Three-dimensional finite-element code for electrosurgery and thermal ablation simulations
A system and method for performing a simulation of an electrosurgical procedure are disclosed. The method includes the steps of generating a three-dimensional medium, which includes one or more material regions representing a physical object. The method also includes the steps of dividing the medium into multiple hexahedron elements to generate a three-dimensional conformal mesh and assigning each element to the material region. The method further includes the steps of calculating an electrical energy solution and a thermal transport solution and generating graphical representations illustrating one or more aspects of the electrical energy and the thermal transport solutions.
1. A computer implemented method for performing a simulation of an electrosurgical procedure on tissue, the method comprising the steps of:
generating a three-dimensional model of a medium comprising at least one material region representing a physical object or a region of the tissue;
dividing the model of the medium into a plurality of hexahedron elements to generate a three-dimensional conformal mesh;
assigning each element to a corresponding at least one material region;
calculating at least one of an electrical energy solution and a thermal transport solution based on at least one mathematical model, the plurality of hexahedron elements and finite element method;
updating at least one property value of the at least one material region at least once in response to temperature changes based on an empirically derived value;
updating at least one of the electrical energy solution and the thermal transport solution as a function of the at least one property value; and
generating and displaying at least one graphical representation representing at least one form of the electrical energy solution and one form of the thermal transport solution on an output device.
2. The method as in claim 1 , wherein the step of calculating the electrical energy solution further comprises a step of solving equations 1 and 2
∇
·
[
(
ɛ
r
-
jσ
ɛ
0
ω
)
∇
ϕ
]
=
0
(
1
)
E
=
-
∇
ϕ
(
2
)
wherein ∈ r is a relative dielectric constant, and σ is electrical conductivity of each of the elements, j is an imaginary number, ∈ 0 is vacuum permittivity, ω is angular frequency, φ is a quasi-static potential, which is a complex number, and E is amplitude and phase of electric field.
3. The method as in claim 2 , wherein the step of calculating the thermal transport solution further comprising a step of solving equations 3 and 4:
q
e
=
σ
E
·
E
*
/
2
(
3
)
ρ
C
p
∂
T
∂
t
=
∇
·
(
k
∇
T
)
+
q
e
+
q
m
+
W
b
(
T
b
-
T
)
(
4
)
wherein ρ is density of the medium, C 92 is specific heat, k is thermal conductivity, q m is heat generated by metabolism, q e is resistive source, and W b (T b −T) represents thermal variations caused by blood flow.
4. The method as in claim 1 , wherein the material region includes a material state, the material state comprising at least one physical property.
5. The method as in claim 4 , wherein the at least one physical property is selected from the group consisting of relative dielectric constant, electrical conductivity, specific heat, thermal conductivity, and blood flow.
6. The method as in claim 5 , wherein the at least one physical property is temperature-dependent.
7. The method as in claim 6 , wherein a tabular function stores a plurality of temperature-dependent values for the at least one physical property.
8. The method as in claim 1 , wherein the plurality of elements are ordered in the three-dimensional mesh according to cubic logic.
9. The method as in claim 1 , wherein the graphical representation is a three-dimensional plot and the at least one form of the thermal solution is an isothermal surface of the medium.
10. The method as in claim 1 , wherein the graphical representation is a two dimensional slice plot and the at least one form of the electrical solution is electrical conductivity of the medium.
11. A computing system for performing a simulation of an electrosurgical procedure on tissue, the system comprising:
at least one processor coupled to a memory storing a program of instructions, wherein when the program is executed on the at least one processor, the at least one processor performs the instructions of:
generating a three-dimensional model of a medium comprising at least one material region representing a physical object or a region of the tissue;
dividing the model of the medium into a plurality of hexahedron elements to generate a three-dimensional conformal mesh;
assigning each element to a corresponding at least one material region;
calculating at least one of an electrical energy solution and a thermal transport solution based on at least one mathematical model, the plurality of hexahedron elements and finite element method;
updating at least one property value of the at least one material region at least once in response to temperature changes based on an empirically derived value; wherein at least one of the electrical energy solution and the thermal transport solution is updated as a function of the at least one property value; and
an output device which outputs at least one of a graphical representation representing at least one form of the electrical energy solution and one form of the thermal transport solution.
12. The system as in claim 11 , wherein the material region includes a material state, the material state comprising at least one physical property.
13. The system as in claim 12 , wherein the at least one physical property is selected from the group consisting of relative dielectric constant, electrical conductivity, specific heat, thermal conductivity, and blood flow.
14. The system as in claim 13 , wherein the at least one physical property is temperature-dependent.
15. The system as in claim 14 wherein a tabular function stores a plurality of temperature-dependent values for the at least one physical property.
16. The system as in claim 11 , wherein the plurality of elements are ordered in the three-dimensional mesh according to cubic logic.
17. The system as in claim 11 , wherein the graphical representation is a three-dimensional plot and the at least one form of the thermal solution is an isothermal surface of the medium.
18. The system as in claim 11 , wherein the graphical representation is a two dimensional slice plot and the at least one form of the electrical solution is electrical conductivity of the medium.
19. A computer-readable storage medium storing a set of computer-executable instructions for performing a simulation of an electrosurgical procedure on tissue, the computer-executable instructions comprising the steps of:
generating a three-dimensional model of a medium comprising at least one material region representing a physical object or a region of the tissue;
dividing the model of the medium into a plurality of hexahedron elements to generate a three-dimensional conformal mesh;
assigning each element to a corresponding at least one material region;
calculating at least one of an electrical energy solution and a thermal transport solution based on at least one mathematical model, the plurality of hexahedron elements and finite element method;
updating at least one property value of the at least one material region at least once in response to temperature changes based on an empirically derived value;
updating at least one of the electrical energy solution and the thermal transport solution as a function of the at least one property value; and
generating and displaying at least one graphical representation representing at least one form of the electrical energy solution and one form of the thermal transport solution on an output device.