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`Computational and Mathematical Methods in MedicineVolume 11 (2010), Issue 4, Pages 341-351doi:10.1080/1748670X.2010.494605`

## Modelling of Peripheral Fluid Accumulation after a Crystalloid Bolus in Female Volunteers – A Mathematical Study

1Department of Clinical Science and Education, Karolinska Institutet, Södersjukhuset, Stockholm, Sweden
2Department of Anesthesiology, Linköping University Hospital, Linköping, Sweden
3Department of Anaesthesia, Faculty of Health Sciences, Linköping University, Linköping, Sweden
4Department of Mathematical Sciences, Chalmers University of Technology and Department of Mathematical Sciences, University of Gothenburg, Gothenburg, Sweden
5Department of Anesthesiology and Intensive Care, Karolinska University Hospital, Solna, Sweden
6Department of Clinical Science and Education, Section of Anesthesiology and Intensive Care, Karolinska Institutet, Södersjukhuset, Stockholm, Sweden

Received 25 November 2009; Accepted 7 May 2010

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Objective. To simultaneously model plasma dilution and urinary output in female volunteers.

Methods. Ten healthy female non-pregnant volunteers, aged 21–39 years (mean 29), with a bodyweight of 58–67 kg (mean 62.5 kg) participated. No oral fluid or food was allowed between midnight and completion of the experiment. The protocol included an infusion of acetated Ringer's solution, 25 ml/kg over 30 min. Blood samples (4 ml) were taken every 5 min during the first 120 min, and thereafter the sampling rate was every 10 min until the end of the experiment at 240 min. A standard bladder catheter connected to a drip counter to monitor urine excretion continuously was used. The data were analysed by empirical calculations as well as by a mathematical model.

Results. Maximum urinary output rate was found to be 19 (13–31) ml/min. The subjects were likely to accumulate three times as much of the infused fluid peripherally as centrally; 1/μ = 2.7 (2.0–5.7). Elimination efficacy, Eeff, was 24 (5–35), and the basal elimination kb was 1.11 (0.28–2.90). The total time delay Ttot of urinary output was estimated as 17 (11–31) min.

Conclusion. The experimental results showed a large variability in spite of a homogenous volunteer group. It was possible to compute the infusion amount, plasma dilution and simultaneous urinary output for each consecutive time point and thereby the empirical peripheral fluid accumulation. The variability between individuals may be explained by differences in tissue and hormonal responses to fluid boluses, which needs to be further explored.