AJR 2005; 184:1347-1352
© American Roentgen Ray Society
Radiofrequency Tumor Ablation: Insight into Improved Efficacy Using Computer Modeling
Zhengjun Liu1,
S. Melvyn Lobo1,
Stanley Humphries2,
Clare Horkan1,
Stephanie A. Solazzo1,
Andrew U. Hines-Peralta1,
Robert E. Lenkinski1 and
S. Nahum Goldberg1
1 Department of Radiology, Beth Israel Deaconess Medical Center, 1 Deaconess
Rd., WCC 308B, Boston, MA 02215.
2 Department of Electrical Engineering, University of New Mexico in Albuquerque,
Albuquerque, NM.
Received May 13, 2004;
accepted after revision September 7, 2004.
Supported by a grant from the National Cancer Institute, National
Institutes of Health, Bethesda (RO1-CA87992-01A1).
Address correspondence to S. N. Goldberg
(sgoldber{at}caregroup.harvard.edu).
Abstract
OBJECTIVE. To use computer modeling of the Bio-Heat equation to
demonstrate factors influencing RF ablation tissue heating.
CONCLUSION. Computer modeling demonstrates the importance of energy
deposition, tumor and background tissue electrical and thermal conductivity,
and perfusion on RF ablation outcomes.
Introduction
Imaging-guided radiofrequency ablation has been gaining significant
acceptance as a minimally invasive thermal therapy for the treatment of focal
neoplasms [1]. Its reduced
morbidity rates when compared with surgical resection has led to expanding
clinical applications from the destruction of small metastatic and primary
liver tumors to now include the treatment of renal cell carcinomas and lung,
bone, and breast tumors [1].
With this increase in opportunities has come a wide variability in ablation
efficacy due largely in part to underlying tissue characteristics. These
parameters have been characterized and mathematically modeled in the form of
electrostatic equations coupled to the Bio-Heat Equation
[2]. From a conceptual
framework, the Bio-Heat Equation has been previously simplified to:
However, analysis of the formal equation:
where 
= density of tissue, blood (kg/m3), c = specific
heat of tissue, blood (Joules/kg-°C), k = thermal conductivity, m =
perfusion (blood flow rate/unit mass tissue) (kg/m3 - sec),
Qp = power absorbed/unit volume tissue, Qm = metabolic heating/unit
volume of tissue shows the potential importance of power, thermal
conductivity, and perfusion on ablation outcomes. In addition, the
electrostatic equations: Qp = j2/
, where j is the
current density and is the electrical conductivity, show the
importance of these two factors on radiofrequency-induced tissue heating
[4]. As such, formal study of
these factors using computer modeling can be performed leading to insights
applicable to clinical practice
[5-9].
Computer Modeling Approach
A finite-element computer simulation of the Bio-Heat equation (ETherm) that
couples radiofrequency electrical fields to thermal transport was used to
predict outcomes [5] (Figs.
1A,
1B, and
1C). Variables identified to
have significant impact on radiofrequency heating include electrical
conductivity of the tumor and surrounding tissue, thermal conductivity of
tissue, tissue perfusion, and radiofrequency generator output were studied
[3]. We show how these
variables impact radiofrequency heating and clinical ramifications of these
variables.
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Fig. 1B. —ETherm computer simulation model template
[5]. These computer simulations
were used to generate heating profiles for 12 min of radiofrequency
application using 3-cm tip, 17-gauge internally cooled electrode and 2,000-mA
output generator. Schematic depicts electrical field from ETherm
simulation.
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Fig. 1C. —ETherm computer simulation model template
[5]. These computer simulations
were used to generate heating profiles for 12 min of radiofrequency
application using 3-cm tip, 17-gauge internally cooled electrode and 2,000-mA
output generator. Schematic depicts ETherm thermal map presented at 12 min.
Temperature at 20 mm from the midpoint of electrode (T2 cm, red
X) and 50°C isotherm at midpoint of electrode were calculated and
used to construct response surface contours such as those presented in
following figures.
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Computer modeling determined radiofrequency tissue heating for large
matrices of possible parameter combinations. This included the inner
compartment radius (representing the region or zone of "tumor")
versus electrical or thermal conductivity of the tumor and surrounding tissue.
Multiple surface responses, 3D graphs plotting two variables against the
50°C isotherm, were generated to show the additional effects of perfusion
and radiofrequency generator output. The ranges for all of these parameters
were chosen so that they would span the expected values of various human
tissues and phantom models (Table
1) and their expected modulation from adjuvant therapy.
Radiofrequency ablation strategies have traditionally taken advantage of
the coagulative effects of high-temperature heating, with optimal desired
temperatures ranging from 50-100°C. Higher temperatures, (i.e.,
>105-110°C) will vaporize tissue, reducing electricity conductivity,
thermal conduction, and energy input
[3]. Thus, the 50°C
isotherm was used as our end point (Fig.
2).
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Fig. 2. —Response contours of 50°C temperature isotherms.
Effective radiofrequency energy for ablation is considered to be thermal dose
of 50-54°C for 4-6 min. We therefore selected 50°C isotherm to allow
standardized means of comparison. Figure represents color-coded schematic
depiction of 50°C temperature isotherms versus distance from 3-cm
internally cooled electrode. Blue represents parameters that can successfully
heat 3-cm zone of ablation, whereas red denotes greater than 7 cm.
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Effect of Inner Electrical Conductivity
We began by studying the effects of inner electrical conductivity on
radiofrequency heating (Figs.
3A, and
3B) because this parameter has
been best studied and modulated in clinical practice by NaCl injection
[10-12].
Previously, both volume and concentration of adjuvant NaCl have been shown to
markedly affect radiofrequency heating efficiency in a mathematically
predictable fashion [11].
Thus, our approach permitted validation of prior mathematic modeling because a
strong correlation (r2 = 0.92) between computer simulation
and the previous model was established. The surface responses also confirm
prior findings that higher concentrations with small volumes are more
effective at producing efficient heating and that the careful selection of
appropriate parameters can enable the ablation of 5- to 6-cm tumors. In
addition, these results suggest that on a clinical level, instillation of
adjuvant NaCl or other agents that may modify local electrical conductivity
must be done with care to prevent "unexpected" increases or
decreases in heating and coagulation.
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Fig. 3A. —Inner electrical conductivity response contours. S/m =
siemens per meter. Response contour represents 3D relationship of temperatures
(T) 2 cm from electrode with varying inner electrical conductivity (I)
and radius.
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Fig. 3B. —Inner electrical conductivity response contours. S/m =
siemens per meter. Response contour depicts 50°C isotherms for varying
inner electrical conductivity from computer simulations. For given tumor
radius or tumor conductivity, increasing either conductivity or radius first
increases heating but then can decrease heating because of limitations in
generator output.
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Effect of Outer Electrical Conductivity
Normal tissue surrounding tumor has significant effects on tumor heating,
in part because of electrical conductivity () of the outer tissue
[13-15].
Computer modeling (Fig. 4)
shows that at low inner conductivities found in many tumors there are limited
effects for outer electrical conductivity. However, at higher inner electrical
conductivities, as seen with adjuvant NaCl injection, there are pronounced
interactions between the outer and inner electrical conductivity,
significantly influencing radiofrequency heating. Nevertheless, because of its
longer distance from the electrode, the tissue on the outside contributes less
of an effect on heating of the tumor than the effect of local tissues around
the electrode. Yet, at an appropriate volume of tumor, high inner electrical
conductivity with low outer electrical conductivity can achieve the most
effective heating.
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Fig. 4. —Effect of background tissue conductivity. 3D response
contours of 50°C isotherms illustrating interaction between tumor volume
and inner and outer electrical conductivity are shown for three different
inner conductivities. Significant interaction between inner and outer
electrical conductivity on radiofrequency heating is shown. S/m = siemens per
meter.
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On a clinical level, these results suggest that modification of the
electrical conductivity with injection of NaCl will have the greatest impact
in tissues with a low outer conductivity. Furthermore, the more electrically
conductive the tumor, the greater is the influence of the background tissue
conductivity. The diameter of the tumor to be ablated also will influence this
interaction between tumor and outer tissue electrical conductivity.
Effect of Thermal Conductivity
Thermal conductivity for many soft tissues such as liver is 0.3-0.5
watts/m-°C, but other sites in which ablation is now commonly performed,
such as fat, bone, and lung, are lower (0.15-0.3 watts/m-°C)
[14]. Thermal conductivity for
fluid environments ranges between 0.7 and 1.5 watts/m-°C. Computer
simulations of response surfaces for thermal conductivities in the range of
0.15-1.5 watts/m-°C illustrate their significant impact on radiofrequency
heating (Fig. 5). By allowing
heat to diffuse more quickly and deeper into tissues, increased thermal
conductivity can in turn allow increased current input and greater ablation
volumes. On a clinical level, knowledge of the tissue thermal conductivity
will help predict ablation size and, when used, the optimal NaCl volume to
maximize heating.
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Fig. 5. —Effects on radiofrequency heating by alteration of thermal
conductivity. Surface response at 0.5 watts/m-°C most closely approximates
empirically determined results in liver, whereas plot at higher thermal
conductivities approximates results in agar phantoms. Increasing thermal
conductivity of entire system (i.e., "tumor" and surrounding
tissue) can achieve bigger ablations. Left shift in response surface is caused
by both increased thermal conductivity and current limitation, where thermal
conductivity increases until it becomes limited by current. For region to
right of maximum, greater energy is needed to obtain larger ablations. S/m =
siemens per meter.
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Effect of Perfusion
In addition to the known heat sink effect of large vessels, global tissue
blood flow has a major impact on radiofrequency ablation
[9].
Figure 6 simulates scenarios
ranging from no perfusion to hypovascular tumors (1 kg/m3-sec), to
normal liver (3.3 kg/m3-sec), to very hypervascular tumors (10
kg/m3- sec). The surface responses confirm that for a wide range of
tumor sizes and conductivities, increasing perfusion makes large volume
ablation very difficult. Indeed, without blood flow it is possible to achieve
ablation of up to 8 cm in diameter. However, with perfusion rates of normal
liver, the volume of ablation is markedly reduced to 4.4 cm. Thus, knowledge
of the relative perfusion of both tumor and background tissue is needed to
predict the volume of coagulation that will be created in any given clinical
setting.
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Fig. 6. —Effect of tissue perfusion on radiofrequency ablation. Range
of perfusion states (0-10 kg/m3-sec) are presented. Hypervascular
tumor perfusion acts as significant thermal sink at all tumor sizes and
electrical conductivities. Height of surface contour lowers as perfusion
increases from 0 to 10 kg/m3-sec, while peak only shifts slightly.
Surface responses show that perfusion significantly affects radiofrequency
heating. S/m = siemens per meter.
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Effect of Radiofrequency Generator Output
Computer simulations enable the study of variables that are currently
limited by existing technology, including prediction of ablation results with
as-of-yet unavailable high-current generators. Simulated temperature response
surfaces (Fig. 7) show
significant impact on radiofrequency heating with increasing radiofrequency
generator current/output. Although increasing electrical and thermal
conductivity can increase ablation volume, greater radiofrequency energy than
available in current generators is necessary to achieve maximal coagulation.
Indeed, our modeling shows that high-power generators could potentially lead
to up to 10-cm zones of coagulation depending on appropriate electrical
conductivity modulation (and perfusion).
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Fig. 7. —Thermal response contours versus radiofrequency generator
output. This figure illustrates effects on radiofrequency heating based on
available radiofrequency generator output. As expected, larger volumes of
ablation are possible with increasing radiofrequency generator output.
Simulated data for 4,000-mA generator not only shows increase in
radiofrequency heating but also stronger interaction under conditions of
greater electrical conductivity within larger volume of tissue surrounding
electrode than is evidenced for low- and medium-power generators. There is
increased height of surface contour and peak shifts to right. Note larger
color scale for this figure. S/m = siemens per meter.
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Conclusion
Variables such as power, perfusion, and the interaction between electrical
and thermal conductivities constitute a dynamic, complex system for
radiofrequency tumor ablation. Our research shows the potential utility of
computer modeling to provide greater insight into anticipated outcomes of
ablation by enabling the rapid generation of large volumes of data over short
periods of time. As such, computer modeling is likely to facilitate our
understanding of how to best control and optimize radiofrequency ablation for
clinical practice because optimal generator settings will be different for
different tissues to produce consistent volumes of coagulation. It is
anticipated that further computer simulation modeling, accompanied by
systematic experimental and clinical validation, will enable clinicians to
tailor strategies for multiple types of tumors in varied tissue environments
and may ultimately allow clinicians to a priori predict the radiofrequency
parameter settings for optimal ablation of a given tumor.
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Abstract
Introduction
