for lesion growth for 4W and 6W ablation was 9 seconds.Haines also investigated the lesion growth in time [14]. He created endocardial lesions in vitro, in perfusedand super fused canine myocardium. He did ablations varying from 10 to 600 seconds, with TC ablationmaintaining an electrode tip temperature of 80C. He also found a mono exponential lesion growth in time,with a half life time t 1

2of 9.6 seconds for lesion depth. This corresponds to a 13.8 seconds time constant.

This time constant is in the same order of the the time constant found by Wittkampf.Furthermore, also Thomas found no significant difference between lesion depth for 60 and 120 seconds duringTC ablation at 85C [31].

10

(a) Lesion size (L) after 5 and 10 seconds (b) Lesion size (L) after 20, 30 and 60 seconds

Figure 6: Data by Wittkampf [9], that suggest that the lesion grows in the first 20 seconds of ablation, and thenis only dependent on power. (a) At 5 and 10 seconds of ablation, the lesion size is dependent on bothablation power and duration. (b) At 20, 30 and 60 seconds of ablation however, the lesion size is dependenton ablation power only.

Wall thickness and ConvectionLesion growth can be limited by the convection of heat by blood, due to both the flow in the cardiac chambersand perfusion of the myocardium. The blood transports heat and thus decreases the temperature rise in thetissue. When RFA is performed epicardially, convection absorbs heat at the endocardial side. Therefore,it might limit the lesion depth achieved in epicardial RFA. During endocardial ablation however, the bloodmay adsorb some of the applied radio frequent energy, but the tissue is not cooled at the opposite side. Therole of perfusion is generally regarded negligible, as perfusion is ceased in and near the heated tissue [33].Thomas et al. studied the difference between epicardial and endocardial ablation in a sheep model [31]. Le-sions in atrial tissue were transmural in 92% of the endocardial, but only in 13% of the epicardial ablations.This suggests a strong influence of convection at epicardial ablation in atrial tissue. Wall thickness of leftand right atrium were 2.9±1.5 and 2.2±0.7 mm respectively. In the thicker ventricular tissue however, nosignificant difference was found between lesion depth of endocardial and epicardial ablation, suggesting thatthe influence of endocardial convection is limited to thinner tissue. A significant difference between the epi-cardial lesion depth for right (3.4±0.6 mm lesion depth at 6.6±1.5 mm wall thickness) and left (4.3±0.9 mmlesion depth at 13.9±2.6 mm wall thickness) ventricle was found, suggesting an influence of wall thicknesson lesion depth besides the influence of convection.

Electrode-Tissue ContactThe contact between the electrode tip and the tissue also has influence on the lesion size. Haines showed,that formed lesions were deeper when there was a stronger contact between the tissue and the electrode tip[14]. When ablation was performed on 1 mm distance from the tissue, the average lesion depth was 2.2 mm.For a contact force of 10 and 400 N, the average lesions depths were 3.3 and 4.6 mm respectively.During the ablation procedure, the contact between the electrode tip and the tissue are hard to determine.Especially during endocardial ablation, when the electrode is positioned on the cardiac tissue guided byelectrophysiology, ultrasound or fluoroscopy [13]. A measure that can be used to predict electrode to tissuecontact is impedance. Figure 7(a) shows a representation of the electric circuit in a ablation setup. Theactive electrode is positioned against the cardiac tissue. The electric current divides over the tissue (withresistance RTissue) and the surrounding fluid (with resistance RBlood). RRemote represents the resistanceof the ablation system (i.e. cables, skin patch, RF generator and the body). Cao [13] regarded the inser-

11

tion depth of the active electrode, using the difference between the resistivity of myocardium and of blood.Because the ablation electrode is relatively small and far away from the dispersive electrode, the currentdensity decreases with distance (1/r2) from this electrode. Therefore the potential gradient is largest nearthe electrode. Thus this region contributes most to the resistivity between the electrodes. Because theresistivity of myocardium is larger than that of blood, the impedance will increase if the electrode is inserteddeeper into the tissue. Cao measured this effect for several frequencies. The result can be seen in Figure7(b). When the electrode comes within 2 mm from the tissue, impedance starts to increase linearly. Theeffect is larger for lower frequencies, as the difference in resistivity of blood and myocardium is larger for lowfrequencies.

(a) Electrical circuit representing the ablation system (b) Relationship between electrode insertion depth andimpedance

Figure 7: Impedance can be used as indicator for electrode to tissue contact: (a) An electrical circuit representingthe ablation circuit, with the resistances of the tissue (RTissue), the surrounding fluid (RBlood), and theablation system (RRemote) Nakagawa [19]. (b) Results of impedance measurements at different electrodeinsertion depths and frequencies. Negative depth is the distance of the electrode from the tissue. ( 1kHz, 10 kHz, N 100 kHz, 500 kHz) Cao [13]

2.2.3 Summary

An overview of experiments concerning lesion depth is given by Table 2. Lesion growth is fastest duringthe first 20 seconds of ablation, and finds a steady state in about a minute. Higher powers, thus highertemperatures, yield deeper lesions, and intracardiac convection can have influence on lesion depth in tissuewith limited wall thickness. The wall thickness itself also has influence on the lesion depth. Furthermore,good tissue-electrode contact is important in lesion development, and this can be predicted by impedancemonitoring.Research has been done on many other aspects in the RFA procedure that influence the lesion growth. Thisincludes electrode design (e.g. radius and length [7, 19, 8]), electrode orientation (e.g. perpendicular orparallel [32, 8]) and irrigation (i.e. active cooling by a fluid, in either a open or closed loop system [2, 23, 8]).Since these aspects are not regarded in this study, they were not discussed in this section. Furthermore, onlyexperimental studies were discussed. A small introduction into modeling of RFA will be given in section 4.1.

12

Table 2: Overview of experiments concerning lesion depth. TC = temperature controlled ablation, CP = constantpower ablation

Author Protocol Energy setting Duration ConclusionTemperature

Haines [15] CP unknown 90 s Tissue pops tend to occur whentemperature exceeds 100C

Power and DurationWittkampf [9] CP 0.3 - 9.3 W 5 - 60 s First 20 seconds growth of lesion depth.

After 20 seconds, lesion depthdepends on power only. Largerpowers yield larger lesions.

Haines [14] TC 80C 10 - 600 s For a mature lesion size,ablation should last 40seconds at least.

Thomas [31] TC 85C 60 and 120 s No significant difference between lesiondepths for 60 and 120 seconds ablation.

Wall ThicknessThomas [31] TC 85C 60 and 120 s Convection of heat by intracardiac blood

flow limits lesion depth in tissue ofless than 3 mm thickness. In thicker tissues,no significant difference was found betweenlesion depth of endocardial orepicardial ablation. LV lesion depth however,was significantly deeper than RV lesion depth.

Electrode ContactHaines [14] TC 80C 90 s When a contact force exists,

lesions are larger than when nocontact force exists. For largercontact force, lesion depthis the same but fora lower applied power.

13

3 Experiments

14

3.1 Methods

3.1.1 Lesion Creation

The experiments were done in the experimental setup shown in Figure 8. It consists of a plexiglass container(length x width x height = 20x20x10 cm), filled with a physiological salt solution (0.9% NaCl in deionizedwater). Tissue was clamped by two bulldog clamps. Ablations were made using a Stockert EP-shuttle byBiosense Webster with a Biosense Webster unipolar 6F 2mm ablation catheter. This electrode was placedagainst the tissue, and the dispersive electrode (3x4 cm) was placed at a distance of 5 to 10 cm on theother side of the tissue. The voltage is automatically adjusted to the impedance between the electrodes,to maintain constant power. Each ablation was done with the active electrode on the endocardium. Thevariables to be set were duration and power.The hearts were excised from the pig half an hour after exsanguination at the local slaughterhouse, and fourto six hours before the beginning of the experiment. The tissue was stored in a plastic bag in a cooler. Forexperiments, a piece of right ventricular (RV) tissue with as little as possible fat was selected and positionedin the setup.During the experiments, the variation in electrode contact was aimed to be minimized by using a perpendic-ular orientation of the electrode tip to the tissue. The electrode was pushed onto the tissue in such a way,that the impedance at the start of the ablation was increased by a certain range compared to the impedancein the setup without tissue. This increase in impedance differed per experimental session. All ablationswere done endocardially, and the powers used during ablation were 10, 15 and 20 Watt. The duration ofexperiments to evaluate the influence of wall thickness and power on lesion depth was 90 seconds. Thisshould be a steady state according to literature (see section 2.2). Ablation settings were applied in a randomorder.

(a) Schematic representation of experimental setup (b) Picture of experimental setup

Figure 8: Experimental setup (a) schematic representation (b) picture. A: active electrode, D: dispersive (ground)electrode. Tissue is clamped by two bulldog clamps.

3.1.2 Performed Experiments

Three different experiments are done. They had a focus on the variation of either power, wall thickness orduration.

• Power: Ablations of 90 seconds were made at 10, 15 and 20 Watt with N=10 for each power, toinvestigate the influence of power on lesion depth. The impedance at the start of ablation was around

15

15 Ω higher than in the experimental setup without tissue.

• Wall thickness: In order to investigate the influence of wall thickness, a series of 20 Watt ablations witha duration of 90 seconds was made randomly on a piece of right ventricular porcine tissue (N=14).These ablations were done in the same session as the Power experiment.

• Duration: The investigation of lesion depth for different duration was done in two sessions:

– Session 1To get a basic idea of lesion growth in time, a series of 20 Watt ablations was done in random orderfor 20, 40, 60 and 80 seconds with N=5 up to N=15 for each duration. As these experiments weredone in an earlier stage, the setup in which the experiments were done had a different geometry (alarger container) and a different saline concentration (0.5% NaCl). Besides, the tissue was storedin a refrigerator overnight before use, and the initial impedance was not monitored.

– Session 2To gain more insight into the early lesion growth, a series of 20 Watt ablations was done fordurations of 5, 10, 15 and 20 seconds. For each power, also 90 and 180 second ablations were done,to investigate if the steady state is indeed reached after 90 seconds. For all ablation combinations(power and duration), N=3 lesions were created.In these experiments, more care was taken to exclude certain side effects. It was aimed to usetissue of relative uniform thickness, and the initial impedance was always 80 Ω. The impedanceand temperature of the experimental setup were measured before and after the ablation sessions,and the impedance and voltage were monitored during the ablations.

3.1.3 Data Acquirement and Analysis

For acquirement of lesion depth, only macroscopy was used. The NTB tablets were solved in a 0.133 MSorenson’s Buffer with a pH of 7.4, with a concentration of 0.5 g/L. The buffer is made by adding 15.1 grams ofNa2HPO4 (dibasic NatriumPhosphate Anhydrous) and 3.7 grams of KHPO4 (monobasic KaliumPhosphate)in one liter deionized water. After ablation, the lesion was cut through the center of the lesion and one halfof the tissue was held in the NTB-buffer solution at 35 degrees Celsius for about 10 minutes. Microscopywas done but not used for data acquirement. The experiment with birefringence and its results are describedin Appendix A.2. The staining protocols can be seen in Appendix C.The lesion depth was defined as the furthest point of transmural damage from the contact point of the tissuewith the electrode. This is illustrated in Figure 9(b) (section 3.2). The distance from the tissue surface tothis furthest transmural point with damage was measured with a digital caliper with an accuracy of 0.01mm.For data analysis, the Statistics Toolbox of Matlab 7.3.0 was used. A normal distribution was tested usinga Lilliefors test. When a normal distribution was assigned, hypothesis tests were done with student t-testsand ANOVA. When normality of the samples can not be proven, a wilcoxon signed rank test is performed.For paired samples, both a paired t-test and a wilcoxon signed rank sum are performed. All tests were doneat a significance level of α = 0.05 . The use of these tests can be found in the Matlab Statistics ToolboxUsers Guide [1].

16

3.2 Results

Tissue in which 20 Watt lesions were created is shown in Figure 9(a). These lesions were created in session2 of the duration experiments. Figure 9(b) shows a lesion of 15 seconds ablation after bisection and NTBstaining. The arrow shows the lesion depth as it is defined in this study.

(a) Tissue with ablation lesions (Front) (b) Cross section of lesion with NTB staining (Side)

Figure 9: Pictures of lesions (a) Lesions of 20 Watt ablations for different durations, in seconds. Orientation of tissueis the same as in the experimental setup. (b) Cross section of a lesion (20 Watt ablation, 15 seconds)after NTB staining. Lesion depth is indicated by white arrow.

The lesion depths obtained by different ablation settings are listed in Table 3. All samples were testedpositive for normal distribution, except for the 20 and 40 seconds samples of session 1 (both N=5). Forthese samples, a ranked test was performed, instead of a student t-test. The sample sizes of session 2 weretoo small to be tested for normal distribution (N=3). No statistical analysis was done on these samples.

Table 3: Lesion depth for each experiment, mean ± standard deviation in mm

Power (90 seconds)10 Watt 15 Watt 20 Watt1.8±0.7 2.4±0.8 3.1±0.4Wall thickness (20 Watt, 90 seconds)5 mm 10 mm

2.9±0.3 3.1±0.3Duration (20 Watt)Session 120 sec 40 sec 60 sec 80 sec

2.1±0.2 2.8±0.4 3.4±0.9 3.6±0.4Session 2

5 sec 10 sec 15 sec 20 sec 90 sec 180 sec0 1.4±0.4 1.5±0.3 2.3±0.3 3.6±0.3 4.5±0.4

17

Lesion Depth versus PowerThe mean and standard error of the mean for lesion depth are shown per power in Figure 10(a). For 15 and20 Watt ablations, the lesions could be clearly distinguished. For 10 Watt however, the existence of lesionswas sometimes hard to determine. A significant difference between all three the groups was concluded witha one way ANOVA test. A t-test yielded p = 0.03 and p = 0.006 for comparison of 10 to 15 Watt and 15 to20 Watt respectively. The impedance of the experimental setup without tissue was 53Ω. At the beginningof ablation it was 74± 3Ω. The wall thickness of the ablated tissue was 6.2±1.3 mm.

Lesion Depth versus Wall ThicknessThese lesions were made in the same session as the Power measurements. The impedance at initiation of theablations was 73± 2Ω. The data points of lesion depth per wall thickness are shown in Figure 10(b). Out ofthe 14 lesions, 10 seemed to be in a thin part of 4.3± 0.2 mm and 4 in a thicker part of 10.4± 0.6 mm wallthickness. The corresponding lesions were 2.9± 0.3 mm and 3.1± 0.3 mm deep. With a two sample t-test,the wall thickness of the groups was shown significantly different (p = 0.00014), but no significant differencecould be shown between the lesion depths (p = 0.16).

(a) Lesion depth versus power (b) Lesion depth versus wall thicknesses.

Figure 10: (a) Lesion depth after 90 seconds of ablation with 10, 15 and 20 Watt, mean ± standard error of themean (b) Lesion depth for 20 Watt ablation of 90 seconds for different wall thicknesses.

Lesion Depth versus DurationThe results for the duration experiments are shown in Figure 11.

Session 1Figure 11(b) shows the mean and standard error of the mean for lesion depth for each duration of ablation inthe first session. The average wall thickness was 6.5±1.4 mm. Statistical difference was found between thegroups of 20 seconds (N=6) and 40 seconds (N=9), with p = 0.047, and that of 40 and 60 seconds (N=15),with p = 0.008, by a signed rank test. Between the groups of 60 seconds and 80 seconds (N=5) no significantdifference was found by a t-test (p = 0.68).

Session 2The mean and standard error of the mean of the lesion depths are shown in Figure 11(a) for lesions of shortduration (5 to 20 seconds) and 11(c) for longer duration (90 and 180 seconds). For the 5 second ablations,only one lesion could be found. Therefore, the result these ablations was regarded as no lesion. The lesion

18

depth of 10 and 15 second have a large overlap in measured lesion depths. For the 15 and 20 seconds lesions,a rise in lesion depth can be seen. When comparing the lesion depth for 90 seconds and 180 seconds, a steadystate cannot be concluded at 90 seconds of ablation.At the beginning of all ablations, the impedance was 80 Ω. After 5 seconds, the impedances had dropped to67±1Ω. Furthermore, at the beginning of the experiments, the temperature of the saline in the experimentalsetup was 21.0C and the impedance of the setup (i.e. without tissue) was 54Ω. After the experiments, thetemperature was 21.6C and the impedance was 53Ω. The initial voltage to maintain a 20 Watt power was36.0 Volt for all ablations. This voltage decreased in time, to 35.5 volt for early lesion development and 35.0Volt for the steady state session. The wall thickness of the ablated tissue regions was 5.5±1.5 mm.

(a) Lesion depths for Session 2 - shortdurations

(b) Lesion depths for Session 1 (c) Lesion depths for Session 2 - longdurations

Figure 11: Mean and standard error of the mean of lesion depth for different durations at 20 Watt ablation (a)Results for short ablations of session 2 (i.e. 10, 15, 20 seconds) (b) Results for session 1 (i.e. 20, 40, 60and 80 seconds of ablation) and (c) Results for longer durations in session 2 (i.e. 90 and 180 seconds ofablation)

19

3.3 Discussion

The relation between lesion depth and power is almost linear. This agrees with the results of Wittkampf inFigure 6(b). Transmurality was achieved in none of the lesions. The 20 Watt power was the upper limit forablation in this setup. For higher powers, tissue pops occurred.No significant difference was found between the lesion depths of ablations in 5.0 mm and 10.0 mm wallthickness. This finding is supported by Figure 12, which shows the lesion depths for all 90 seconds 20 Wattablations from this study. This does not agree with the findings of Thomas [31], who found significantlarger lesions in thicker ventricle tissue. This was during epicardial ablation, but the tissue was thickenough to exclude influence of intracardial convection. However, his experiments were done in vivo and aftercardioplegia, which might cause a different tissue health and geometry of the ablation setup. He used TCablation and a 7F (2.3 mm) electrode.

Figure 12: Lesion depth in mm versus wall thickness in mm for all 20 Watt, 90 second ablations (from the series:power, wall thickness and session 2)

The results for lesion depth in time show a fast growth in the beginning, that decreases after 10 to 20 seconds.This was expected on basis of literature. After five seconds of ablation however, no lesion could be found.Also, there seemed to be no difference between the lesion depths after 10 and 15 seconds of ablation. Thetemperature in the tissue temperature might be increased, but the duration might be too short to inducenecrosis. This was earlier explained with use of the work of Henriques (section 2.2). Furthermore, themeasurement insecurities have a relatively larger influence in small lesions.The difference between the lesions depth after 90 and 180 seconds in session 2 was unexpected, as nosignificant difference was found between the lesion depths for 60 and 80 seconds in session 1. Also, thelesion depths of the 80 seconds ablation lesions in session 1 and 90 seconds ablation lesions in session 2had the same average. These misleading results might be due to the small sample sizes of the durationmeasurements. Furthermore, the lesions were created in a different tissue, and the tissue of session 1 wasstored in a refrigerator overnight. Thus a difference in tissue properties may have had influence on themaximum lesion size as well.The lesions in shown in Figure 9(a) look like white flames on the surface of the tissue. This shape is dueto upward movement of heated saline around the tissue, which could be seen during the ablation procedure.Apparently the temperature of the saline is high enough to induce necrosis on the tissue surface. Whenthe lesions were bisected it could be seen that this was only superficial. Therefore, it is not expected that

20

this hot fluid flow affects the tissue in deeper regions, but some heating of the tissue above the location ofablation will take place. It does also point out that the flow of this saline continuously convects a significantamount of heat away from the site of ablation.From the same picture it can be seen, that some lesions are only at a distance of 5 mm away from each other,although the center of the lesions are 1 cm apart. The width of lesions decreases rapidly in the direction oflesion depth, but tissue may be affected by a previous ablation. Randomization was done on the ablationsettings, but not on the location of ablation. Therefore, some lesions may have had more heating thanthought. A time span of at least one minute existed between the ablations.Lesion borders could be clearly distinguished after NTB staining. A small disadvantage of the method is,that the tissue has to be bisected before fixation. This makes it harder to cut exactly through the centerof the lesion. Thus this introduces an uncertainty in the measured lesion depth. Furthermore, the lesiondepths were measured at normal sight with a caliper. This induces some inaccuracy to the measurements.With aid of digital imaging or magnification equipment, measurements could be more accurate.The performed experiments differed amongst each other in geometry, saline concentration and impedance.Thus care should be taken when comparing the data to each other, although the influence of the differencesis not expected to be large. The differences between session 1 and 2 for example, are a larger container(length x width x height = 42x30x15 cm versus 20x20x10 cm), a larger distance of the dispersive electrodeto the tissue (15 to 20 versus 5 to 10 cm) and a different saline concentration (0.5% versus 0.9%). Becausethe current density decreases rapidly with distance from the active electrode (this will be explained in section4.1), the larger distance of the dispersive electrode will be of small influence. The changes in temperatureand impedance of the smaller experimental setup after 18 ablations were only 0.6V C and 1Ω, thus no effectis expected from the change in container size. The properties of 0.5% and 0.9% saline are expected to berelatively small.To investigate the influence of these differences between the experiments on lesion depth, the lesion depthsof the ablations of 90 seconds duration and 20 Watt power from all experiments are compared. The lesiondepths are shown in Table 4, with the corresponding wall thicknesses and initial impedances. Unfortunately,the information on initial impedance is not complete. It remains unclear from this data set, why the finallesion depths in the of duration measurements are larger than those in the measurements for power and wallthickness. The difference however, is less than a millimeter.

Table 4: Lesion depths (LD [mm]) for all experiments with 20 W, 90 s ablations. WT: wall thickness [mm], II:initial impedance [Ω]

Experiment WT LD II RemarksPower20 Watt 5.8±1.5 3.1±0.4 74±3Wall thicknessThinner tissue 4.3±0.2 2.9±0.3 unknownThicker tissue 10.4±0.6 3.1±0.3 unknownAll tissue 6.4±2.7 3.0±0.3 73±2DurationSession 1 7.3±1.0 3.6±0.4 unknown Duration was different (80 seconds)

Saline concentration was different (0.5%)Experimental setup was larger (42x30x15 cm)

Session 2 6.3±3.1 3.6±0.3 80

21

4 Finite Element Model

22

4.1 Physics of Radiofrequency Ablation

The mechanism of RFA is a combination of several events occurring at the same time. The basic principleis the heating of tissue by ohmic heating: The applied electrical energy is converted into heat due to theresistivity of the tissue. Because the majority of this energy is dissipated very near the active electrode,a temperature gradient through the tissue exists. Due to this temperature gradient the heat is conductedthrough the tissue. Furthermore, the surrounding fluid will transport heat away from the location of treat-ment. Figure 13 shows the mechanism of RFA in a schematic manner.

Figure 13: RFA mechanism, in three steps: (A) Potential difference between the two electrodes (blue in this image)causes current density through the tissue. This causes temperature elevation in the tissue by ohmicheating. (B) Temperature gradient in tissue causes conduction of heat through the tissue. (C) Heatingof surrounding fluid causes flow in the fluid, which causes heat convection.

4.1.1 Electric Heating

An alternating potential is applied to the tissue. This is typically a sine-wave with a frequency of 500 kHz,and a RMS of about 30 Volts. A small active electrode is held against directly the tissue and a largerdispersive electrode is placed at a distance. Due to the applied voltage, a current density ~J [A/m2] existsthrough the tissue and the surrounding fluid. As there are no other sources and the current can not bestored, the divergence of the current is described by equation (4).

∇ · ~J = 0 (4)

Ohm’s law is assumed, as in equation (5) with E [V/m] the electric field, σ [S/m] the electrical conductivity,and r [m] the distance from the active electrode. Note, that the electric field E and thus the current densityis a function of the distance from the active electrode.

~J(r) = σ ~E(r) (5)

Furthermore, the electric field is defined as in equation (6), with V [V ] the electric potential.

~E = −~∇V (6)

By combining equation (5) and (6) with equation (4), the expression for potential in the field becomesequation (7). For an isotropic electrical conductivity σ, this equation is called the Laplace equation.

∇ · (σ ~∇V ) = 0 (7)

23

The dissipated amount of heat Q [W/m3] is dependent on the current density J and the field strength E atthat point, as is expressed by equation (8).

Qdiss = ~J · ~E (8)

In combination with equation (5), this becomes equation (9).

Qdiss = σ | ~E|2 (9)

4.1.2 Heat Conduction and Convection

The dissipated heat Qdiss can be split into three parts. One part, Qheat [W/m3], elevates the temperatureT [K] of the tissue and the fluid. The second part, Qcond [W/m3], is conducted through the tissue. Thethird, Qconv [W/m3], part is convected by flow of the fluid. External heat sources, like metabolic heat, aregenerally considered as negligible in this problem [5]. Thus Qdiss can be regarded as in equation (10).

Qdiss = Qheat +Qcond +Qconv (10)

The amount of energy that is stored by temperature rise, Qheat, is related to the density ρ [kg/m3] and heatcapacity c [J/kg K], as in equation (11).

Qheat = ρ c∂T

∂t(11)

This heat rise will mainly occur in a small rim of tissue and fluid around the active electrode, as the currentdensity is highest there. Due to the created temperature gradient, a part of this heat is conducted by a heatflux ~h [W/m2] over the surface of the volume. This flux can be described by the diffusion term in equation(12), with k [W/m K] the thermal conductivity of the tissue and ~∇T [K/m] the temperature gradient.

~h = −k ~∇T (12)

With use of the divergence theorem, the conductive heat loss for the total volume Qconv can be describedby equation (13). Here, ~∇2T is the divergence of the gradient of the temperature.

Qcond = −k~∇2T (13)

Furthermore, convection of heat is caused by flow in the surrounding fluid. This amount of heat, Qconv, thatis convected depends on the temperature gradient ~∇T , the velocity of the fluid ~u [m/s], and the materialproperties ρ and c of the fluid. This relation is given in equation (14).

Qconv = ρ c ~u · ~∇T (14)

Combining equation (10) with equation (11), (13) and (14) results in the heat equation given by equation (15).

ρ c∂T

∂t= Qdiss + k~∇2T − ρ c ~u · ~∇T (15)

TissueIn the tissue no flow exists (~u = 0). Therefore, the dissipated heat is divided in a part of storage and oneof conduction. Thus the temperature rise in the tissue can be described by equation (16). This equation ismade dimensionless in Appendix B.

ρ c∂T

∂t= Qdiss + k~∇2T (16)

24

FluidIn the experimental setup, only natural convection exists. Due to heating, the liquid surrounding the activeelectrode expands. This expansion is dependent on the coefficient of expansion (α [1/K]) of the fluid andthe change in temperature (∆T ) as in equation (17). Here, W0 [m3] is the original volume of the fluid, and∆W [m3] is the new volume.

∆WW0

= α ∆T (17)

Due to the expansion, the density ρ of the fluid decreases, a therewith the gravitational force on the fluid.This yields an upward buoyancy force on the heated fluid. This can be calculated by Archimedes’ Law, asin equation (18).

~F = ρ g∆W (18)

Combined with equation (17), this yields equation (19).

~F = ρ g α W0 ∆T (19)

This change in gravitational force induces a velocity ~u in the fluid, which can be calculated by the Navier-Stokes equations for incompressible fluid. These are given in equation 20. They describe the velocity in thefluid, based on both the viscous and non-viscous forces on the fluid.

ρ~u · ∇~u = ∇ · [−pI + η(∇~u+ (∇~uT ))] + F (20)

In the model, the Boussinesq approximation is used. In that case, it is assumed that the inertia influencesof this density change is negligible. Thus, only the the changes in the gravity force due to the change indensity are of influence.

25

4.2 Model Implementation

A FEM model of the experiments has been made based of the equation discussed in section 4.1. The FEMpackage used is COMSOL Multiphysics 3.3a, with use of the ”Conductive Media”, ”Incompressible Navier-Stokes” and ”Heat Conduction and Convection” Application Modes. As the velocity field and temperaturegradient influence each other, the equations are coupled. This means, that the temperature field is used forthe Navier-Stokes equations, and the velocity components from the incompressible Navier-Stokes equationsare used as the velocity field for the convective heat transfer [26].

4.2.1 Model Geometry

The model, which can be seen in Figure 4.2.1, has a vertical symmetry axis of rotation. It consists of areservoir with a height of 7.5 cm and radius of 5.0 cm and is filled with saline. Within the saline, there is ahorizontally oriented piece of cardiac tissue with a radius of 3.0 cm, and a variable thickness (3.0, 5.0 or 10.0mm). The active electrode is situated on the symmetry axis and has a tip diameter of 2.0 mm and length of4.0 mm. The dispersive electrode with a radius of 2.0 cm is positioned on the bottom of the reservoir (3.6cm from the bottom of the tissue).

(a) Model geometry (b) Model boundaries

Figure 14: Geometry and Boundaries of the FEM model

4.2.2 Boundary Conditions

The boundaries and subdomains of the model are shown in Figure 14(b). Ω1 is the tissue, and Ω2 the saline.Boundary Γ1 is the active electrode tip. This exists of two boundaries, but these are treated the same wayin all cases. Then Γ2 is the wire, Γ3 the dispersive electrode, and Γ4, Γ5 and Γ6 are the top, side and bottomboundaries of the setup respectively. The boundaries of the tissue are denoted by Γ7, Γ8 and Γ9. A list ofboundary conditions is given by Table 5.

26

Electric HeatingFor the electric problem, Γ1 is set to a constant electric potential. Γ3 is set as ground electrode. All otherboundaries for this problem (Γ2,Γ4,Γ5,Γ6) are electrically insulated. The symmetry axis is of rotationalsymmetry, meaning that there is no potential difference across this axis.

TemperatureFor the thermal problem, all outer boundaries (Γ4,Γ5,Γ6) are set to 20C. The electrode tip and wire (Γ1,Γ2)are set to thermal insulation. Again, there is axial symmetry at the rotational axis. This means, that thereis no temperature gradient over this axis.

ConvectionFor the calculation of the natural convection velocity, Γ4 is the open surface of the fluid to the air. All otherboundaries are set to no-slip, including the tissue boundaries Γ7, Γ8 and Γ9. In the initial situation, there isno flow in the system. Across the rotational axis, no flow is possible.

Table 5: Boundary conditions for the FEM model. Here, V is potential, J is current density, q is the total heatflux (conductive and convective: q = −k∇T + ρc~uT ), ~u is velocity, and t ·K is the tangential force of theviscous force, with K the viscous boundary force per unit area. For more information, see the ComsolManual [26].

Boundary Boundary conditionΓ1 Constant potential V = V0

Γ3 Ground V = 0Γ2,Γ4,Γ5,Γ6 Electric insulation n · J = 0Symmetry axis n · J = 0Γ4,Γ5,Γ6 Constant Temperature T = T0

Γ1,Γ2 Thermal insulation n · q = 0Symmetry axis n · q = 0Γ1,Γ2,Γ3,Γ5,Γ6,Γ7,Γ8,Γ9 No slip ~v = 0Γ4 Slip ~v · ~n = 0 , t ·K = 0Symmetry axis Symmetry ~v · ~n = 0 , t ·K = 0

4.2.3 Mesh Generation and Simulation Protocol

The mesh is generated with triangular Lagrange elements. Refinement is done around the electrodes, as canbe seen in see Figure 15(a). For calculation, two different Lagrange elements are used. For the Electricalproblem, quadratic elements are used, with one degree of freedom (Potential [V]). The same accounts forthe thermal problem (Temperature [K]). For the flow problem however, the quadratic element is used fortwo degrees of freedom (the velocity in two directions ~u and ~v [m/s]), and at the same time linear for thepressure p [Pa]. The linear and quadratic Lagrange elements can be seen in Figure 15(b).Simulations were done to investigate the relation of the applied voltage (and thus the power) and duration

of ablation with lesion depth. The depth of the 50C isotherm perpendicular to the tissue surface wasdefined as the lesion depth, independent of the duration of this temperature rise. Simulations were donewith constant potentials of 25, 30 and 35 Volt on the active electrode surface, for wall thicknesses of 3.0, 5.0and 10.0 mm. Simulations were done for 90 seconds of ablation, and lesion depths were read out at 5, 10,15, 20, 30, 40, 60, and 90 seconds. Additionally, for each potential and wall thickness combination, a steadystate lesion depth was calculated with a stationary analysis. For evaluation of the modeling steps, images ofthe subresults for the electric and heat problem were made. The constants had the values shown in Table 6.Note, that the electric conductivity is modeled here as a constant. The value for isotonic saline is the same

27

(a) Mesh of triangular Lagrange elements. Refine-ment takes place around the electrodes.

(b) Lagrange elements of the first (A)and second (B) order. The squarednodes are used for pressure.

Figure 15: Mesh of the FEM model

as that of blood [27].

Table 6: Constants used in the FEM model [27, 25, 5].

Constant Symbol Tissue Saline UnitsThermal conductivity k 0.70 0.55 W/mKElectrical conductivity σ 0.61 0.95 S/mHeat capacity c 3200 4180 J/kgKDensity ρ 1200 1000 kg/m3

Viscosity η - 0.001 Pa sExpansion coefficient α - 207 10−6/K

28

4.3 Results

4.3.1 Physics of Radiofrequency Ablation

All images in this subsection are for a 30 Volt ablation on a 5.0 mm thick RV, after 60 seconds of simulatedablation. Table 7 gives an overview of the maximum value for each of the physical properties.

Electric HeatingFigure 16(a) shows the electric field. The potential is shown by the surface, and is 30 V at the ablationelectrode and 0 V at the dispersive electrode. The direction of the electric field is given by normalized arrows.The maximum electric field strength is 6.7 · 108 V/m. The current density and ohmic heating have theirmaximum values at the same locations. The current density has a maximum of 6.3 · 104 A/m2, and at thesame location the resistive heating has a maximum of 4.2 · 109 W/m3.

(a) Result for Electric Field (b) Result for Fluid Velocity

Figure 16: Model results for electric field and fluid velocity (a) Solution for electric problem by the model. Back-ground: Electric potential [V ], Arrows (normalized): Electric field [V/m] (b) Solution for fluid velocity.Background: Magnitude of fluid velocity [m/s]. Arrows (normalized): Direction of velocity.

Heat Conduction and ConvectionFigure 16(b) shows the magnitude and the direction of the velocity field. The maximum velocity appearingin the field (along the wire of the electrode) is 0.014 m/s, where also the rise in pressure has its maximumof 0.17Pa. The results for conduction and convection are shown in Figure 17(a) and 17(b) respectively. Themaximum conductive heat flux is 8.9 · 104 W/m2 and the maximum convective heat flux is 1.3 · 106 W/m2.The arrows in Figure 17(a) show, that at a part of the heat is conducted towards the surface of the tissue,

29

and transported into the water. A net conductive heat flux of 22.1 W is found to flow into the tissue.

(a) Conductive Heat Flux (zoomed in). (b) Convective Heat Flux (zoomed in).

Figure 17: Model results for heat distribution (a) Zoom on Conductive Heat Flux. Background: Magnitude of con-ductive heat flux [W/m2], Arrows (normalized): Direction of conductive heat flux (direction) (b) Zoomon convective heat flux. Background: Magnitude of convective heat flux [W/m2]. Arrows (normalized):Direction of convective heat flux. Scale: The tissue is 5 mm thick.

Final Temperature distributionThe final temperature distribution in the model is shown in Figure 18(a), with the 50C isotherm. Themaximum temperature is 115C. Figure 18(b) shows the temperature of the electrode tip to tissue surfacecontact point. The temperature shows a fast increase in the first 10 seconds of ablation.

30

(a) Final temperature distribution of the model. (b) Electrode Tip and Tissue surface temperature in time.

Figure 18: Temperature distribution in the model after a 60 seconds simulation with a potential of 30 Volts and wallthickness of 5.0 mm. Left: Image of temperature distribution in the model (zoomed in). Background:Temperature [C], Isotherm: Border of lesion [50C]. Right: Graph of temperature in time at theelectrode tip.

Table 7: Maximum occurring value for the physical properties of the model

Physical Property Symbol Maximum value UnitsElectric Potential V 30.0 VElectric Field strength |E| 6.67 · 108 V/mCurrent Density J 6.33 · 104 A/m2

Resistive Heating Q 4.22 · 109 W/m3

Velocity v 0.0144 m/sPressure p 0.168 PaTemperature T 114.7 CConductive Heat flux magnitude |φcond| 8.92 · 104 W/m2

Convective Heat flux magnitude |φconv| 1.33 · 106 W/m2

Temperature Gradient ∆T 1.62 · 105 K/m

31

4.3.2 Lesion Depth

The results of the simulations are shown in Figure 19. Table 8 gives the lesion depths for an ablation of 90seconds and for steady state analysis, per potential and wall thickness.

Figure 19: Model Results: Lesion depths in mm for simulations with a potential of 25, 30, 35 Volt and wall thicknessof 3.0, 5.0 and 10.0 mm in time (0 to 90 seconds)

Table 8: Lesion depths in mm calculated by the model, for different voltages and wall thicknesses, d90 after 90seconds of simulation and dSS for steady state analysis.

Potential → 25 V 30 V 35 VWall thickness ↓ d90 dSS d90 dSS d90 dSS

3 mm 1.9 2.0 2.4 2.5 2.8 2.95 mm 2.0 2.1 2.8 2.9 3.4 3.6

10 mm 2.0 2.3 2.9 3.4 3.8 4.6

Lesion Depth versus PowerThe simulations of 25, 30 and 35 Volt ablations approached 10, 15 and 20 Watt ablations respectively. Thevalues of resistive heating power for each case are shown in Table 9. It is clear that for a higher potential (andthus for a higher power) at a similar wall thickness, the lesion is deeper. The final lesion depths however,are also dependent on wall thickness.

32

Table 9: Ohmic heating [W ] in model per voltage and wall thickness, and the tissue heating (i.e. how much of thetotal power is dissipated in the tissue) in [%].

25 Volt 30 Volt 35 Volt Tissue heating [%]3 mm 10.30 W 14.83 W 20.19 W 10.05 mm 10.11 W 14.56 W 19.82 W 13.5

10 mm 10.03 W 14.44 W 19.65 W 10.0

Lesion Depth versus Wall thicknessFor 25 Volt there is no difference between the final lesion depth of the three wall thicknesses (1.9, 2.0 and2.0 mm). For 30 V the final lesion depth in the 3 mm wall thickness is smaller than those for the 5 and 10mm wall thickness (2.4, 2.8 and 2.9 mm). For 35 Volt all lesion depths are different (2.8, 3.4 and 3.8 mm).In none of the cases, the lesion is transmural.

Lesion Depth versus DurationThere is a fast lesion growth in the first 10 to 20 seconds. For 3.0 mm wall thickness the lesion growth seemsto have ceased after 30 to 40 seconds. The steady state lesion depths in Table 8, are only 0.1 mm or 0.2mm larger than the final lesion depths (at 90 seconds) for all three potentials. The same can be said for the5.0 mm wall thicknesses, although there it takes 60 to 90 seconds to come this near to steady state lesiondepth. For 10.0 mm wall thickness, the difference of lesion depth for 90 second ablation and steady stateanalysis is 0.5 mm for 30 Volt and 0.8 mm for 35 Volt. Time constants were derived with a fit to a modelof exponential growth: d = A(1 − e− t

τ ). The lesion depth at 90 seconds was taken as value for A, and theτ was selected based on the lowest RMS value of the difference with the data points. Time constants of 8(average for 3 mm tissue) to 16 seconds (average for 10 mm tissue) were found.

33

4.4 Discussion

The quick lesion growth in the first seconds of ablation, leading towards a steady state after about a minute,agrees with the findings in literature (section 2.2). After 90 seconds of ablation, only the 10.0 mm wall thick-ness simulations have not reached 90% of the steady state lesion depth. All other lesions have almost reachedtheir maximum depth, and no transmurality will be reached in any of the simulations. An explanation forthis, is cooling at the backside of the tissue by surrounding fluid. With 20C, the temperature of this fluidis lower than body temperature, which may explain differences to studies is which transmurality is reached.Steady state lesion depth is larger for higher voltages. This relation is, however, also influenced by the wallthickness. It seems that for the higher potentials, the wall thickness limits the lesion growth. For 25 Volt,the maximum lesion depth is already approached (within 0.1 mm) in the 3 mm tissue. For 30 Volt however,this is obtained in the 5 mm tissue, and the lesion depth is smaller in the 3 mm tissue. For 35 Volt, thelesion depth is also limited by wall thickness when ablating in 5 mm tissue. Thus there is a maximum lesiondepth for each voltage, which can be limited by a small wall thickness.To examine the maximum lesion size per voltage and wall thickness further, several simulations were donefor voltages between 20 and 40 Volt and the three different wall thicknesses. The result is shown in Figure21. It can be seen, that for 3 mm wall thickness, the increase in steady state lesion depth decreases after 32Volt at 2.5 mm lesion depth. For 5 mm the decay is smaller, and for 10 mm there is no decay. Thus thelesion depth in thicker tissue is limited by the power. Note, that high powers may be impossible to use inpractice, due to the high risk on tissue pops.The model does not account for the anisotropy and temperature dependent changes of the electric conductiv-ity σ and thermal conductivity k of both the tissue and the saline. Especially the temperature dependencyof the electrical conductivity of the cardiac tissue is of importance [30, 4]. A 2% rise in conductivity for eachdegree Celsius of temperature rise is applied in literature [4, 21, 25]. Above 90C, the tissue conductivitydecreases due to structural changes in the tissue [22]. This increases the current density through the tissuesurface at the ablation electrode, and thus increases the amount of ohmic heating in the tissue. This wasinvestigated with simulation of 35 Volt, 5 mm wall thickness and 180 seconds, and with an electrical con-ductivity twice as high as used in the model. This resembles a 35 C temperature rise in the tissue. Theresult can be seen in Figure 20. The lesion depth grows as fast as with the normal conductivity, but to alarger size (4.0 versus 3.5 mm). The 100C isotherm was twice as deep as with the normal conductivity (2.0mm). Thus larger lesion depths are reached, but the risk for tissue pops increases.

Figure 20: Lesion depth in time for normal anddoubled electrical conductivity (30 Volt,5 mm wall thickness simulation)

Figure 21: Relation of steady state lesion depth with ap-plied voltage

34

The convective heat flux was 15 times as large as the conductive heat flux. This was larger than expected.A simulation without convection was done, with a potential of 30 Volt and a 5.0 mm wall thickness. After90 seconds, the lesion was transmural whereas it was only 2.8 mm with convection. The 100C isothermreached a transmural depth of 1.7 mm, which is 3.5 times larger than when convection takes place. Themaximum temperature in the tissue was 3 times as high. Thus the natural convection seems to protectthe tissue against popping at these voltages. The power used in cardiac ablation should be adjusted to theamount of flow around the ablated tissue.

35

5 Model versus Experiments

36

5.1 Combined Results

Figure 22 and 23 show the results for both the model and the experiments. The results are again separatedinto lesion depth versus power, wall thickness and duration. The experimental data are represented bythe mean and the standard error of the mean. The differences in lesion depth between the model and theexperiment varies between 0.0 and 1.0 mm. The average of the absolute difference is 0.4 mm, which is anaverage of 14% difference of the model towards the experiments.

(a) Lesion depth per power (b) Lesion depth per wall thickness

Figure 22: Comparison of experimental data with those of the model model for different powers (and thus voltages)and wall thickness (a) Influence of power: lesion depths after 90 seconds of ablation for 10, 15 and 20Watt in experiments and 25, 30 and 35 Volt for 90 seconds at 5 mm tissue in the model (b) Influence ofwall thickness: lesion depth for 90 second ablations with 20 Watt and 35 Volt simulations in 5 and 10mm wall thickness

Lesion Depth versus PowerThe 10, 15 and 20 Watt ablations are compared to the 25, 30 and 35 Volt ablation simulations respectively.This was done based on the results in Table 9 in section 4.3.2. The results are shown in Figure 22(a), and thedata are listed in Table 10. The lesion depths are all for 90 seconds of ablation. The average wall thicknessesin the experiments were closest to those of the 5.0 mm simulations (6.6±1.4, 6.0±1.1 and 5.8±1.5 mm for10, 15 and 20 Watt respectively).The difference between lesion depth derived from the model and the experiments are 0.2 to 0.4 mm, whichis a 8 to 14% difference. For the experiments, lesion depth increased 30% (0.6 mm) to 33% (0.7 mm) for anincrease in power of 10 to 15 Watt and 15 to 20 Watt respectively. In the model, the increase was 40% (0.8mm) between 25 and 30 Volt, but only 20 % (0.6 mm) between 30 and 35 Volt.

DiscussionThe smaller increase in lesion depth for higher voltage in the model can be explained by the difference inenergy application. During the experiments, constant power is used. In the model however, constant voltageis applied. The lesion size is related to the power which is applied to the tissue. As the resistance in theablation setup rises due to thicker tissue, the power of the ablation decreases. This effect can also be seen inTable 9. Furthermore, this power is dissipated in a larger piece of tissue. Therefore, the amount of dissipatedheat decreases compared to the increase at constant power ablation.

Lesion Depth versus Wall ThicknessFor wall thickness, the experiments were done with 20 Watt ablation, which is closest to the 35.0 Volt abla-

37

Table 10: Lesion Depths LD in mm for different powers in the experiments (10, 50, 20 W) and voltages in the model(25, 30 and 35 V respectively). The lesion sizes are derived from 90 second ablation, and a 5 mm wallthickness in the model.

Experiment 10 W 15 W 20 WLD 1.8±0.7 2.4±0.8 3.1±0.4

Model 25 V 30 V 35 VLD 2.0 2.8 3.4

tion simulations. The duration was 90 seconds in all cases. The data from the model for 5.0 and 10.0 mmwall thickness, and the experiment for 4.3±0.2 and 10.4±0.6 mm are listed in Table 11.The mean lesions depth of the experiments differ from the model by 0.5 mm (15%) and 0.7 mm (18%) forthe thinner and thicker tissue respectively. In the experiments the lesions grow by 0.2 mm (7%) and in themodel by 0.4 mm (11%) for the 5 mm increase in wall thickness.

DiscussionBoth the experiment and the model show a larger lesion depth for thicker wall thickness. The increase oflesion depth in the experiments is smaller than that in the model, although the increase in tissue thicknessis larger (6.1 mm versus 5.0 mm). Care should be taken however in drawing conclusions, as no significantdifference was found between the experimental data for 5 and 10 mm wall thickness ablations in section 3.2.

Table 11: Experimental (20 W, 90 s) and Model (35 V, 90 s) Lesion Depths in mm for different wall thickness.

Wall thickness 5 mm 10 mmLesion depth [mm] Experiment 2.9±0.3 3.1±0.3

Lesion depth [mm] Model 3.4 3.8

Lesion Depth versus DurationAgain, 20 Watt data are compared to the data of the 35 V simulations for 90 seconds of duration. The aver-age wall thickness in the tissue was 6.0 mm, which is closest to the 5.0 mm wall thickness of the simulations.The data are listed in Table 12. The lesion depths in time for the experiments and simulation are shown inFigure 23. Also an exponential fit for the model is shown for the exponential growth, with a time constantτ of 14 seconds. The RMS of the differences between this fit and the lesion depths obtained from the modelis 0.17 mm. In both the model and experiment, no transmural lesion was achieved.Because of the difference in experimental setup, the data for session 1 and 2 are shown separately. Thesteady state lesion depth from the model was 3.6 mm. The mean lesion depths of the experiment differ morethan 0.5 mm from the model, for 10 (0.6 mm), 15 (0.9 mm) and 180 (1.0 mm) seconds. The differences inlesion depths for 20, 40, 60 and 80 seconds were smaller (0 to 0.5 mm). Above 60 seconds, the experimentallesion depths are larger than those obtained from the model. There is only a clear difference at the 180seconds however. For shorter durations, the lesion depths in the model were always larger.

DiscussionThe experiments show a slower start of growth and larger final lesion depth than the model. The slowerstart may be caused by the duration of elevated temperature that is needed to induce necrosis, as discussedin section 2.2. The model could be adapted to this, by using a time and temperature dependent relation for

38

Figure 23: The lesion depths for the experiments (20 Watt) and simulations (35 Volt, 5 mm wall thickness). Theexperiments are shown with the mean (datapoint) and standard error of the mean (errorbar). To themodel, a fit was applied of mono exponential growth with a time constant τ of 13 seconds

the lesion border, like the Arrhenius equation. Furthermore, existence of latent heat in the tissue could leadto larger lesions in the experiments than actually existed at the used duration of ablation [10]. The modelcould be adapted to this, by keeping the simulation running after the potential has been switched off.

Table 12: Experimental and Model Lesion Depths for different durations (LD: lesion depth, S1: session 1 and S2:session 2 of duration experiments, M: FEM model. Model settings were 35 V and a 5 mm wall thickness.

Duration 5 s 10 s 15 s 20 s 40 s 60 s 80 s 90 s 180 sLD S1 [mm] 2.1±0.2 2.8±0.4 3.4±0.9 3.6±0.4LD S2 [mm] 1.4±0.4 1.5±0.3 2.3±0.3 3.6±0.3 4.5±0.4LD M [mm] 1.4 2.0 2.4 2.6 3.2 3.4 3.4 3.4 3.5

39

5.2 Limitations

A difference in geometry between the model and experimental setup is the orientation of the tissue and theelectrode. In the experimental setup, these are rotated over a 90 angle (see picture) compared to the model.Implementing a similar geometry would complicate the model due to problems concerning the symmetry.An effect of this orientation in the experiments, is the flamelike shape of ablation lesions on the surface ofthe tissue. This difference takes place only at a small region on the surface, and not too deep into the tissue.The effect of this difference in geometry on lesion depth development is therefore assumed to be small.Another difference is that the experiments are done using constant power in stead of voltage. The powerapplied in the simulations is calculated afterwards. The simulations could better be done for constant power,or next experiments should be done using constant voltage. Because for changes in resistance, the power ofconstant voltage ablation will vary.The model does not account the anisotropy and temperature related changes in the tissue properties. Tem-perature dependency of the electrical conductivity would cause larger lesions, as discussed in section 4.4.Furthermore, the model should include a relation for time and temperature equivalency (e.g. the Arrheniusequation), and for latent heat (e.g. do not stop the simulation directly at the end of the ablation).Deriving time constants for the experimental results using a mono-exponential growth model could be usefulin comparison of the model to the experimental lesion depths. That way, trends can be regarded in steadof values. However, the sample size was small and measurement points to scarce to make trustable fits.Furthermore, the steady state lesion depths for the experiments remains unknown.Another difficulty in comparing the data from the model to those of the experiments is, that there is noinformation available on the insertion depth of the active electrode into the tissue during the experiments.Therefore, it is unknown if the amount of power dissipated in the tissue is similar to that calculated in themodel.

40

6 Conclusion and Recommendations

The aim of this study was to gain more insight in the development of lesion depth during radiofrequencyablation (RFA). The focus in this study was on the power used during constant power ablation, duration ofablation, and the thickness of the tissue. The influences of these determinants on lesion depth were studiedwith experiments and a finite element model. The experiments were done in vitro on porcine cardiac tissue.Lesions were created with constant powers of 10, 15 and 20 Watt, for durations varying from 5 to 180seconds. The model was based on equations for ohmic heating, heat conduction and convection, and fluidflow. Ablations were simulated with constant voltages of 25, 30 and 35 Volt for durations up to 180 seconds,and steady state analyses were performed. In the model, wall thicknesses of 3, 5 and 10 mm were used. Thelesion depths obtained by the experiment and by the model were compared amongst each other and to eachother.Both the model and the experiments show an increase in final lesion depth for higher power. This relationis almost linear. In the model, this effect decreases for higher powers due to the constant voltage ablation.Besides, the lesion depth in the model depends on wall thickness as well. For smaller wall thickness, thehigher power ablations were limited by cooling of the fluid on the back of the tissue. In the experiments, nodifference was found between lesion depths of similar ablation settings in different wall thickness.An exponential growth of lesion depth in time was found in both the model and the experiments. The timeconstant is in the order of ten seconds. The experiments have a slower growth in the beginning. This is dueto the duration needed for tissue to become necrotic at a certain temperature. After 60 seconds of ablation,the lesion depths in the model with 3 and 5 mm wall thickness, had approximated their steady state value.In the experiment however, the lesion depth continued increasing after 90 seconds of ablation. This lategrowth may be due to latent heat in the tissue after ablation.The influence of natural convection was found to be large in the model. Without this convection, the tissuewas overheated very quickly. In the experiments, natural convection cannot be controlled. The appearanceof the lesions however, showed that heat is convected by flow in the surrounding liquid.The model can be optimized further towards the situation in the experiments. One important advice is tointroduce a time and temperature equivalency in the definition of lesion size. This takes account for theduration that is needed to induce necrosis in a cell at a certain temperature. Another important one, is toaccount for the temperature dependency of the electrical conductivity of the tissue. Other alterations canbe to model different layers in the tissue, and to account for the anisotropy and temperature dependency ofthe physical tissue properties of both the tissue and the surrounding fluid.The model can be used in future to investigate the influence of alterations in the ablation procedure. Itgives insight into the influence of convection, wall thickness and the power and duration of ablation, andthus can help predicting ideal ablation settings when more specific information about the ablation is known.Furthermore, it can be easily adapted to different electrode dimensions, irrigated tip ablation, pulsed ablationand ablation with varying power.In conclusion it can be said, that the experiments and the finite element model provided insight into thedevelopment of lesion depth during RFA. This insight can be used in optimization of the ablation procedure,to control the lesion development. This latter is important to achieve successful ablations by transmurallesions, without damage to the surrounding tissue.

41

References

[1] MATLAB 7.3.0. Statistics Toolbox Users Guide 7. The Mathworks, 2008.

[2] P. Gutierrez O. Vragovic J.N. Ruskin M.E. Josephson V.Y. Reddy A. d’Avila, C. Houghtaling. Catheterablation of ventricular epicardial tissue - a comparison of standard and cooled-tip radiofrequency energy.Circulation, (109):2363–2369, 2004.

[3] Olympus Industrial America. Basics of Polarizing Microscopy.

[4] Enrique J. Berjano. Theoretical modeling for radiofrequency ablation: state-of-the-art and challengesfor the future [review]. Biomedical Engineering Online, 5(24), 2006.

[5] Enrique J. Berjano and Fernando Hornero. Thermal-electrical modeling for epicardial atrial radiofre-quency ablation. IEEE Transactions on Biomedical Engineering, 51(8), 2004.

[6] I.A. Chang and U.D. Nguyen. Thermal modeling of lesion growth with radiofrequency ablation devices.BioMedical Engineering Online, 3(27), 2004.

[7] Danny D. Watson David E. Haines and Anthony F. Verow. Electrode radius predicts lesion radiusduring radiofrequency energy heating. Circulation Research, 67:124–129, 1990.

[8] O.J. Eick. Factors influencing lesion formation during radiofrequency catheter ablation. Indian PacingElectrophysiology Journal, (3):117–128, 2003.

[9] E.O. Robles de Medina F.H. Wittkampf, R.N. Hauer. Control of radiofrequency lesion size by powerregulation. Circulation, 80:962–968, 1989.

[10] William S. Yamanashi Shinobu Imai Warren M. Jackman Fred H.M. Wittkampf, Hiroshi Nakagawa.Thermal latency in radiofrequency ablation. Circulation, 93:1083–1086, 1996.

[11] M.R. Williams MD G.M. Comas MD, I. Yildirim MD. An overview of energy sources in clinical use forthe ablation of atrial fibrillation. Thoracic and Cardiovascular Surgery, 19:16–24, 2007.

[12] A.C. Guyton and J.E. Hall. Textbook of Medical Physiology. W.B. Saunders Company, 10th edition,2000.

[13] Y.B. Choy J.Z. Tsai V.R. Vorperian J.G. Webster H. Cao, S. Tungjitkusolmum. Using electricalimpedance to predict catheter-endocardial contact during rf cardiac ablation. IEEE Transactions onBiomedical Engineering, 49(3), 2002.

[14] David E. Haines. Determinants of lesion size during radiofrequency catheter ablation: The role ofelectrode-tissue contact pressure and duration of energy delivery. J Cardiovasc Electrophysiol, 2:509–515, December 1991.

[15] David E. Haines and Anthony F. Verow. Observations on electrode-tissue interface temperature andeffect on electrical impedance during radiofrequency ablation of ventricular myocardium. Circulation,82:1034–1038, 1990.

[16] E. Hecht. Optics. Addison Wesley, 4th edition, 2002.

[17] Thomas Walther Cris Ullmann Heinz-Adolf Schoon Friedrich Wilhelm Mohr Heike Aupperle, Nico-las Doll. Histological findings induced by different energy sources in experimental atrial ablation insheep. Interactive Cardiovascular and Thoracic Surgery, (4):450–455, 2005.

[18] F.C. Henriques. Studies in thermal injury, v: The predictability and the significance of thermallyinduced rate processes leading to irreversible epidermal injury. Arch. Pathol, 43:489–502, 1947.

42

[19] William S. Yamanashi-Jan V. Pitha Shinobu Imai Barclay Campbell Mauricio Arruda Ralph LazzaraHiroshi Nagakawa, Fred H. M. Wittkampf and Warren M. Jackman. Inverse relationship betweenelectrode size and lesion size during radiofrequency ablation with active electrode cooling. Circulation,98:458–465, 1998.

[20] J.D. Humphrey. Continuum thermodunamics and the clinical treatment of disease and injury. ApplMech Rev, 56(2), March 2003.

[21] Mudit K. Jain and Patrick D. Wolf. Temperature-controlled and constant-power radio-frequency abla-tion: What affects lesion growth? IEEE Transactions on Biomedical Engineering, 46(12), 1999.

[22] R. Platt J.S. Dadd, T.P. Ryan. Tissue impedance as a function of temperature and time. BiomedicalScience and Instrumentation, 32:205–214, 1996.

[23] F.H.M. Wittkampf J.V. Pitha R. Lazarra W.M. Jackman K. Yokoyama, H. Nakagawa. Comparisonof electrode cooling between internal and open irrigation in radopfrequency ablation lesion depth andincidence of thrombus and steam pop. Circulation, 113:11–19, 2006.

[24] J.A. Kiernan. Histological and histochemical methods, theory and practice. Scion, 4th edition, 2008.

[25] Sylvian Labonte. A computer simulation of radio-frequency ablation of the endocardium. IEEE Trans-actions on Biomedical Engineering, 41(9), 1994.

[26] COMSOL MultiPhysics. Modeling Guide. COMSOL, version 3.3 edition, 2006.

[27] X. Chen J.H. Svendsen N. Stagegaard, H.H. Petersen. Indication of the radiofrequency induced lesionsize by pre-ablation measurements. Europace, 7:525–534, 2005.

[28] D.R. Boughner J.G. Pickering P. Whittaker, R.A. Kloner. Quantitative assessment of myocardial col-lagen woth picosirius red staining and circularly polarized light. Cardiology, 89:397–410, 1994.

[29] M.J. Patterson R.A. Kloner K.E. Daly R.A. Hartman P. Whittaker, S. Zheng. Histologic signaturesof thermal injury: Applications in transmyocardial laser revascularization and radiofrequency ablation.Lasers in Surgery and Medicine, 27:305–318, 2000.

[30] Daniel Panescu and John G. Webster. Effects of changes in electrical and thermal conductivities onradiofrequancy lesion diemnsions. IEEE Proceedings - 19th International Conference, 1997.

[31] Anita C. Boyd Vivki E. Eipper David L. Ross Stuart P. Thomas, Duncan J.R. Guy and Richard B.Chard. Comparison of epicardial and endocardial linear ablation using handheld probes. The Annansof Thoracic Surgery, 75:543–548, 2003.

[32] Susan B. Johnson Sumeet S. Chugh, Rodrigo C. Chan and Douglas L. Packer. Catheter tip orientationaffects radiofrequency ablation lesion size in the canine left ventricle. Pace, 22:413–420, 1998.

[33] Sanjiv Kaul MD N. Craig Goodman BS Amanda R. Jayaweera PhD David E. Haines MD SunilNath MD, James G. Whayne MS. Effects of radiofrequency catheter ablation on regional myocardialblood flow. Circulation, 89:2667–2672, 1994.

[34] N.T. Wright and J.D. Humphrey. Denaturation of collagen via heating: An irriversible rate process.Annu. Rev. Biomed. Eng., 4:109–28, 2002.

43

A Polarization Microscopy

A.1 Theory

Strongly anisotropic materials have birefringent properties. This means, that the refractive index, and thusthe speed of light, is direction dependent. Assume that a material has a breaking index in direction a (na)and b (nb), perpendicular to each other. When linearly polarized light ~E0 falls into the material under anangle θ between the a and b axes, it is split into two components, ~Ea and ~Eb:

~Ea = ~E0 cos θ (21)~Eb = ~E0 sin θ (22)

The velocity of propagation is larger in the one direction than in the other direction. This induces a phasedifference between the polarization components that is dependent on the difference in velocity and thedistance it travels through the material as in equation 23. Due to the phase difference, the light is no longerplane polarized upon leaving the material [16].

δ =2πdλ

(na − nb) (23)

For polarization microscopy, two polarization filters are used after each other, as shown in Figure 24. Whenthe directions of polarization are perpendicular (see 1a), no light in transmitted through the second filter.When the direction is parallel (see 1b), all light is transmitted through the second filter. The angles inbetween will transmit the light partially. When however, a specimen with birefringent properties (see 2)is placed between two filters with perpendicular directions (see 3), the light is also partially transmitted.As birefringence of cardiac tissue is decreased or even lost when the tissue is damaged, this is a measurefor tissue damage [29]. As the birefringence is caused by the anisotropy of the tissue itself, no staining isnecessary to visualize this property. However, with a staining like Picosirius red, which is a long moleculethat lines up along the fibre, birefringence can be enhanced [28].

Figure 24: Basics of polarizing microscopy. Olympus [3]

A.2 Experiments

The tissue was fixated with formalin, and embedded with paraffin. Slices of 5 mircon were stained andstudied. The following stainings were studied: H&E, Masson’s and Chomorri’s Tri-Chrome stainings, andPicosirius red. For birefringence, both stained and unstained samples were regarded. Under a microscope,two polarization filters were used. First, the sample was studied with parallel polarization filters. Then, oneof the polarization filters was rotated over 90 degrees. The shutter time of the camera was adjusted until agood image was retrieved. Protocols for staining can be found in Appendix C.

44

ResultsThe results are shown in Figure 25. The top row shows images for healthy cardiac tissue. As can be seen inthe right images, birefringence is detected. In the top row, it is shown that birefringence is lost in thermaldamage. In the images of the left two columns, the fibers are oriented parallel to the surface. This is optimalfor measurement of birefringence.

Figure 25: A,B,C: Healthy cardiac tissue, showing birefringence under polarized light microscopy. D,E,F: damagedcardiac tissue, birefringence is lost. A,B: H&E staining. C,D,E,F: Masson’s trichrome staining. A,B,D,E:parallel orientation of myofibers, C,F: perpendicular orientation

In conclusion, birefringence can be used as a marker for thermal damage to cardiac tissue. The amount oflight transmitted through the second polarization filter can be measured and integrated, to get an measurefor amount of damage. However, this method is very time consuming and the precise cause of the loss ofbirefringence in cardiac tissue remains unclear. Therefore it was chosen not to regard microscopy further inthis study.

45

B Nondimensionalization of the Heat Equation

Nondimensionalization is a useful tool to examine (partial) differential equations prior to modeling. Byderiving dimensionless quantities of the equation, physical parameters (e.g. length, time and temperature)can be compared to characteristic scales independently of other parameters, and the relative importanceof dimensionless groups towards important factors can be determined. Considering the geometry of themodel and experiments, a transformation is made to the cylindrical coordinate system. The heat equationin cylindrical coordinates is shown in equation 24.

ρc∂T

∂t= k(

1r

∂

∂r(r∂T

∂r) +

∂2T

∂z2) +Q (24)

In the nondimensionalization process three important steps are taken. The first is, to identify all dependentand independent variables and define a scale for the characteristics. Then, the variables are substituted bytheir dimensionless form. The final step is to divide all terms by the factor of the strongest term and rewritethe equation.

Step 1: Choosing scalesTo replace the independent and dependent variables in the equation, the original equation (24) is regarded.The variables to be substituted are r, z, T and t. For the ablation heat problem, the following scales seemuseful: [the wall thickness or the lesion depth], [the initial temperature (20C) or the ablation temperatures(50C or 100C)] and [ablation time (normally about 60 seconds)].

r∗ =r

Lc(25)

z∗ =z

Lc(26)

T ∗ =T − T0

Tc(27)

t∗ =t

tc(28)

Step 2: Substituting variablesIn order to substitute the variables, the following equations are used:

∂

∂r=

1Lc

∂

∂r∗(29)

∂

∂z=

1Lc

∂

∂z∗(30)

∂

∂t=

1tc

∂

∂t∗(31)

∂T = Tc ∂T∗ (32)

By substituting the dimensionless variables equation the Heat Equation becomes

ρcTc

tc

∂T ∗

∂t∗= k

Tc

L2c

1r∗

∂

∂r∗(r∗

∂T ∗

∂r∗) + k

T0

L2c

∂2T ∗

∂z∗2+Q (33)

46

Step 3: Divide by factors of most important termThen by choosing the radial temperature distribution as the most important term, the equation becomes:

1α

L2c

tc

∂T ∗

∂t∗=

1r∗

∂

∂r∗(r∗

∂T ∗

∂r∗) +

∂2T ∗

∂z∗2+

L2c

k TcQ (34)

in which α [m2/s] is the thermal diffusivity:

α =k

ρc(35)

Then, in the left term, the dimensionless α can be detected:

α∗ = αtcL2

c

(36)

And from the right term the dimensionless heat source in [W/m3]:

Q∗ = QL2

c

k Tc(37)

Which leads to the final result:

1α∗

∂T ∗

∂t∗=

1r∗

∂

∂r∗(r∗

∂T ∗

∂r∗) +

∂2T ∗

∂z∗2+Q∗ (38)

with in α∗ and Q∗ the following constants: tc the time constant of cooling and heating of cardiac tissue, αand k the diffusivity and conductivity of the tissue, Lc the thickness of the tissue, Q the power applied bythe heat source and (Tabl − T0) the aimed rise in temperature in the tissue.

Derived relationsTwo relations that can derived, are given by equation (39) and (40). Here, t is ablation duration, d is lesiondepth, T is the temperature and Q is the dissipated ablation energy.

d ∝√t (39)

Equation (39) relates the depth of the characteristic temperature in the tissue with the ablation duration t.As lesion depth is related to this temperature, this implies that the depth of a lesion develops proportionallyto the square root of the duration of ablation for a characteristic period of time (about 60 seconds). Thus,there will be a quick growth of lesion depth in the early ablation.

T ∝ Q t (40)

The relation of the temperatures reached in the ablation procedure and the dissipated power and durationof ablation is given by equation (40). A higher amount of dissipated power will induce a higher temperaturein the tissue. An important conclusion is, that at a higher power the same temperature will be reached in ashorter time.

47

C Protocols for Histological Staining

C.1 General Methods

FixationSamples were stored in formaldehyde solution for at least 48 hours

EmbeddingSamples were embedded in parrafin with an automated program

DeparrafinizationWash in Xylene, 3x10 minutesWash in 100% Ethanol, 5 minutesWash in 100% Ethanol, 30 secondsWash in 70% Ethanol, 30 secondsWash in running tap water, 1 minute

DehydrationWash in 70% Ethanol, 30 secondsWash in 100% Ethanol, 2x30 secondsWash in Xylene, 3x30 seconds

C.2 Staining

C.2.1 Hematoxylin and Eosin

Haematoxylin, 3 minutesMilliQ, 1 minuteWater with ammonia, 30 secondsRunning tapwater, 1 minuteMilliQ, 1 minuteEosin, 2 minutesTapwater, 1 minute

C.2.2 Masson’s TriChrome

preparationPrepare Working Phosphotungstic/Phosphomolybdic Acid Solution by mixing 1 volume of PhosphotungsticAcid Solution, Sigma Catalog No. HT15-2, and 1 volume Phosphomolybdic Acid Solution, Sigma CatalogNo. HT15-3, with 2 volumes of deionized water. Discard after one use. Biebrich Scarlet-Acid Fuchsin,Bouin’s solution, are ready to use. Weigert’s Iron Hematoxylin solution is prepared by mixing equal partsof Solution A and Solution B. Prepare 1% Acetic Acid

procedureBouin’s Solution at 56C , 15 minutesWash in running tap water to remove yellow color from sectionsWeigert’s Iron Hematoxylin Solution, 5 minutesRunning tap water, 5 minutesRinse in deionized waterBiebrich Scarlet-Acid Fucshin, for 5 minutesRinse in deionized water

48

Phosphotungstic/Phosphomolybdic Acid Solution, 5 minutesAniline Blue Solution, 5 minutesAcetic Acid 1%, for 2 minutesRinse slides in deionized water

49

D Lesions of Duration Experiments, Session 2

(a) 5 seconds, before NTB (b) 5 seconds, after NTB (c) 10 seconds, before NTB

(d) 10 seconds, after NTB (e) 15 seconds, before NTB (f) 15 seconds, after NTB

(g) 20 seconds, before NTB (h) 20 seconds, after NTB (i) 90 seconds, before NTB

(j) 90 seconds, after NTB (k) 180 seconds, before NTB (l) 180 seconds, after NTB

Figure 26: Lesions of 20 Watt, for 5, 10, 15, 20, 90 and 180 seconds duration from session 2. All lesions are shownbefore and after NTB.

50