Kohei OKITA

Research Themes 
Development of HIFU simulator for highintensity focused ultrasound therapy
Numerical analysis of the focus control in microbubbleenhanced HIFU
Development of fluid dynamics solver using signed distance function for representation of objects in Cartesian mesh
Modeling of multiple fluid flows based on the diffuse interface model
Numerical analysis of the cavitation erosion and it's mitigation in neutron spallation source

Research Subjects and Results 
Development of HIFU simulator for highintensity focused ultrasound therapy
Highintensity focused ultrasound (HIFU) has been developed as a noninvasive cancer treatment. HIFU provides a heat coagulation of tissue around the focus. The objectives of the present study are to realize appropriate focus control using the array transducer, to support preoperative planning of HIFU therapy, and to support the development of HIFU devices by enabling computational prediction of ablation regions. To these ends, we develop an HIFU simulator. Figure 1 shows the flow of input data for the HIFU simulation. A volume model of the human body (a voxel data) was constructed from CT/MRI data on a living human body. The shape of a transducer defined using CAD is represented by the volume data of the Signed Distance Function (SDF). Then, a simulation of ultrasound propagation from the transducer through the voxel data is performed numerically. HIFU therapy for liver cancer using the array transducer was reproduced as shown in Fig.2. Although the results without the phase delay showed displacement and diffusion of the focal point due to the inhomogeneity of the body, a clear focal point was obtained by using the array transducer with an appropriate phase delay, which is provided by precomputation of the ultrasound propagation from the target.
Figure 1: Schematic diagram of data flows to HIFU simulation
Figure 2: Numerical simulation of HIFU therapy for liver cancer using array transducer
Development of fluid dynamics solver using signed distance function for representation of objects in Cartesian mesh
A fluid solver using signed distance function (SDF) for shape representation was developed based on the immersed boundary method to simulate incompressible viscous flows. The forcing velocities near boundary are extrapolated by trilinear interpolation with taking into account a boundary condition using SDF. SMAC method is employed for solving basic equations for unsteady incompressible flows. The equations are discretized in space by 2ndorder central difference method, where the discretization near boundary is improved by SDF to satisfy a Dirichlet boundary condition for velocity. The fluid solver was verified in both steady and oscillating threedimensional Poiseuille flows as shown in Fig.3. Figure 4 shows the grid dependency of the error of axial velocity for the oscillating flow. As the grid spacing decreases, L2 and L∞ norm of the error of the axial velocity profile respectively decrease by the order of 1.96 and 1.89 for the oscillating flow. Therefore, the fluid solver enables to analyze the Poiseuille flow using Cartesian mesh by 2ndorder of accuracy in space.
Figure 3: Schematic diagram of the numerical model for the Poiseuille flow through the cylindrical pipe which is arranged in the numerical domain of Cartesian mesh.
Figure 4: Grid dependency of the error of axial velocity (Oscillating flow, Reτ=1, angle of cylinder arrangement θ = arctan(3/4) = 36.9°)
Modeling of multiple fluid flows using diffuse interface model
A free energy model for immiscible multiple fluids based on the diffuse interface model was proposed. A triple junction problem was simulated for the verification of the model. A contact angle depends on the surface tension of each interface at triple junction. The numerical results were compared with the theory for various contact angles as shown in Fig.5. The represented contact angle agrees with the theoretical contact angle using the proposed free energy model for immiscible multiple fluids.
Figure 5: The represented contact angle of the blue fluid at triple junction as function of the theoretical contact angle. Symbols are compared for the resolution of the diffuse interface.
The microgravity driven motion of two immiscible droplets in the other immiscible fluid was simulated as shown in Fig.6. The red and blue fluids are respectively lighter and heavier than the surrounding fluid. The motions of the two droplets such as coalescence, rotation, covering and detachment were reproduced reasonably. The present free energy model enables to reproduce the threedimensional motion of immiscible multiple fluids in the surface tension dominant flows.
(a) Rotating motion (sRG=1.0, sGB=1.0, sBR=1.0)
(b) Covering motion (sRG=0.7, sGB=1.0, sBR=0.7)
Figure 6: Gravity driven motion of the two immiscible droplets in the other immiscible fluid. The red and blue fluids are respectively lighter and heavier than the surrounding fluid.

VCAD Public Software 
VSDFlib
SPHERE:HIFU
Software Block Page
Selected Publications
【Papers】
K. Okita, K. Ono
「Numerical Accuracy of Fluid Solver using Signed Distance Function for Shape Representation」
Transaction JSME Ser.B in Japanese (submitted) (2011)
K. Okita, K. Ono, S. Takagi, Y. Matsumoto
「Development of High Intensity Focused Ultrasound Simulator for Large Scale Computing」
Int. J. Numerical Methods in Fluids, Vol.65, pp.4366 (2011)
K. Okita, K. Ono, S. Takagi, Y. Matsumoto
「Numerical Simulation of the Tissue Ablation in High Intensity Focused Ultrasound Therapy with Array Transducer」
Int. J. Numerical Methods in Fluids, Vol.64, pp.13951411 (2010)
K. Okita
「Numerical Simulation of the Tissue Ablation in HighIntensity Focused Ultrasound Therapy」
J. JSCES, Vol.14，No.4, pp.1112 in Japanese (2009)
K. Okita, H. Ugajin, Y. Matsumoto
「Numerical Analysis of the influence of the tip clearance flows on the Unsteady Cavitating Flows in a Threedimensional Inducer」
Journal of Hydrodynamics, Ser. B, Vol.21, Issue 1, pp.3440 (2009)
K. Okita, S. Takagi, Y. Matsumoto
「Propagation of Pressure Waves, Caused by a Thermal Shock, in Liquid Metals Containing Gas Bubbles」
Journal of Fluid Science and Technology, Vol.3, No.1, pp.116128 (2008)
K. Okita, K. Ono, S. Takagi, Y. Matsumoto,
「Modeling and Simulation of the Tissue Ablation in High Intensity Focused Ultrasound Therapy with Array Transducer」
VPH2010, Brussels, Belgium, September 30 ? October 1, pp.178180 (2010)
Matsumoto, K. Okita, K. Ono, S. Takagi
「The Tissue Ablation in High Intensity Focused Ultrasound Therapy with an Array Transducer」
WCCM / APCOM 2010, Sydney, Australia, 1923, July (2010)
K. Okita, K. Ono, S. Takagi, Y. Matsumoto
「Numerical Simulation of the Tissue Ablation in High Intensity Focused Ultrasound Therapy with an Array Transducer」
ECCOMAS CFD 2010, Lisbon, Portugal, June 14?17, No.1132 (2010)
K. Okita, K. Sugiyama, K. Ono, S. Takagi, Y. Matsumoto
「Numerical Study on the Effective Combination of Microbubble and Ultrasound in HIFU Therapy」
10th International Symposium on Therapeutic Ultrasound, Tokyo, Japan, June 912 (2010)
N. Leduc, K. Okita, K. Sugiyama, S. Takagi, Y. Matsumoto
「A TRinduced algorithm for hot spots elimination through CTscan HIFU simulations」
10th International Symposium on Therapeutic Ultrasound, Tokyo, Japan, June 912 (2010)
T. Shimura, K. Okita, S. Takagi, Y. Matsumoto
「The Effect of the Elastic Body on the Focusing of Ultrasounds in Inhomogeneous Media」
10th International Symposium on Therapeutic Ultrasound, Tokyo, Japan, June 912 (2010)
K. Okita, K. Ono, S. Takagi, Y. Matsumoto
「Numerical Simulation of the Tissue Ablation in HIFU therapy with an Array Transducer」
2nd Biosupercomputing symposium, Tokyo, Japan, March 1819, p.140 (2010)
K. Okita, K. Sugiyama, K. Ono, S. Takagi, Y. Matsumoto
「Numerical study on high intensity focused ultrasound therapy using array transducer」
Physics Procedia, Vol. 3(1), pp.315322 (2010)
Y. Matsumoto, K. Okita, K. Ono, S. Takagi
「Numerical Simulation on High Intensity Focused Ultrasound Therapy I, II」
2009 ASME International Mechanical Engineering Congress & Exposition, November 1319, Lake Buena Vista, Florida (2009)
K. Okita, K. Sugiyama, K. Ono, S. Takagi, Y. Matsumoto
「Numerical Simulation of High Intensity Focused Ultrasound Therapy with Volume Model of Human Body」
9th International Symposium on Therapeutic Ultrasound, September 2123, Aixen Province, France, pp.371374 (2009)
Y. Matsumoto, K. Okita, K. Ono, S. Takagi
「Numerical Simulation of Therapeutic Ultrasound」
FEF09, April 13, Tokyo, Japan (2009)
K. Okita, K. Sugiyama, K. Ono, S. Takagi, Y. Matsumoto
「Numerical Study on High Intensity Focused Ultrasound Therapy using Array Transducer」
International Congress on ULTRASONICS, January, 1117, Santiago, Chile (2009)
K. Okita, H. Ugajin, Y. Matsumoto
「Numerical Analysis of the Influence of the Tip Clearance Flows on the Unsteady Cavitating Flows in a Three Dimensional Inducer」
Cavitation: Turbomachinery & Medical Applications, WIMRC FORUM 2008, Warwick University, UK, 79 July, pp.246250 (2008)
K. Okita, T. Tawara, K. Ono
「Shape Representation by Signed Distance Function for Immersed Boundary Method」
WCCM8 and ECCOMAS2008, June 31July 5, Venice, Italy (2008)
K. Okita, K. Ono, S. Takagi, Y. Matsumoto
「High Intensity Focused Ultrasound in Human Body」
WCCM8 and ECCOMAS2008, June 31July 5, Venice, Italy (2008)
K. Okita, K. Ono
「Numerical Simulation of Immiscible Multiple Fluids Flow by Diffuse Interface Model」
APS 60th Annual Meeting of the Division of Fluid Dynamics, Salt Lake City, USA, Nov.(2007)
K. Okita, K. Ono
「Numerical Simulation of Multiple Fluids Flow by Diffuse Interface Model」
6th International Conference on Multiphase Flow ICMF2007, Leipzig, Germany, July, S1_Fri_B_66 (2007).
K. Okita, S. Takagi, M. Futakawa, Y. Matsumoto
「Pressure Wave Phenomena in Liquid Metals Containing Micro Gas Bubbles」
APCOM’07 in conjunction with EPMESC XI, December 36, Kyoto, Japan, MS2011 (2007)
K. Okita, A. Fujiwara, S. Takagi, Y. Matsumoto, M. Futakawa
「Numerical Study on a Mitigation Strategy Using Micro Bubbles for Cavitation Erosion Caused by a Thermal Shock in Liquid Mercury」
Sixth International Symposium on Cavitation, Wageningen, Netherlands, Sep 1115 (2006).
Selected Publications Page