The passage of a diffusible indicator through a microvascular system.

THE AIM: (1) To develop a mathematical model of the passage of a diffusible indicator through microcirculation based on a stochastic description of diffusion and flow; (2) To use Goresky transform of the dilution curves of the diffusible indicators for the estimation of the permeability of a tissue-capillary barrier. THE METHOD: We assume that there are two causes for flow to be stochastic: (a) All microvessels are divided between open and closed microvessels. There exists random exchange between the two groups. (b) The flow through open microvessels is also random. We assume that each diffusing tracer has a probability to leave the intravascular space, and has a probability to return. We also assume that all considered processes are stationary (stability of microcirculation). CONCLUSION: (a) The distribution of the time to pass microcirculation by diffusing indicator is given by a compound Poisson distribution; (b) The permeability of tissue-capillary barrier can be obtained from the means, delay, and dispersions of the dilutions of intravascular and diffusing traces.

Theory and in vitro validation of a new extracorporeal arteriovenous loop approach for hemodynamic assessment in pediatric and neonatal intensive care unit patients.

OBJECTIVES: No simple method exists for repeatedly measuring cardiac output in intensive care pediatric and neonatal patients. The purpose of this study is to present the theory and examine the in vitro accuracy of a new ultrasound dilution cardiac output measurement technology in which an extracorporeal arteriovenous tubing loop is inserted between existing arterial and venous catheters. DESIGN: Laboratory experiments. SETTING: Research laboratory. SUBJECTS: None. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: In vitro validations of cardiac output, central blood volume, total end-diastolic volume, and active circulation volume were performed in a model mimicking pediatric (children 2-10 kg) and neonatal (0.5-3 kg) flows and volumes against flows and volumes measured volumetrically. Reusable sensors were clamped onto the arterial and venous limbs of the arteriovenous loop. A peristaltic pump was used to circulate liquid at 6-12 mL/min from the artery to the vein through the arteriovenous loop. Body temperature injections of isotonic saline (0.3-10 mL) were performed. In the pediatric setting, the absolute difference between cardiac output measured by dilution and cardiac output measured volumetrically was 3.97% +/- 2.97% (range 212-1200 mL/min); for central blood volume the difference was 4.59% +/- 3.14% (range 59-315 mL); for total end-diastolic volume the difference was 4.10% +/- 3.08% (range 24-211 mL); and for active circulation volume the difference was 3.30% +/- 3.07% (range 247-645 mL). In the neonatal setting the difference for cardiac output was 4.40% +/- 4.09% (range 106-370 mL/min); for central blood volume the difference was 4.90% +/- 3.69% (range 50-62 mL); and for active circulation volume the difference was 5.39% +/- 4.42% (range 104-247 mL). CONCLUSIONS: In vitro validation confirmed the ability of the ultrasound dilution technology to accurately measure small flows and volumes required for hemodynamic assessments in small pediatric and neonatal patients. Clinical studies are in progress to assess the reliability of this technology under different clinical situations.

Regulation of oxygen consumption by vasomotion.

OBJECTIVE: To describe a stochastic model of the variability and heterogeneity of blood flow through the microcirculation, and to show the ability of vasomotion to vary oxygen consumption at a steady blood flow. METHODS: The description of vasomotion is based on whether each microvessel is open for blood flow or closed. Over a unit time period, let alpha be the probability that a given vessel is open and will remain open, beta be the probability that an open vessel will close, nu be the probability that a closed vessel will remain closed, and mu be the probability that a closed vessel will become open. Two main parameters that characterize such a scheme are: the fraction of open microvessels [n o= mu/(beta+mu)], and the rate of vasomotion defined as the rate of switching between open and closed microvessels (R=beta+mu). A model of O2 transport to tissues is based on the following assumptions: (a) the flux of O2 is due to passive diffusion, (b) the amount of O2 dissolved in tissue is negligible as compared with that contained in arterial blood, and (c) aerobic metabolism is proportional to the delivery of O2. RESULTS: The stochastic model substantiates the possibility that vasomotion can control O2 consumption. The rate of vasomotion activity can change O2 consumption by 2-8-fold, depending on the fraction of open microvessels. CONCLUSION: A stochastic description of blood flow through the microcirculation system demonstrates that vasomotion rate could be a factor influencing O2 consumption.

Vasomotion model explanation for urea rebound.

Urea rebound after hemodialysis is generally attributed to urea entering the circulation from poorly perfused tissue and/or entering from regions with low membrane permeability for urea. Another explanation for rebound is based on disorders in the microcirculation, connected with the phenomenon of vasomotion, i.e., cyclic opening and closing of microvessels. The purpose of the following mathematical model is to explain observed urea rebound by the vasomotion phenomenon. The significance of vasomotion is related to the fact that a significant fraction, up to 80-95%, of all microvessels are closed while others are being perfused. The rate with which open microvessels "migrate" through the tissue determines quality of perfusion. A stochastic scheme for describing vasomotion is developed. Probabilities to change the state of microvessels are defined as follows: alpha = probability to be open and remain open; beta = to be open and become closed; v = to be closed and remain closed; mu = to be closed and become open. The activity of vasomotion is defined by the rate of vasomotion, R, R = beta + mu, and can be measured using a curve of urea concentration.