Abstract

Radio frequency ablation (RFA) has become a popular method for the minimally invasive treatment of liver cancer. However, the success rate of these treatments depends heavily on the amount of experience the clinician possesses. Mathematical modeling can help mitigate this problem by providing an indication of the treatment outcome. Thermal lesions in RFA are affected by the cooling effect of both fine-scale and large-scale blood vessels. The exact model for large-scale blood vessels is advection-diffusion, i.e., a model capable of producing directional effects, which are known to occur in certain cases. In previous research, in situations where directional effects do not occur, the advection term in the blood vessel model has been typically replaced with the Pennes perfusion term, albeit with a higher-than-usual perfusion rate. Whether these values of the perfusion rate appearing in literature are optimal for the particular vessel radii in question, has not been investigated so far. This work aims to address this issue. An attempt has been made to determine, for values of vessel radius between 0.55 mm and 5 mm, best estimates for the perfusion rate which minimize the error in thermal lesion volumes between the perfusion-based model and the advection-based model. The results for the best estimate of the perfusion rate presented may be used in existing methods for fast estimation of RFA outcomes. Furthermore, the possible improvements to the presented methodology have been highlighted.

References

1.
Wild
,
C. P.
,
Weiderpass
,
E.
, and
Stewart
,
B. W.
, eds.,
2020
,
World Cancer Report: Cancer Research for Cancer Prevention
,
International Agency for Research on Cancer, Lyon, France
.
2.
Curley
,
S. A.
,
2001
, “
Radiofrequency Ablation of Malignant Liver Tumors
,”
Oncology
,
6
(
1
), pp.
14
23
.
3.
Garrean
,
S.
,
Hering
,
J.
,
Saied
,
A.
,
Helton
,
W. S.
, and
Espat
,
N. J.
,
2008
, “
Radiofrequency Ablation of Primary and Metastatic Liver Tumors: A Critical Review of the Literature
,”
Am. J. Surg.
,
195
(
4
), pp.
508
520
.10.1016/j.amjsurg.2007.06.024
4.
Payne
,
S.
,
Flanagan
,
R.
,
Pollari
,
M.
,
Alhonnoro
,
T.
,
Bost
,
C.
,
O'Neill
,
D.
,
Peng
,
T.
, and
Stiegler
,
P.
,
2011
, “
Image-Based Multi-Scale Modelling and Validation of Radio-Frequency Ablation in Liver Tumours
,”
Philos. Trans. R. Soc. London A
,
369
(
1954
), pp.
4233
4254
.
5.
Shrivastava
,
D.
, and
Roemer
,
R. B.
,
2006
, “
Readdressing the Issue of Thermally Significant Blood Vessels Using a Countercurrent Vessel Network
,”
ASME J. Biomech. Eng.
,
128
(
2
), pp.
210
216
.10.1115/1.2165693
6.
Nakayama
,
A.
, and
Kuwahara
,
F.
,
2008
, “
A General Bioheat Transfer Model Based on the Theory of Porous Media
,”
Int. J. Heat Mass Transfer
,
51
(
11–12
), pp.
3190
3199
.10.1016/j.ijheatmasstransfer.2007.05.030
7.
Shrivastava
,
D.
, and
Vaughan
,
J. T.
,
2009
, “
A Generic Bioheat Transfer Thermal Model for a Perfused Tissue
,”
ASME J. Biomech. Eng.
,
131
(
7
), p.
074506
.10.1115/1.3127260
8.
Pennes
,
H. H.
,
1948
, “
Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm
,”
J. Appl. Physiol.
,
1
(
2
), pp.
93
122
.10.1152/jappl.1948.1.2.93
9.
Vaidya
,
N.
,
Baragona
,
M.
,
Lavezzo
,
V.
,
Maessen
,
R.
, and
Veroy
,
K.
,
2021
, “
Simulation Study of the Cooling Effect of Blood Vessels and Blood Coagulation in Hepatic Radio-Frequency Ablation
,”
Int. J. Hyperthermia
,
38
(
1
), pp.
95
104
.10.1080/02656736.2020.1866217
10.
Huang
,
H.-W.
,
2013
, “
Influence of Blood Vessel on the Thermal Lesion Formation During Radiofrequency Ablation for Liver Tumors
,”
Med. Phys.
,
40
(
7
), p.
073303
.10.1118/1.4811135
11.
Kröger
,
T.
,
Altrogge
,
I.
,
Preusser
,
T.
,
Pereira
,
P. L.
,
Schmidt
,
D.
,
Weihusen
,
A.
, and
Peitgen
,
H.-O.
,
2006
, “
Numerical Simulation of Radio Frequency Ablation With State Dependent Material Parameters in Three Space Dimensions
,”
Medical Image Computing and Computer-Assisted Intervention – MICCAI 2006
,
R.
Larsen
,
M.
Nielsen
, and
J.
Sporring
, eds.,
Springer Berlin Heidelberg
,
Berlin, Heidelberg
, pp.
380
388
.
12.
Audigier
,
C.
,
2015
, “
Computational Modeling of Radiofrequency Ablation for the Planning and Guidance of Abdominal Tumor Treatment
,” Ph.D. thesis,
University of Nice - Sophia Antipolis
, Nice, France.
13.
Sutera
,
S. P.
, and
Skalak
,
R.
,
1993
, “
The History of Poiseuille's Law
,”
Annu. Rev. Fluid. Mech.
,
25
(
1
), pp.
1
20
.10.1146/annurev.fl.25.010193.000245
14.
Williams
,
H. R.
,
Trask
,
R. S.
,
Weaver
,
P. M.
, and
Bond
,
I. P.
,
2008
, “
Minimum Mass Vascular Networks in Multifunctional Materials
,”
J. R. Soc. Interface
,
5
(
18
), pp.
55
65
.10.1098/rsif.2007.1022
15.
van Wijk
,
Y.
,
2015
, “
Treatment Planning for Microwave Ablation of Hepatic Tumors in the Proximity of Hepatic Veins
,” Master's thesis,
Eindhoven University of Technology
, Eindhoven, The Netherlands.
16.
Hasgall
,
P. A.
,
Neufeld
,
E.
,
Gosselin
,
M. C.
,
Klingenböck
,
A.
, and
Kuster
,
N.
,
2015
, “
IT'IS Database for Thermal and Electromagnetic Parameters of Biological Tissues
,” epub.https://www.scienceopen.com/document?vid=a95fbaa4-efd8-429a-a59e-5e208fea2e45
17.
Valvano
,
J. W.
,
Cochran
,
J. R.
, and
Diller
,
K. R.
,
1985
, “
Thermal Conductivity and Diffusivity of Biomaterials Measured With Self-Heated Thermistors
,”
Int. J. Thermophys.
,
6
(
3
), pp.
301
311
.10.1007/BF00522151
18.
Zurbuchen
,
U.
,
Holmer
,
C.
,
Lehmann
,
K. S.
,
Stein
,
T.
,
Roggan
,
A.
,
Seifarth
,
C.
,
Buhr
,
H.-J.
, and
Ritz
,
J.-P.
,
2010
, “
Determination of the Temperature-Dependent Electric Conductivity of Liver Tissue Ex Vivo and In Vivo: Importance for Therapy Planning for the Radiofrequency Ablation of Liver Tumours
,”
Int. J. Hyperth.
,
26
(
1
), pp.
26
33
.10.3109/02656730903436442
19.
Chen
,
C.-C. R.
,
Miga
,
M. I.
, and
Galloway
, and
R. L.
, Jr
,
2009
, “
Optimizing Electrode Placement Using Finite-Element Models in Radiofrequency Ablation Treatment Planning
,”
IEEE Trans. Biomed. Eng.
,
56
(
2
), pp.
237
245
.10.1109/TBME.2008.2010383
20.
Duck
,
F. A.
,
2013
,
Physical Properties of Tissues: A Comprehensive Reference Book
,
Academic Press
, London, UK.
21.
Mohapatra
,
S. N.
, and
Hill
,
D. W.
,
1975
, “
The Changes in Blood Resistivity With Haematocrit and Temperature
,”
Eur. J. Intensive Care Med.
,
1
(
4
), pp.
153
162
.10.1007/BF00624433
22.
Gaston
,
D.
,
Newman
,
C.
,
Hansen
,
G.
, and
Lebrun-Grandié
,
D.
,
2009
, “
MOOSE: A Parallel Computational Framework for Coupled Systems of Nonlinear Equations
,”
Nucl. Eng. Des.
,
239
(
10
), pp.
1768
1778
.10.1016/j.nucengdes.2009.05.021
23.
Codina
,
R.
,
1998
, “
Comparison of Some Finite Element Methods for Solving the Diffusion-Convection-Reaction Equation
,”
Comput. Methods Appl. Mech. Eng.
,
156
(
1–4
), pp.
185
210
.10.1016/S0045-7825(97)00206-5
24.
Geuzaine
,
C.
, and
Remacle
,
J.-F.
,
2009
, “
Gmsh: A 3-D Finite Element Mesh Generator With Built-in Pre-and Post-Processing Facilities
,”
Int. J. Numer. Methods Eng.
,
79
(
11
), pp.
1309
1331
.10.1002/nme.2579
25.
Fletcher
,
R.
, and
Reeves
,
C. M.
,
1964
, “
Function Minimization by Conjugate Gradients
,”
Comput. J.
,
7
(
2
), pp.
149
154
.10.1093/comjnl/7.2.149
26.
Adams
,
B. M.
,
Bohnhoff
,
W. J.
,
Dalbey
,
K. R.
,
Ebeida
,
M. S.
,
Eddy
,
J. P.
,
Eldred
,
M. S.
,
Geraci
,
G.
,
Hooper
,
R. W.
,
Hough
,
P. D.
,
Hu
,
K. T.
,
Jakeman
,
J. D.
,
Khalil
,
M.
,
Maupin
,
K. A.
,
Monschke
,
J. A.
,
Ridgway
,
E. M.
,
Rushdi
,
A. A.
,
Stephens
,
J. A.
,
Swiler
,
L. P.
,
Vigil
,
D. M.
,
Wildey
,
T. M.
, and
Winokur
,
J. G.
,
2016
, “
Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.5 User's Manual
,” Sandia National Laboratories, Albuquerque, NM, Report No.
SAND2014-4633
.https://dakota.sandia.gov/sites/default/files/docs/6.0/Users-6.0.0.pdf
27.
Michaleris
,
P.
,
Tortorelli
,
D. A.
, and
Vidal
,
C. A.
,
1994
, “
Tangent Operators and Design Sensitivity Formulations for Transient Non-Linear Coupled Problems With Applications to Elastoplasticity
,”
Int. J. Numer. Methods Eng.
,
37
(
14
), pp.
2471
2499
.10.1002/nme.1620371408
28.
Akima
,
H.
,
1970
, “
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
,”
J. ACM (JACM)
,
17
(
4
), pp.
589
602
.10.1145/321607.321609
You do not currently have access to this content.