Mathematical modelling of clinical applications in fluid therapy

Abstract

Background: This thesis presents a new application of fluid kinetic analysis using mathematical tools to evaluate fluid therapy problems. Several models were developed to mathematically handle fluid distribution concerning bleeding and anaesthesia, arterio-venous differences in plasma dilution, peripheral fluid accumulation and differences in fluid distribution among young and elderly patients. Non-linear regression models were used to fit equations to sampled haemoglobin data.

Methods: I: Six chronically instrumented sheep were subjected to four randomly ordered experiments while conscious or during anesthesia with isoflurane. After plasma volume measurement 15% or 45% of the blood volume was withdrawn. To quantify transcapillary refill, mass balance and kinetic calculations utilized repeated measurements of haemoglobin concentration. II: Fifteen volunteers received an intravenous (iv) infusion of 15 mL/kg of lactated Ringer s solution during 10 min. Simultaneous arterial and venous blood haemoglobin (Hb) samples were obtained and Hb concentrations measured. III: Ten healthy female non-pregnant volunteers participated. The protocol included an infusion of acetated Ringer s solution, 25 ml/kg over 30 minutes. Blood samples were repeatedly. A standard bladder catheter was continuously monitoring urine excretion. Plasma dilution, peripheral accumulation and urine output were modelled simultaneously. IV: Twenty four volunteers participated. Two age groups, a young group (age 18-25) and an elderly group (age 70-90) were formed. On separate occasions, the subjects in both groups were given a crystalloid 25 mg/ml glucose solution, either orally (ORAL) or intravenously (IV) in a crossover design with at least two weeks in between. On each occasion, the subjects got 7 ml/kg of the crystalloid solution during 15 minutes.

Results: I: After either normotensive or hypotensive hemorrhage, transcapillary refill occurred more rapidly during the first 40 min than during the next 140 min (p < 0.001). In conscious sheep, at 180 min, 57% and 42% of the bled volume had been restored after normotensive and hypotensive hemorrhage, respectively, in contrast to only 13% and 27% (p < 0.001) in isoflurane-anesthetized sheep. Using parameters derived from kinetic analysis, simulations illustrate that both the hydrostatic and colloid osmotic forces are weaker in the presence of isoflurane than in the awake state.

II: The AV difference in plasma dilution was only positive during the infusion and for 2.5 min thereafter, which represents the period of net flow of fluid from plasma to tissue. Kinetic analysis showed that volume expansion of the peripheral fluid space began to decrease 14 min (arterial blood) and 20 min (venous blood) after the infusion ended.

III: 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; 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 to 17 (11 - 31) min.

IV: The lag-time of glucose given orally was estimated to be 17 (8 25) min for the younger group and 18 (13 22) min for the elderly. For fluid, the lag-time was estimated to 29 (21 - 34) min for the younger and 25 (16 39) min for the elderly.

Conclusions: Final conclusion is that mathematical modelling of clinical applications can be done in several different clinical settings and will improve the understanding of fluid distribution. It is possible to continuously model fluid behaviour in the body as seen in Papers II-III. This should enhance the understanding of accumulating oedema in the body which is an apparent problem for all clinicians.