Yoshiki Sugitani

Norikazu Saito, Yoshiki Sugitani

Convergence results for the immersed boundary method applied to a model Stokes problem with the homogeneous Dirichlet boundary condition are presented. As a discretization method, we deal with the finite element method. First, the immersed force field is approximated using a regularized delta function and its error in the $W^{-1,p}$ norm is examined for $1\le p<n/(n-1)$, $n$ being the space dimension. Then, we consider the immersed boundary discretization of the Stokes problem and study the regularization and discretization errors separately. Consequently, error estimate of order $h^{1-α}$ in the $W^{1,1}\times L^1$ norm for the velocity and pressure is derived, where $α$ is an arbitrarily small positive number. Error estimate of order $h^{1-α}$ in the $L^r$ norm for the velocity is also derived with $r=n/(n-1-α)$. The validity of those theoretical results are confirmed by numerical examples.

Toshiaki Ohara, Hiroshi Ikeda, Yoshiki Sugitani et al.

Anemia, for which erythropoiesis-stimulating agents (ESAs) and iron supplements (ISs) are used as preventive measures, presents important difficulties for hemodialysis patients. Nevertheless, the number of physicians able to manage such medications appropriately is not keeping pace with the rapid increase of hemodialysis patients. Moreover, the high cost of ESAs imposes heavy burdens on medical insurance systems. An artificial-intelligence-supported anemia control system (AISACS) trained using administration direction data from experienced physicians has been developed by the authors. For the system, appropriate data selection and rectification techniques play important roles. Decision making related to ESAs poses a multi-class classification problem for which a two-step classification technique is introduced. Several validations have demonstrated that AISACS exhibits high performance with correct classification rates of 72-87% and clinically appropriate classification rates of 92-98%.