Method for Estimating Thermal Ablation Volume and Geometry

Abstract

This invention pertains a system and methods for ablation treatment of tissues. The invention aims to improve current models that allow predicting the volume and geometry of thermal ablations. Particularly the invention consists in a method that allows accounting for effects that occur when vapor that forms at the ablation site is able to seep in cavities that might encroach the ablation site and to deliver heat to the tissues of those cavities, creating an ablation geometry that is not described by current ablation models.

Claims

1. A method for estimating the volume and geometry of tissues necrotized by thermal ablations making use of models which account for the thermal effects of vapor traveling in ducts, interstitial spaces, holes, cavities present in the tissues and encroaching the ablations site, comprising the steps of: computing the temperature in the tissues under the effect of the ablation power applied to the tissues, where this power might be, for example, of electrical or electromagnetic nature; accounting for the thermal power absorbed from the tissues by the evaporation of water present in the tissues; redistributing part of the thermal power absorbed from evaporation to the volumes and/or surfaces of said ducts, interstitial spaces, holes, cavities encroaching the ablations site, thus modeling the heating that vapor causes by traveling through those structures and/or by condensing in those structures; updating the computed temperature based on the redistribution of heat to the volumes and/or surfaces of said ducts, interstitial spaces, holes, cavities encroaching the ablations site; computing which tissues are necrotized by the ablation using a relationship that links, at least, but not limited to, the temperature in the tissues to the damage of tissues.

2. The method of claim 1 where part of the thermal power absorbed from evaporation is redistributed in a region along the shaft of a needle-shaped ablation device to model the heating effect of vapor that infiltrates the track in the tissues created by the insertion of the needle-shaped device, similarly to the particular embodiment shown in FIG. 6 where this region is cylindrical (603).

3. The method of claim 1 where part of the power absorbed from evaporation is redistributed to surfaces of liver fissures, to model the heating effect of vapor that infiltrates such fissures, similarly to the particular embodiment shown in FIG. 10 where these surfaces are indicated as (1006).

4. The method of claim 1 applied to the study or design of ablation devices.

5. The method of claim 1 applied in systems for treatment planning.

6. The method of claim 1 applied in systems for intraoperative guidance.

7. The method of claim 2 applied to the study or design of ablation devices.

8. The method of claim 2 applied in systems for treatment planning.

9. The method of claim 2 applied in systems for intraoperative guidance.

10. The method of claim 3 applied to the study or design of ablation devices.

11. The method of claim 3 applied in systems for treatment planning.

12. The method of claim 3 applied in systems for intraoperative guidance.

13. The method of using a deformable liver model carrying information about the anatomy of the liver fissures, and adapted to medical images of the patient, in order to estimate the true intracorporal position of the fissures in the patient from the adapted deformable liver model.

14. The method of injecting high-contrast media such as gases, powders, or liquids at the ablation site, where these gases, powders, or liquids might travel to ducts, interstitial spaces, holes, cavities present in the tissues and render these structures visible in medical images by virtue of enhancing contrast, and possibly by virtue of enlarging these gaps.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] FIG. 1 depicts an example of a common commercial RFA electrode design which deploys tines.

[0036] FIG. 2 depicts a CT image where a tumor is visible as an enhancing area of lighter color.

[0037] FIG. 3 depicts the CT image of FIG. 2 with superimposed the volume/geometry of an ablation as computed with a computer model simulating RFA physics.

[0038] FIG. 4 depicts an RFA electrode and the 100 C., 80 C., and 60 C. iso-temperature lines for the temperature field established in the tissues.

[0039] FIG. 5 depicts a CT image of the liver of a pig immediately after RFA. In the image is visible the RFA electrode inserted in the tissues and it is possible to appreciate the fact that vapor has formed in a region in the proximity of the needle of the electrode.

[0040] FIG. 6 depicts a computer model of an RFA electrode and a cylindrical volume around the needle of the electrode where a quantity of thermal power is delivered to account for the thermal power which is transported in this region of tissues by vapor traveling along the needle interstitial space.

[0041] FIGS. 7A, 7B, 7C depicts the geometry of necrotized tissues as captured in a liver RFA pig study (FIG. 7A), the equivalent volume generated by the current state-of-the-art evaporation model (FIG. 7B), and a model which is a particular embodiment of the present invention (FIG. 7C). This last model produces a predicted ablation volume which is dose to the true ablation volume captured by in-vivo imaging.

[0042] FIG. 8 depicts an ablation site where the presence of a liver fissure allows vapor to use this physical path to escape the ablation site and to necrotize tissues that are not expected to be involved in the ablation. This results in an ablation volume which departs from the information provided by the RE ablation needle manufacturer and from the ablation geometry produced by current models.

[0043] FIG. 9 depicts harvested pig liver tissues after RFA, showing that vapor has traveled in a fissure and has necrotized tissues on the two sides of the fissure.

[0044] FIG. 10 depicts two lobes of the liver separated by a fissure which is encroached by an RFA electrode. In the figure are indicated facing surfaces of the fissure where heat from condensing vapor is redistributed to account for the effects of vapor traveling in the fissure and heating tissues.

[0045] FIGS. 11A, 11B, 11C depict respectively: a deformable liver model (FIG. 11A); a CT image of a liver (FIG. 11B); the deformable liver model fitted to the liver in the CT image (FIG. 11C).

[0046] TABLE 1 reports data showing the model used to compute the ablation geometry, which is a particular embodiment of this invention, is able to improve the accuracy of the predicted volume/geometry, reducing the maximum error from 9.4 mm to 5.2 mm, on average across six analyzed ablations.

DETAILED DESCRIPTION OF THE INVENTION

Detailed Background Description

[0047] Modeling in thermal ablation is commonly based on the Bioheat equation [1]. As during ablation tissue temperatures in RFA and MWA often exceed 100 C., the Bioheat equation is generally expanded to account for the effect of evaporation of water in the tissues, as for example as in [1], leading to (1)

[00001]$\begin{array}{cc}.Math..Math.c.Math.\frac{T}{t}=.Math.k.Math.T+Q_{\mathrm{PWR}}+Q_{\mathrm{PERF}}+Q_E& \left(1\right)\end{array}$

where is the tissue density, c is the tissue thermal capacitance, T is the temperature in the tissues, t is time, k is the tissue thermal conductivity, Q.sub.PWR is the dissipated power density resulting by the applied RF or MW power, Q.sub.PERF is the heat density lost to perfusion, Q.sub.E is the heat density lost to evaporation, or gained from condensation of vapor in the tissues. The quantities , k, c, T, Q.sub.PWR, Q.sub.PERF, Q.sub.E are functions of space (scalar fields), while, of course, t, the variable indicating time, is a scalar quantity. The quantities , k, c are properties of tissues, which can be considered as given fixed values, or as functions of temperature themselves. The term Q.sub.PWR models the RF or MW power density applied by the RF/MW needle and dissipated in the tissues. This is a distributed heat source. The perfusion term Q.sub.PERF is a power density that models the fact that a quantity of heat is lost to the capillary bed in the region around the ablation site. This loss occurs as the temperature of blood (37 C.) is lower than the temperature reached by tissues during ablation, therefore an amount of heat will flow from the heated tissues to the capillaries, and later this heat will be taken away by the blood flow (perfusion). This term is therefore a distributed heat sink term.

[0048] The Q.sub.E term is a power density that describes instead the effects of evaporation/condensation of water in the tissues. During an ablation, temperatures in excess of 100 C. are reached in the tissues at locations in the proximity of the needle. At these locations a certain fraction of the water present in the tissues evaporates. During the state change from liquid to gas the water absorbs a quantity of heat called latent heat. Vapor will diffuse in the tissues, under the pressure it generates, and as it meets tissues at a lower temperatures it will condense, and release in those lower temperature tissues the latent heat. The term Q.sub.E is therefore negative (heat sink) at locations where evaporation occurs (heat is absorbed from tissues) and positive (heat source) at locations where the vapor condenses (heat is released to tissues). The magnitude of the term Q.sub.E will depend, at any point in the tissues, by the rate of at which water is evaporating or condensing at that location.

[0049] Overall, this mechanism is therefore a heat transport mechanism mediated by vapor, where heat is subtracted from tissues where evaporation occurs and re-delivered to tissues where vapor condenses.

[0050] Modeling this heat transport mechanism requires therefore determining in which regions of the simulated domain evaporation occurs and in which regions condensation occurs.

[0051] Regions in which evaporation occurs are those where the local tissues temperature reaches the evaporation temperature of water (100 C., or a similar temperature which might be determined by the local pressure).

[0052] In these regions the term Q.sub.E can be expressed as:

[00002]$\begin{array}{cc}{Q}_E=-.Math.\frac{\mathrm{dW}}{\mathrm{dt}}& \left(2\right)\end{array}$

where is the latent heat constant for water and W is the tissue water density, and t is time. Equation (2) applies to any point in the tissues where evaporation occurs, and Q.sub.E is the thermal power density absorbed from tissues. The total thermal power absorbed from tissues from evaporation at any instant in time, which we label Q.sub.E.sub._.sub.TOT, is found by integrating (2) over a volume that encapsulates all the tissues where evaporation occurs, and can be expressed as:

[00003]$\begin{array}{cc}{Q}_{E_{}.Math.\mathrm{TOT}}=-.Math.\frac{\mathrm{dW}}{\mathrm{dt}}.Math.d.Math..Math.& \left(3\right)\end{array}$

where represents the region of tissues over which the integration is carried out.

[0053] To summarize: 1) evaporation occurs at points where the tissue temperature is greater than the evaporation temperature of water; 2) the thermal power density absorbed at any point in tissues from evaporation is (2); 3) the total thermal power absorbed from evaporation from all the tissues at any point in time is (3).

[0054] The evaporation/condensation models which are object of this invention are pertinent to percutaneous ablation, where vapor forming from evaporation of tissue water has no path to escape the body of the patient. It is assumed therefore that all the vapor that has formed will condense in tissues.

[0055] Determining the regions where vapor condenses requires determining how vapor diffuses in the tissues.

[0056] In the evaporation/condensation model [1], which constitutes the state-of-the-art, it is empirically assumed that at any time all the thermal power absorbed by evaporation (Q.sub.E.sub._.sub.TOT) will be re-distributed uniformly to tissues where the temperature is comprised between 60 C. and 80 C. These tissues are typically a region of tissues in the proximity of the ablation site, where condensation is likely to occur. FIG. 4 shows as an example an RFA electrode formed by a needle shaped cannula (401), and by a number of tines (402). The isolines for temperatures of 100 C., 80 C., and 60 C. are respectively (403), (404), and (405). Under model assumptions in [1] evaporation would occur in the volume enclosed by the 100 C. isoline, and condensation would occur in the volume enclosed between the 80 C. and 60 C. isolines.

[0057] The state-of-the-art evaporation model [1] can be summarized therefore as follows: [0058] Evaporation region defined by T>100 C.;

[00004]$Q_E=-.Math.\frac{\mathrm{dW}}{\mathrm{dt}}$

[0059] Condensation region defined by 60 C.<T<80 C.; Q.sub.E.sub._.sub.TOT/Vol.sub.6080 [0060] In any other region Q.sub.E=0
where Vol.sub.6080 is the volume of tissues with 60 C.<T<80 C., where condensation occurs.

[0061] The model proposed in [1], representing the state-of-the-art, allows therefore to define regions in tissues where evaporation or condensation occurs and to determine the value of Q.sub.E in these regions, allowing to use this value of Q.sub.E in (1) and to compute the temperatures in tissues subject to the effects of evaporation/condensation.

[0062] This evaporation/condensation model is empirical and works well where tissues are uniform.

Invention Description

[0063] Vapor diffusion in tissues during thermal ablations is driven by the pressure that forms at the ablation site caused by the evaporation itself. In certain circumstances preferential paths (preferential to diffusion in tissues) might be available to vapor for traveling from points at a higher pressure to points at a lower pressure. These paths consist in interstitial spaces in the organs, in ducts, in tracks present in the tissues which encroach the ablation site, and which represent a possible escape path for the vapor. As vapor travels through these paths it will encounter tissues at temperatures inferior to the evaporation temperature and it will release heat to these tissues and condense. This results in a distribution of heat which is determined, in part, by the geometry of these paths where vapor travels. As a consequence the overall heat distribution around the ablation site can be quite different from the case where vapor simply diffuses in uniform tissuesas assumed by current evaporation/condensation models.

[0064] In general, when these paths are present, a certain proportion of all the generated vapor will travel in them and a certain proportion will continue to diffuse in the tissue because of their porosity. To model this, we split the term Q.sub.E.sub._.sub.TOT in two quantities. A quantity (1-b) Q.sub.E.sub._.sub.TOT of thermal power is redistributed to the tissues uniformly (the scalar b is in the range 0 to 1 and sets the amount of vapor that is redistributed uniformly) to those tissues having a temperature comprised between a lower and a higher specified threshold (e.g. 60 C. and 80 C.), modeling diffusion and condensation in tissues similarly to what proposed in [1]. A quantity b Q.sub.E.sub._.sub.TOT of power is instead redistributed along those surfaces, or in those volumes, representing the preferential paths where vapor travels and condenses (tracks, ducts, interstitial spaces, holes); this models the effects of heat which is transported and released by condensing vapor to those locations.

Embodiment Example, Modeling Vapor Diffusion and Condensation Along the Needle Shaft

[0065] In the specific case of RFA and MWA, where percutaneous ablation devices are shaped like needles, we have observed in animal experiments that vapor seeps in the track created in the tissues by the insertion of the needle-shaped ablation device. Specifically vapor generated at the distal end of the device, where the ablation occurs, travels for a certain length along the interstitial space between the needle and tissues, following the needle track towards the proximal-end.

[0066] FIG. 5 shows, as an example, a CT image of percutaneous liver RFA in a pig, conducted under institutional IACUC approval. The image was collected immediately after RFA was performed. The dotted line (501) indicates the direction and position of the shaft of the needle electrode. The white dots (502) indicate the tines, which are intersecting the imaging plane, and appear as bright dots as they are metallic objects. The dark dots (503) indicate the presence of vapor in the proximity of the location where the shaft of the electrode meets the tines, which happens to be the hottest point in the ablation volume. The tissues necrotized be the ablation are visible in a slightly darker shade of gray compared to normal tissues. The bulk of the volume of necrotized tissues (504) is encompassed by the tines and it extends towards the shaft of the electrode, becoming narrower, and forming overall a triangular shape.

[0067] Necrotized tissues extend for some length along the shaft of the electrode (505). The presence of necrotized tissues extending along the shaft of the electrode is not expected, as the shaft is electrically insulated and thus does not actively heat the tissues. The presence of necrotized tissues is instead explained by the fact that vapor, under pressure, is able to penetrate the interstitial space between the shaft of the electrode and the tissues, and to follow this track for some length along the shaft of the electrode. The vapor that infiltrates this space delivers a certain amount of heat to tissues in this region and necrotizes them.

[0068] In order to account for this phenomenon, in a particular embodiment of the method proposed, where this specific case being discussed is modeled, we redistribute the power b Q.sub.E.sup.Tot uniformaly in a cylindrical region around the shaft of the electrode, accounting in this way for the heating that occurs in such region due to vapor traveling in the interstitial space between the electrode shaft and tissues. FIG. 6 shows a model of an RFA electrode formed by a shaft (601) and a number of tines (602). The darker cyclindrical volume (603) indicates the region where the power b Q.sub.E.sup.Tot is redistributed.

[0069] Use of this model improves the accuracy with which the abaltion volume can be predicted.

[0070] FIG. 7A shows the geometry of an abaltion performed in a pig liver. In the figure is visible a computer model of the RFA electrode, compraised of a shaft (701) and tines (702). The gray surface (703) represents the volume/geoemtry of the abaltion, which was captured by imaging with contrast-CT the liver immediately after the abaltion was performed, and by segmenting the tissues that appear to be necrotized. The volume of the abaltion extens for a certain length along the electrode shafy (704). For comparision purposes, FIG. 7B shows the abaltion volume estimated using the state-of-the-art model [1]. The predicted ablation volume/geoemtry is flatter at the top, and the volume of necrtized tissues does almost not extend upwords along the shaft of the electrode, point (708), the top of the abaltion volume, is lower than point (704).

[0071] FIG. 7C shows the same abaltion volume estimated with a model which is a particular embodiment of this invention. In FIG. 7C is visible a computer model of the RFA electrode compraised of a shaft (709) and tines (710). In this particular embodiment of the invention, the thermal power b Q.sub.E.sup.Tot, with b=0.2, was redistributed to a cylinder aligned to the electrode shaft, as in FIG. 6, with a diameter of 5 mm. The cylinder starts at the point where the shaft connects to the tines, and has a height of 2 cm. The remaining power (1-b) Q.sub.E.sup.Tot was distributed, as in [1], to tissues with temperatures between 60 C. and 80 C. Use of this model resulted in a more accurate prediction of the true abaltion volume and geometry compared to the state of the art. The top of the ablation volume, point (712), is now more elevated compared to the predictions from state-of-the-art models (point (708)), mimichking better the true abaltion geoemtry as captured by imaging in-vivo experiments, where the abaltion volume raises along the electrode shaft (704).

[0072] The improvements brought this invention, in the particular embodiment described above, were evaluated on six percutaneous liver ablations in pigs. Table 1 reports quantitative results. The first six rows of the table report results for each ablation site, and the last row of the table reports results averaged over the six ablation sites. The first column of the table, titled Error Uniform Vap. Redist., reports the model error defined as the maximum distance between the surface of the ablation captured in-vivo by CT imaging and the surface of the ablation as computed with the model proposed in [1]. The column titled Error Vap. Redist. Along Shaft reports the error defined as the maximum distance between the surface of the ablation captured in-vivo by CT imaging, and the surface of the ablation as computed with the particular embodiment of this invention described above, where 20% (b=0.2) of thermal power from condensing vapor is distributed in a cylindrical region around the shaft, and all the remaining thermal power (80%) is distributed is the regions of tissues issues with a temperature between 60 C. and 80 C. The last column of the table reports the error reduction obtained by using the model which is a particular embodiment of this invention, compared to the model proposed in [1]. On average, across the 6 analyzed abaltion sites, the maximum error was reduced from 9.42 mm to 5.18 mm, a reduction of 44% using the particular embodiment of this invention.

Embodiment Example, Modeling the Effect of Liver Fissures

[0073] Fissures are present in the liver and they can offer a path to vapor generated during thermal ablations to escape the ablation site. As vapor travels in the fissure it delivers heat to the tissues facing the fissure and this results in a different ablation pattern than normally expected. FIG. 8 shows, as an example, a CT image of percutaneous liver RFA in a pig, conducted under institutional IACUC approval. The dashed line (801) indicates the position and orientation of the RFA electrode shaft (not visible as the imaging plane does not intersect it). The bright dots (802) indicate the position of the tines of the RFA electrode, as they intersect the imaging plane. The dash-dotted line (803) highlights the contour of the ablation, where necrotized tissues are visible in a darker shade of gray. The dark feature (804) indicates the gallbladder. In this specific ablation, a fissure that connects the ablation site to the gallbladder allowed vapor to escape the ablation site by traveling in the fissure towards the gallbladder. As a result the ablation is asymmetrical with respect to the electrode shaft, and the ablation has a plume shape that bends towards the gallbladder. The geometry of this ablation is not accounted for by models in the literature representing the state-of-the-art.

[0074] Post-mortem harvesting of the liver confirmed that vapor was able to necrotize tissues on the facing sides of the fissure. FIG. 9 shows the harvested liver which has been resected in a plane intersecting the ablation site. The dotted line (901) indicated the position and orientation of the RFA electrode shaft. The dotted line (902) highlights the fissure separating two lobes of the liver. Tissues that appear in lighter color in the proximity of the electrode shaft (903) are necrotized tissues. These tissues are normally expected to be necrotized by the ablation. Other necrotized tissues (904) are visible along the fissure and at a distance from the ablation site; these tissues have been necrotized by vapor that has formed in the fissure and that has delivered heat to the tissues facing the fissure, and normally not expected to be necrotized.

[0075] This particular situation can be modelled by redistributing a portion of the thermal power that vapor releases to tissues b Q.sub.E.sup.Tot to surface of the fissure. FIG. 10 shows an illustration where two lobes of a liver (1001) and (1002) are separated by a fissure (1003). An RFA electrode is used formed by a shaft (1004) and by a number of tines (1005). In this illustration the RFA electrode, and therefore the abaltion site, encroaches the fissure, and vapor forming at the abaltion site will seep in the fissure and heat the tissues facing the fissure. In order to model this phenomenon, a portion of the total thermal power absorbed by vapor b Q.sub.E.sup.Tot should be delivered to the surfaces of the fissure of the abaltion site (1006). This is similar to the approach discussed in the previous embodiment, where part of the heat of the condensing vapor was distributed in a cylindrical region of tissues (FIG. 6) to account for the effects of vapor.

[0076] In order to model the effects of vapor traveling in fissure according to the proposed embodiment, it is necessary to know the geoemtry of the fissure. Fissures are extremely thin interstitial spaces and they do not offer particular contrast, therefore they are not visible in medical images.

[0077] In a particular embodiment of this invention we propose to utilize a deformable liver model, as illustrated in FIGS. 11A, 11B, and 11C, to estimate the geoemtry of the fissures of the patient. In FIG. 11A is shown the contour of a deformable liver model (1101). The model includes a representation of the geoemtry of the fissure (1102). In FIG. 11B is shown a CT image of a human liver, where an RFA electrode has been deployed (1103). Fitting of the boundary (1101) of the deformable liver model to the true liver boundary (1104) available from CT images allows to update the shape of the liver model in such a way that the deformed model is a good representation of the patient's liver. This in turn allows to estimate whether the fissures of the model (1102) would encroach the abaltion site (1105). At this point at least two options are available. In the first option, the geometry of the fissures in the model is assumed to be a good representation of the true geoemtry of the fissures of the patient, and the volume/geoemtry of the abaltion is computed distributing an amount of thermal power b Q.sub.E.sup.Tot to these surfaces, while an amount of thermal power (1-b) Q.sub.E.sup.Tot is distributed to tissues simulating a diffusion of vapor in tissues. In a second option, the physician is simply warned that the current ablation site encroaces a fissure and that the abaltion geoemtry might be altered by the presence of the fissure.

[0078] Additionally to the approach of using a deformable model to estimate the geometry of the fissures, we propose to render them visible in images by injecting in them high-contrast media (e.g. high-contrast liquids, gases, powders) which could be delivered by the ablation device itself, and make the fissures visible, as this media penetrates the fissures and enhances their contrast.

REFERENCES

[0079] [1] Yang, Deshan, Mark C. Converse, David M. Mahvi, and John G. Webster. Expanding the bioheat equation to include tissue internal water evaporation during heating. IEEE Transactions on Biomedical Engineering 54, no. 8 (2007): 1382-1388.