An Analytical Study of Cryosurgery in the Lung

1992 ◽  
Vol 114 (4) ◽  
pp. 467-472 ◽  
Author(s):  
J. C. Bischof ◽  
J. Bastacky ◽  
B. Rubinsky
Keyword(s):  
Finite Difference ◽  
Analytical Study ◽  
Outer Boundary ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Thermal Phenomenon ◽  
Healthy Lung Tissue ◽  
Close Form ◽  
Finite Difference Techniques ◽  
Healthy Lung

The process of freezing in healthy lung tissue and in tumors in the lung during cryosurgery was modeled using one-dimensional close form techniques and finite difference techniques to determine the temperature profiles and the propagation of the freezing interface in the tissue. A thermal phenomenon was observed during freezing of lung tumors embedded in healthy tissue, (a) the freezing interface suddenly accelerates at the transition between the tumor and the healthy lung, (b) the frozen tumor temperature drops to low values once the freezing interface moves into the healthy lung, and (c) the outer boundary temperature has a point of sharp inflection corresponding to the time at which the tumor is completely frozen.

scholarly journals Asymptotic stability of porous-elastic system with thermoelasticity of type III

2021 ◽  
Author(s):  
Ilyes Lacheheb ◽  
Salim A. Messaoudi ◽  
Mostafa Zahri
Keyword(s):  
Wave Propagation ◽  
Asymptotic Stability ◽  
Finite Difference ◽  
Elastic System ◽  
Well Posedness ◽  
One Dimensional ◽  
Type Iii ◽  
The Stability ◽  
Theoretical Results ◽  
Finite Difference Techniques

AbstractIn this work, we investigate a one-dimensional porous-elastic system with thermoelasticity of type III. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation. At the end, we use some numerical approximations based on finite difference techniques to validate the theoretical results.

Efficient microcomputer‐based finite‐difference resistivity modeling via Polozhii decomposition

Geophysics ◽  
1985 ◽  
Vol 50 (3) ◽  
pp. 443-465 ◽  
Author(s):  
Bryan A. James
Keyword(s):  
Finite Difference ◽  
Outer Boundary ◽  
Three Dimensional ◽  
Single Plane ◽  
Property Variation ◽  
One Dimensional ◽  
Decomposition Procedure ◽  
Arbitrary Plane ◽  
The Fourier Transform ◽  
Matrix Transforms

Finite‐difference modeling for direct current resistivity problems can be cast in a form allowing rapid and efficient solution on a microcomputer. Almost a million nodes can be accommodated on a microcomputer with only 256 kilobytes of memory. The Polozhii decomposition procedure (Polozhii, 1965) allows a three‐dimensional (3-D) problem with no more than a one‐dimensional (1-D) property variation to be transformed into a series of decoupled and independent one‐dimensional problems. The decomposition utilizes matrix transforms analogous to analytic spatial Fourier and Hankel transforms. These matrix transforms, along with recursive formulas for the solution of the 1-D problems, yield a process which can be thought of as a continuation operator when compared with current popular methods of potential field continuation using the Fourier transform. The result is that only a single plane of node potentials needs to be determined fully. By setting up more complicated models as separate regions with differing 1-D models the above procedures can be used to create a problem where the unknown potentials along the boundary planes between the regions are cast in terms of known outer boundary potentials and known applied source terms. Once all interior boundary potentials have been calculated, the solution on any arbitrary plane of nodes in any region can be quickly calculated using the standard Polozhii decomposition procedure. Execution times for a variety of grid sizes composed of two such regions show much slower growth with increasing numbers of nodes than conventional finite‐difference solution schemes. Test cases for comparison with analytic calculations yield errors of 5 percent or less for problems composed of 756 000 nodes. The choice of boundary condition, however, has a significant influence on the accuracy obtained.

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