  During thermal heating surgical procedures such as electrosurgery, thermal
ablative treatment and hyperthermia, soft tissue deformation due to tool-tissue
interaction and patients' motion can affect the distribution of induced thermal
energy. Tissue temperature must be efficiently and accurately obtained from
deformed tissues for precise thermal energy delivery; however, the classical
Pennes bio-heat transfer can handle only the static non-moving state of soft
tissue. This paper presents a formulation of bio-heat transfer under the effect
of tissue deformation for fast or near real-time tissue temperature
computation, based on fast explicit dynamics finite element algorithm for
transient heat transfer. The proposed computation is achieved by transformation
of the unknown deformed tissue state to the known initial non-moving state via
a mapping function. The appropriateness and effectiveness of the proposed
methodology are evaluated on a realistic virtual human liver with blood vessels
to demonstrate a clinically relevant scenario of thermal ablation of hepatic
cancer. Compared against the established non-linear procedures from commercial
finite element analysis package, ABAQUS/CAE, the proposed methodology can
achieve a typical 1.0e-3 level of normalized relative error at nodes and
between 1.0e-4 and 1.0e-5 level of total errors, which is in good agreement
with ABAQUS solutions. The proposed method consumes slightly more time than the
formulation without soft tissue deformation, and computation performance of
five different formulations are examined. The proposed method can be applied
with bio-mechanical deformable models for fast or near real-time computation of
non-linear bio-heat transfer, leading to translational potential in dynamic
tissue temperature predictive analysis and thermal dosimetry computation for
computer-integrated medical education and personalized treatments.
