Estimation of lesion size

Abstract

A method, consisting of ablating tissue for a time period, measuring a contact force applied during the time period, and measuring a power used during the time period. The method further includes ceasing ablating the tissue when a desired size of a lesion produced in the tissue, as estimated using an integral over the time period of a product of the contact force raised to a first non-unity exponent and the power raised to a second non-unity exponent, is reached.

Claims

1. A method for ablating tissue over a time period, comprising: providing a probe; selecting a desired depth for a lesion as estimated by an ablation index defined as
Depth.sup.γ(T)=C∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t)dt wherein F is an instantaneous contact force applied by the probe during the time period; P is an instantaneous power applied by the probe during the time period; T is the time period; α, β and γ are numerical exponents having values not equal to unity; and C is a constant of proportionality; selecting values of α, β and γ; ablating the tissue with the probe; measuring the instantaneous contact force F; measuring the instantaneous power; and ceasing ablating the tissue when the desired depth of the lesion is produced in the tissue, as estimated using the ablation index.

2. The method according to claim 1, wherein a has α value in a range of 0.6-0.8.

3. The method according to claim 1, wherein β has a value in a range of 1.4-1.8.

4. The method according to claim 1, wherein γ has a value of 2.78.

5. The method according to claim 1, wherein measuring the instantaneous power comprises measuring a current generating the instantaneous power.

6. An apparatus, comprising: a probe configured to ablate tissue for a time period; and a processor configured to: energize the probe in accordance with an ablation index defined as:
Depth.sup.γ(T)=C∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t)dt wherein F is an instantaneous contact force applied by the probe during the time period; P is an instantaneous power applied by the probe during the time period; T is the time period; α, β and γ are user-selected numerical exponents having values not equal to unity; and C is a constant of proportionality; measure an instantaneous contact force applied by the probe during the time period, measure an instantaneous power used for ablating the tissue during the time period, and cease ablating the tissue when a desired depth of lesion is produced in the tissue, as estimated using the ablation index.

7. The apparatus according to claim 6, wherein α has a value in a range of 0.6-0.8.

8. The apparatus according to claim 6, wherein β has a value in a range of 1.4-1.8.

9. The apparatus according to claim 6, wherein the processor is further configured to measure a current generating the instantaneous power.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a graph of measured lesion depth vs. estimated lesion depth, according to an embodiment of the present invention;

(2) FIGS. 2A, 2B, and 2C are graphs of force, power, depth and an index vs. time, according to an embodiment of the present invention;

(3) FIG. 3 is a schematic illustration of an ablation procedure being performed by an ablation apparatus, according to an embodiment of the present invention;

(4) FIG. 4 is a flowchart of steps performed in using the ablation apparatus, according to an embodiment of the present invention;

(5) FIG. 5 is a histogram comparing true and assumed average contact forces, according to an embodiment of the present invention; and

(6) FIGS. 6-10 are Bland-Altman plots for different sets of data, according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(7) Overview

(8) The inventors have found that estimates given by equation (1), as well as similar relations, are inexact, and have found that the relationship between lesion size and F, P, and T is in fact highly non-linear. Following this observation, a process has been developed for making a more exact estimate of the size of a lesion, from the values of F, P, and T. The inventors have found, and have verified by experiment, that a more exact estimate of lesion size is given by finding an integral over time of an expression comprising non-linear functions of F, P, and T. The estimate may be applied during ablation of tissue separately to estimating the volume of the lesion, the depth of the lesion, and/or the diameter of the lesion produced in the tissue, so as to cease the ablation when a desired size is reached.

(9) In an embodiment of the present invention, tissue is ablated for a time period. During the time period a contact force applied to the tissue by a probe performing the ablation is measured, and the power is also measured. An estimate of the size of the lesion produced is made using an integral over the time period of a product of the contact force raised to a first non-unity exponent and the power raised to a second non-unity exponent. When the estimated size reaches a desired size, the ablation stops.

DETAILED DESCRIPTION

(10) The inventors have found that equation (2) gives a very good estimate of the volume of a lesion that is produced by ablation of tissue with electromagnetic power.
V(T)=C∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t)dt  (2)

(11) where V(T) is the volume of the lesion produced by ablation over a time period T;

(12) C is a constant of proportionality;

(13) CF(t) is a value of the instantaneous contact force, at a time t, applied to the tissue during the ablation;

(14) P(t) is a value of the instantaneous power, at a time t, dissipated during the ablation; and

(15) α, β are numerical exponents having values not equal to 1 (unity).

(16) Since, as stated above, the power P can be expressed in terms of the current I flowing as P=G.Math.I.sup.2, equation (2) can also be written as:
V(T)=C.Math.G∫.sub.0.sup.αCF.sup.α(t)I.sup.2β(t)dt  (2a)

(17) where G is a constant, and

(18) where I(t) is a value of the instantaneous current flowing at time t.

(19) In the following description of results the units used for each of the variables in evaluating equations (2) and (2a) are assumed, by way of example, to be as in Table I.

(20) TABLE-US-00001 TABLE I Variable Units V(T) mm.sup.3 CF(t) g(grams) P(t) W(watts) I(t) A(amps) t, T s(seconds) C $\frac{{\mathrm{mm}}^3}{g.Math.W.Math.s}$ α, β dimensionless

(21) Those having ordinary skill in the art will be able to adapt the results for units different from those of Table I.

(22) Alternative equations to equation (2) and ((2a) are equations (3) and (4);
Depth.sup.γ(T)=C∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t)dt=C.Math.G∫.sub.0.sup.TCF.sup.α(t)I.sup.2β(t)dt  (3)

(23) where each of the terms are as defined above with respect to equations (2) and (2a), and where

(24) Depth is the depth of the lesion in mm; and

(25) γ is a numerical exponent not equal to 1 (unity).
Diam.sup.δ(T)=C∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t t)dt=C.Math.G∫.sub.0.sup.TCF.sup.α(t)I.sup.2β(t)dt  (4)

(26) where each of the terms are as defined above with respect to equations (2) and (2a), and where

(27) Diam is the diameter of the lesion in mm; and

(28) δ is a numerical exponent not equal to unity.

(29) The inventors have found that equations (3) and (4) give very good estimates respectively of the depth and diameter of a lesion, so that taken together or separately, equations (2), (2a), (3), (4) give very good estimates of a size of the lesion.

(30) Approximations to the Equations

(31) Equations (2), (2a), (3), and (4) may be approximated by assuming that CF or P or I do not vary over the time period T. The following description describes approximations for equation (3), but those having ordinary skill in the art will be able to apply similar approximations for equations (2) and (4).

(32) For simplicity, in the following description equation (3) assumes that the equation only incorporates the first equality, i.e., that the equation is:
Depth.sup.γ(T)=C∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t)dt  (3′)

(33) Those having ordinary skill in the art will be able to change equation (3′) if current I is considered.

(34) If P is assumed to have a fixed value over the time period T of the ablation, then equation (3′) can be rewritten:
Depth.sup.γ(T)=CP.sup.β∫.sub.0.sup.TCF.sup.α(t)dt  (5)

(35) If CF is almost fixed or if α≈1 then
∫.sub.0.sup.TCF.sup.α(t)dt≈ACF.sup.α.Math.T  (6)

(36) where ACF is an average value of CF over time T.

(37) Substituting equation (6) into equation (5) gives:
Depth.sup.γ=C.Math.ACF.sup.α.Math.P.sup.β.Math.T  (7)

(38) Values of C, α, β, and γ

(39) Taking logs of both sides of equation (7) gives:

(40) $\begin{array}{cc}\mathrm{Log}\left(\mathrm{Depth}\right)=\frac{1}{\gamma }\mathrm{Log}\left(C\right)+\frac{\alpha }{\gamma }\mathrm{Log}\left(\mathrm{ACF}\right)+\frac{\beta }{\gamma }\mathrm{Log}\left(P\right)+\frac{1}{\gamma }\mathrm{Log}\left(T\right)& \left(8\right)\end{array}$

(41) The inventors performed 180 ablation sessions to derive values of C, α, β, and γ in equation (8). Using results from 158 valid ablations generated in the sessions, the inventors applied linear regression analysis to evaluate C, α, β, and γ. The regression analysis gave the following results:

(42) $\gamma =2.78;\alpha =0.67;\beta =1.58;C=\frac{1}{503.82}$

(43) Inserting these values into equation (3′) gives:

(44) $\begin{array}{cc}\mathrm{Depth}\left(T\right)={\left[\frac{1}{503.82}{\int }_0^T{\mathrm{CF}}^{0.67}\left(t\right)P^{1.58}\left(t\right)\mathrm{dt}\right]}^{0.36}& \left(9\right)\end{array}$

(45) FIG. 1 is a graph of measured lesion depth vs. lesion depth estimated from equation (9), according to an embodiment of the present invention. The graph illustrates the good correlation between the values of the estimated lesion depth and the measured values:

(46) In the graph “Transmural” points are where the cardiac tissue was penetrated, “Imp rise” points are where a rise in impedance was observed, “Pop” points are where steam pops occurred during the RF application, and “Legit” are valid points apart from those listed above.

(47) The correlation between the estimated and measured values of depth for the 158 results is very good. A calculated correlation coefficient R for the values gives R.sup.2=82.9%, so that R=0.910.

(48) Appendix II below provides an alternative analysis of the 158 results, and gives the following values for C, α, β, and γ:

(49) $\gamma =2.83;\alpha =0.68;\beta =1.63;C=\frac{1}{531.88}.$

(50) Using these values, equation (3) becomes

(51) $\begin{array}{cc}\mathrm{Depth}\left(T\right)={\left[\frac{1}{531.88}{\int }_0^T{\mathrm{CF}}^{0.68}\left(t\right)P^{1.63}\left(t\right)\mathrm{dt}\right]}^{0.35}& \left(10\right)\end{array}$

(52) Comparing the results of equation (10) with the measured depth results gives R.sup.2=83.1%, so that R=0.911.

(53) For both sets of values (of C, α, β, and γ), α≈ 3/2,

(54) The inventors believe that α may have a value in the range of 0.6-0.8, and that β may have a value in the range of 1.4-1.8.

(55) The integral ∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t)dt is herein termed an ablation index, and is referred to as I.sub.FTP or as FPTI. Thus,
I.sub.FTP=∫.sub.0.sup.TCF.sup.α(t)P.sup.β(t)dt≈∫.sub.0.sup.TCF.sup.2/3(t)P.sup.3/2(t)dt  (11)

(56) FIGS. 2A, 2B, and 2C are graphs of force, power, depth and FTPI vs. time, according to an embodiment of the present invention. The graphs provide an example of the estimated depth and of the ablation index when both the power and the force change. The graph of depth vs. time shows that the estimated depth is always positive and is always monotonically increasing.

(57) The inventors have determined that for a given type of cardiac structure and a given tissue characteristic the value of the ablation index is a very good, and repeatable, predictor of lesion size. Furthermore, lesion size for a given value of ablation index may be different for different structures and tissue characteristics.

(58) In a retrospective study, of 159 patients, each ablation site was reviewed offline to identify the ablation index for each CPVI (circumferential pulmonary vein isolation) segment according to a 9-segment model around the CPVI circumferences. For example, the median ablation index for segments with adenosine-mediated acute reconnection (ARc) was 293, as compared to the median index for segments without ARc of 342, and for posterior/inferior segments with ARc the median index was significantly lower (286) than for those without ARc (321).

(59) FIG. 3 is a schematic illustration of an ablation procedure performed using apparatus 12, according to an embodiment of the present invention. As explained below with reference to the flowchart of FIG. 4, the procedure uses estimates of lesion size that may be derived from one or more of equations (2)-(11).

(60) The procedure is performed by a physician 14, and, by way of example, the procedure in the description herein below is assumed to comprise ablation of a portion of a myocardium 16 of the heart of a human patient 18.

(61) In order to perform the ablation, physician 14 inserts a probe 20 into a lumen of the patient, so that a distal end 22 of the probe enters the heart of the patient. Distal end 22 comprises an electrode 24 mounted on the outside of the distal end, the electrode contacting a location of the myocardium. Distal end 22 also comprises a force sensor 25. Probe 20 has a proximal end 28.

(62) Apparatus 12 is controlled by a system processor 46, which is located in an operating console 48 of the apparatus. Console 48 comprises controls 49 which are used by physician 14 to communicate with the processor. During the procedure, processor 46 typically tracks a location and an orientation of distal end 22 of the probe, using any method known in the art. For example, processor 46 may use a magnetic tracking method, wherein magnetic transmitters external to patient 18 generate signals in coils positioned in the distal end. The Carto® system produced by Biosense Webster, of Diamond Bar, Calif., uses such a tracking method.

(63) The software for processor 46 may be downloaded to the processor in electronic form, over a network, for example. Alternatively or additionally, the software may be provided on non-transitory tangible media, such as optical, magnetic, or electronic storage media. The track of distal end 22 is typically displayed on a three-dimensional representation 60 of the heart of patient 18 on a screen 62. The progress of the ablation performed with apparatus 12 is typically also displayed on screen 62, as a graphic 64 and/or alphanumeric data 66.

(64) In order to operate apparatus 12, processor 46 communicates with a memory 50, which has a number of modules used by the processor to operate the apparatus. Thus, memory 50 comprises a power control module 54, and a force module 56. Power control module 54 delivers radiofrequency (RF) power to one of electrodes 24, and also measures the instantaneous power P(t) delivered at a time t, typically by measuring the instantaneous current I(t) delivered by the electrode. Force module 56 measures the instantaneous contact force CF(t) at time t, by acquiring and evaluating signals from force sensor 25 in distal end 22. Memory 50 may also comprise other modules, such as a temperature measuring module and an irrigation module. For simplicity such other modules are not described further in this application. The modules of memory 50 may comprise hardware as well as software elements.

(65) FIG. 4 is a flowchart of steps performed by physician 14 in using apparatus 12, according to an embodiment of the present invention. In an initial step 100, the physician selects a desired size for the lesion. By way of example, the physician may select a desired depth that is in the range of 1 mm-5 mm. In addition, the physician selects values of C, α, β, and γ to be used in an equation for depth estimation to be used, herein assumed to be equation (3). For example, values of C, α, β, and γ may be selected to be as given above for equation (9), i.e., γ=2.78; α=0.67; β=1.58;

(66) $C=\frac{1}{503.82}.$
However, the physician may determine, without undue experimentation, other values for C, α, β, and γ, and may use these values.

(67) For clarity, in the remaining steps of the flowchart, equations (9) and (11) are assumed to be used for determining an estimated depth of the lesion.

(68) In a start ablation step 102, the physician uses controls 49 to select a nominal power to be delivered by power control module 54. Typically the power selected is in the range of 10 W to 20 W, although a power outside this range may be selected. After the nominal power has been selected, the physician uses controls 49 to begin the ablation.

(69) In a measuring step 104, as the ablation is being performed, power control module 54 measures the instantaneous power P(t) dissipated by electrode 24, which is typically different from the nominal power. In addition force module 56 measures the instantaneous contact force CF(t) on distal end 22.

(70) In a calculation step 106, as the ablation proceeds processor 46 calculates, on a recurring basis, the value of the integral used in equation (9), i.e., the value of ablation index I.sub.FTP in equation (11). In a size estimation step 108, the processor calculates a value of the estimated size, i.e., the estimated depth, using the integral value and equation (9).

(71) In a decision step 110 the processor checks if the estimated size is equal to the desired size. If the decision returns positive, in a final step 112 the processor ceases the ablation. If the decision returns negative the processor, in a continuing ablation step 114 continues to ablate and the flowchart returns to measuring step 104.

(72) The following Appendices provide more detail on aspects of the invention.

Appendix I

(73) In the regression analysis regarding equation (8) the inventors assumed ∫.sub.0.sup.TCF.sup.α(t)dt≈ACF.sup.α.Math.T. The assumption was checked using the value of α(=0.67).

(74) A true CF average is given by equation (12):

(75) $\begin{array}{cc}\mathrm{True}\mathrm{CF}\mathrm{average}=\frac{1}{T}{\int }_0^T{\mathrm{CF}}^{0.67}\left(t\right)\mathrm{dt}& \left(12\right)\end{array}$

(76) An assumed CF average is given by equation (13):

(77) $\begin{array}{cc}\mathrm{Assumed}\mathrm{CF}\mathrm{average}={\left(\frac{1}{T}{\int }_0^T\mathrm{CF}\left(t\right)\mathrm{dt}\right)}^{0.67}& \left(13\right)\end{array}$

(78) FIG. 5 is a histogram comparing the true and assumed average contact forces, according to an embodiment of the present invention. The histogram gives the frequencies of the ratio of the two quantities,

(79) 0$\frac{\mathrm{Assumed}\mathrm{CF}\mathrm{average}}{\mathrm{True}\mathrm{CF}\mathrm{average}},$
for the 158 ablations studied.

(80) The histogram illustrates that in 95% of the ablations, the deviation between the two quantities is less than 5%, and has an average deviation of 2%. The assumption is thus justified.

Appendix II

(81) An alternative method for analyzing the 158 results estimates an RMS value (given by equation (14) below), and finds values of C, α, β, and γ which minimize the RMS value.

(82) $\begin{array}{cc}\mathrm{Estimated}{\mathrm{Depth}}_i={\left[\frac{1}{C}\underset{t=1}{\overset{N_i}{.Math.}}{\mathrm{CF}}_i^{\alpha }\left(t\right)P_i^{\beta }\left(t\right)\mathrm{dt}\right]}^{\frac{1}{\gamma }}& \left(14\right)\end{array}$

(83) where

(84) $\mathrm{RMS}=\sqrt{\underset{i=1}{\overset{158}{.Math.}}({\left(\mathrm{Log}\left(\mathrm{Measured}{\mathrm{Depth}}_i\right)-\mathrm{Log}\left(\mathrm{Estimated}{\mathrm{Depth}}_i\right)\right)}^2}$

(85) The inventors used the Matlab fminsearch function, using as starting points the values of C, α, β, and γ determined by the regression analysis, i.e., γ.sub.0=2.78; α.sub.0=0.67; β.sub.0=1.58; C.sub.0=1/503.82. The function returned the values γ.sub.min=2.83; α.sub.min=0.68; β.sub.min=1.63; C.sub.0=1/531.88, as used in equation (10) above.

Appendix III

(86) The inventors analyzed the data from the 158 results using Bland-Altman plots, looking for any fixed bias in the measurements. As is known in the art, if the mean value of the differences differs significantly from 0 then a fixed bias is indicated.

(87) A first plot was constructed for all the data, and then four separate plots were constructed for sub-groups of data. The data and the plots are given below.

(88) Inspection of all five sets of data and plots shows that in no case does the mean value differ significantly from 0.

(89) FIG. 6 is a Bland-Altman plot for the following first set of data, according to an embodiment of the present invention.

(90) 1. All data N=158

(91) TABLE-US-00002 Min 20.00% 50.00% 80.00% Max Mean STD −2.23 −0.69 0.01 0.58 1.58 −0.05 0.74

(92) FIG. 7 is a Bland-Altman plot for the following second set of data, according to an embodiment of the present invention.

(93) 2. (depth+model)/2=2-4 mm N=34

(94) TABLE-US-00003 Min 20.00% 50.00% 80.00% Max Mean STD −0.76 −0.38 0.10 0.58 1.37 0.10 0.53

(95) FIG. 8 is a Bland-Altman plot for the following third set of data, according to an embodiment of the present invention.

(96) 3. (depth+model)/2=4-6 mm N=77

(97) TABLE-US-00004 Min 20.00% 50.00% 80.00% Max Mean STD −1.45 −0.63 0.03 0.60 1.52 0.00 0.68

(98) FIG. 9 is a Bland-Altman plot for the following fourth set of data, according to an embodiment of the present invention.

(99) 4. (depth+model)/2=6-8 mm N=32

(100) TABLE-US-00005 Min 20.00% 50.00% 80.00% Max Mean STD −2.00 −0.99 −0.07 0.73 1.58 −0.10 0.90

(101) FIG. 10 is a Bland-Altman plot for the following fifth set of data, according to an embodiment of the present invention.

(102) 5. (depth+model)/2=8-10 mm N=14

(103) TABLE-US-00006 Min 20.00% 50.00% 80.00% Max Mean STD −1.63 −1.08 −0.49 0.49 1.38 −0.36 0.88

(104) It will be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.