著者
Yusuke Imoto Naoya Yamanaka Takeo Uramoto Masato Tanaka Masaki Fujikawa Naoto Mitsume
出版者
The Japan Society for Industrial and Applied Mathematics
雑誌
JSIAM Letters (ISSN:18830609)
巻号頁・発行日
vol.12, pp.29-32, 2020 (Released:2020-06-01)
参考文献数
7

Hyper-dual numbers (HDN) are numbers defined by using nilpotent elements that differ from each other. The introduction of an operator to extend the domain of functions to HDN space based on Taylor expansion allows higher-order derivatives to be obtained from the coefficients. This study inductively defines matrix representations of HDN and proposes a numerical method for higher-order derivatives, called HDN-M differentiation, based on the matrix representations of HDN. The proposed method is characterized so that higher-order derivatives can be computed with matrix operation rules without implementations of the operation rules of HDN.
著者
Yusuke Yamamoto Eiichiro Iwata Hideki Shigematsu Hiroshi Nakajima Masato Tanaka Akinori Okuda Yasuhiko Morimoto Keisuke Masuda Munehisa Koizumi Yasuhito Tanaka
出版者
The Japanese Society for Spine Surgery and Related Research
雑誌
Spine Surgery and Related Research (ISSN:2432261X)
巻号頁・発行日
pp.2017-0052, (Released:2018-02-28)
被引用文献数
2

Introduction To identify the temporal comparison of biochemical markers for early detection of surgical site infection (SSI) following instrumented spinal fusion that are not affected by operative factors.Materials and methods We reviewed data on C-reactive protein level and total white blood cell count and differential count before instrumented spinal fusion and at 1, 4, and 7 days postoperatively. The 141 patients in our sample were divided into an SSI group (patients who developed deep SSI) and a non-SSI group. We investigated the peak or nadir value day and identified those not affected by operative circumstances (operating time, intraoperative blood loss, and number of fusion segments) in the non-SSI group. If there was a significant difference between the peak or nadir value day and the next survey day, we considered the temporal comparison between these unaffected markers as an indicator of SSI and examined the usefulness of these indicators by calculating sensitivity and specificity. Furthermore, we investigated the usefulness of the combination of these markers (if even each one marker was recognized, we considered it positive).Results Four biochemical markers of SSI were selected: neutrophil percentage at postoperative day 4 more than day 1 (sensitivity 36%, specificity 95%), neutrophil count at postoperative day 4 more than day 1 (sensitivity 46%, specificity 93%), lymphocyte percentage at postoperative day 4 less than day 1 (sensitivity 36%, specificity 90%), and lymphocyte count at postoperative day 4 less than day 1 (sensitivity 36%, specificity 90%). The combination of these markers showed sensitivity 100%, specificity 80%, respectively.Conclusions Four markers are reliable indicators for early detection of SSI following spinal instrumented fusion because they are not affected by operative factor. The combination of each indicator had both high sensitivity and specificity. Therefore, it is reliable and much useful for early detection of SSI.