Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution.

IF 2.3 Q3 ENGINEERING, BIOMEDICAL
Biomedical Engineering and Computational Biology Pub Date : 2017-10-26 eCollection Date: 2017-01-01 DOI:10.1177/1179597217730305
Glen Atlas, John K-J Li, Shawn Amin, Robert G Hahn
{"title":"Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution.","authors":"Glen Atlas,&nbsp;John K-J Li,&nbsp;Shawn Amin,&nbsp;Robert G Hahn","doi":"10.1177/1179597217730305","DOIUrl":null,"url":null,"abstract":"<p><p>A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler's formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly \"adaptable\" and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.</p>","PeriodicalId":42484,"journal":{"name":"Biomedical Engineering and Computational Biology","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2017-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1179597217730305","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biomedical Engineering and Computational Biology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1177/1179597217730305","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2017/1/1 0:00:00","PubModel":"eCollection","JCR":"Q3","JCRName":"ENGINEERING, BIOMEDICAL","Score":null,"Total":0}
引用次数: 3

Abstract

A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler's formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly "adaptable" and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.

Abstract Image

Abstract Image

Abstract Image

血浆稀释患者特异性闭式积分-微分方程模型的建立和回顾性临床评估。
本文建立了一种反映晶体药物静脉输注和输注后血浆稀释(PD)的闭型积分-微分方程(IDE)模型。具体地说,PD是用常数比、微分和积分分量的组合在数学上表示的。此外,该模型已成功应用于先前存在的数据,来自先前的人类研究,在甲状腺手术开始时注入晶体30分钟。使用欧拉公式和IDE的拉普拉斯变换解,可以根据患者在输注期间对PD的反应将患者分为两组。明确地,1组患者有基于输注的PD反应,使用指数衰减双曲正弦函数建模,而2组患者有基于输注的PD反应,使用指数衰减三角正弦函数建模。1组和2组患者均有输注后PD反应,采用双曲正弦和双曲余弦函数的相同组合建模。1组和2组在输注期间和输注后PD曲线下的面积有统计学上的显著差异。具体来说,第2组患者对PD的反应很可能与术前低血容量一致。总的来说,PD的IDE模型似乎具有高度的“适应性”,并且在输注和输注后阶段成功地适应了临床获得的针对患者的人类数据。此外,PD患者特异性IDE模型可能是围手术期液体管理和实时评估临床体积动力学晶体溶液的有用辅助手段。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
1
审稿时长
8 weeks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信