Jamal Siam is a doctoral candidate at the Department of Biomedical

Engineering at Tel Aviv University, Israel, and a lecturer at Birzeit University, Palestine (email: jsiam@birzeit.edu).

Ofer Barnea is a Professor of Biomedical Engineering at the Department of

Biomedical Engineering at Tel Aviv University, Ramat Aviv 69978, Israel (e-mail: barneao@eng.tau.ac.il).

\ \

Abstract Fluid resuscitation affects blood flow and oxygen

concentration. Administered fluid increases blood flow and

oxygen delivery rate but also decreases blood oxygen

concentration. This study aims at analyzing these two effects on

oxygen supply to tissue to determine an optimal fluid regimen.

For this purpose a hemodynamic model of the cardiovascular

system and a model of oxygen transfer to tissue were developed

and combined. Simulation results showed that indeed fluid

administration increases oxygen delivery by the blood stream.

However, oxygen transfer to tissue deteriorates during the

course of the fluid therapy due to the high sensitivity of oxygen

diffusion to oxygen partial pressure in the blood.

I. INTRODUCTION

Hemorrhagic shock is one of the most frequent aspects of

injury that trauma care emergency units have to deal with.

Advanced Trauma Life Support (ATLS) and the British

National Institute for Clinical Excellence (NHS) consider

fluid resuscitation as one of the essential procedures that

must be followed in the treatment of the hemorrhage trauma

[1,2]. Fluid resuscitation aims at maintaining oxygen

delivery to tissue and restoring hemodynamic stability.

Effectiveness of fluid resuscitation and clinical endpoint are

determined using general clinical symptoms. These

symptoms are generally a cumulative effect of several

shock and fluid therapy. Several studies used animal

experiments and other used mathematical modeling to study

and better understand the effects of hemorrhage and fluid

resuscitation on oxygen delivery and tissue perfusion. Some

of these studies focused on the cardiovascular,

hemodynamic and oxygen related phenomena at the system

level [3-17], while others developed tissue and oxygen

diffusion models using specific parameters at the tissue side

[18-30].

Despite the results of studies that indicated that fluid

infusion should be limited, many issues regarding type of

fluid, infusion rate, and infusion volume remain

controversial. Fluid replacement with crystalloid and colloid

fluids is believed to improve the hemodynamic stability, but

it has the collateral effect of diluting blood and reducing the

concentration of oxygen carriers. Therefore, there is need to

better understand the effects fluid on the actual target

parameters, i.e. oxygen partial pressure in the tissue that is

directly related to oxygen supply to the mitochondria.

II. METHODS

Two models were developed and combined: a model of

cardiovascular hemodynamics and a model of a capillary

irrigating a tissue segment. The cardiovascular model was

developed to generate a hemodynamic response and predict

blood pressure and flow as well as oxygen content in the

blood in normal conditions, hemorrhage and fluid

resuscitation. The model is described in [3]. It considers a

human body of 75 kg with a total blood volume of 5600 and

initial hematocrit of 44%. The model assumes autoregulation

mechanisms have been exhausted. The model is composed

of four cardiac chambers, a nine-segment aorta, seven

systemic branches, a systemic vein, and a pulmonary

circulation (Fig. 1). Important effects such as blood dilution,

effects of hematocrit on blood viscosity, fluid exchange

between the intravascular space and the interstitium,

bleeding and fluid infusion are also included in this module.

The tissue model was structured as a cascade of identical

tissue sample volumes (Fig. 2). Each sample volume is

based on structure and is composed of a set of

parallel cylindrical fibers [25]. Oxygen is delivered to each

cylindrical tissue segment by a concentric cylindrical blood

capillary. The model represents a single tissue element; this

into hollow tubes of equal radial thickness and equal axial

length (Fig.2). The tissue element and the capillary are both

axially segmented. Blood oxygen is assumed to diffuse

Tissue Perfusion in Fluid Therapy

Jamal Siam, and Ofer Barnea, Senior Member, IEEE

Figure 1. Structure of the hemodynamic model

Figure 2. Structure of the capillary-tissue model.

2014 Middle East Conference on Biomedical Engineering (MECBME)February 17-20, 2014, Hilton Hotel, Doha, Qatar

978-1-4799-4799-7/14/$31.00 ©2014 IEEE 196

between the capillary and the tissue cylinder in the radial

direction. However, the diffusion in the tissue is not limited

to the radial direction as in other models. The model

-

symmetric structure and no-flux condition among the

parallel cylinders from the cylindrical surfaces but the

restrictions and boundary condition have been dramatically

relaxed. Moreover, we do not impose any conditions on the

oxygen partial pressure at the venous-end of the capillary.

To study the effects of fluid therapy in controlled

hemorrhagic shock, several hemorrhagic conditions were

simulated. The hemodynamic model provided pressure and

capillary flow, hematocrit (HCT) during blood loss, infusion

and stabilization period with no infusion. Oxygen delivery

rate ( ) was calculated as the product of blood flow and

blood oxygen content. Capillary blood flow and oxygen

content were used in the capillary-tissue model to calculate

the oxygen partial pressure field in the tissue and to

determine the mean in the tissue.

III. RESULTS

The total blood losses for the various hemorrhage

conditions (class II, III, and IV) were 1100 ml, 1540 ml, and

2420 ml, respectively. Infusion of fluid caused a significant

increase in blood pressure in parallel with marked reduction

in hematocrit. Higher infusion rates induced a more

substantial increase in blood volume and arterial pressures

resulting in greater capillary flow and decrease in HCT.

After the termination of fluid infusion, intravascular fluid

volume continued to filtrate into the interstitial compartment

resulting in decrease of blood volume and mean arterial

pressure (MAP) while HCT increased.

The time-dependent pattern of the oxygen delivery rate

was similar between all classes of hemorrhage and fluid

infusion rates as shown in (Fig. 3) for class II hemorrhage.

Fluid treatment caused a significant increase in oxygen

delivery rates up to a maximum that was lower for higher

bleeding volume (905 mlO2/min, 821 mlO2/min, and 650

mlO2/min for the classes II, III, and IV, respectively).

Interestingly, similar values of maximum delivery rates were

obtained for all three infusion rates, however, higher

infusion rates were associated with earlier appearance of that

maximum. The maximal oxygen delivery rate point was

followed by a continuous decrease which was faster for

higher infusion rates and continued to decrease as long as

fluid was administrated. Following discontinuation of fluid

infusion, there was a second increase in oxygen delivery

rate, which was caused by fluid shifts from the intravascular

into the interstitial compartment and the resulting hematocrit

increase that caused an increase in oxygen delivery.

Changes in oxygen delivery occurred due to changes in

blood flow and Hct. The relative effect of each was studied

to assess the contribution of each parameter in the capillary-

tissue model. Capillary blood flow (Qc) and hematocrit (Hct)

changes during infusion are shown in Fig. 4 for class II

hemorrhage with fluid infusion rate of 80 (ml/min).

Fig. 4 starts at the point in time when hemorrhage was

controlled, hematocrit and capillary flow were decreased to

41.8% and 5.24x10-9 ml/sec, from the original normal

values of 44% and 7.7x10-9 ml/sec, respectively. During

fluid infusion capillary flow was increased while hematocrit

decreased continuously. The final value of hematocrit at the

complete recovery of capillary flow (7.7x10-9 ml/sec) was

35.7% (Fig. 4).

Using the capillary-tissue model, assuming 98%

saturation, a field in a tissue segment was generated for

different values of capillary flow and Hct. The mean value

of oxygen partial pressure in the tissue segment

was calculated for each combination of capillary flow and

blood oxygen content. Fig. 5 shows a contour map where

in a tissue segment is depicted as a function of

capillary flow and Hct.

Figure 4. Effects of infusion on HCT and capillary blood flow. Blood

volume represents the amount remaining after hemorrhage was

controlled plus infused fluid.

Figure 3. Oxygen delivery rate ( ) as a function of time during

bleeding, fluid infusion and following end of infusion for class II

hemorrhage.

197

Fig. 5 shows that is more sensitive to Hct than to

capillary flow, especially in the low capillary flow and low

Hct values. In the normal range, the line are approximately

at 45 degrees, indicating same sensitivity to the two

parameters.

Combinations of Capillary flow and Hct taken from Fig 4

were marked by black circles in Fig 5. The temporal

direction of this trajectory begins on the right at high values

of Hct and low values of capillary flow as occurs following

hemorrhage and hemorrhage control. The trajectory moves

up and to the left while crossing isobaric lines into lower

levels of oxygen partial pressure. Average partial pressure of

oxygen in the tissue segment decreased continuously from

22.8 mmHg to 21 mmHg during all the course of fluid

replacement as shown by Fig.5.

Fig 6 summarizes the effects of the two parameters on

mean tissue oxygen partial pressure . It shows that

indeed is more sensitive to Hct than it is to flow.

IV. DISCUSSION

Fluid infusion increases blood flow. It is perceived as

restoration of the circulation and that it improves oxygen

delivery to the tissue. According to our study, this is true to a

limited extent. According to our model predictions,

continuing fluid infusion beyond the point of maximum

oxygen delivery will be harmful due to the continuing drop

in . Therefore, based on oxygen delivery rate, restoring

hemodynamic stability should be practiced only during the

increasing phase. During this phase the effect of

increased cardiac output on oxygen delivery is higher than

the deterioration caused by blood dilution. Fluid infusion

should be terminated before this point to maintain the

advantages of fluid therapy on oxygen transport. Looking

deeper into the tissue allows better insight into the actual

oxygen supply t luid therapy indeed seems

to be useful in increasing before the maximum point.

However, analysis of tissue oxygenation during fluid

administration reveals that tissue perfusion is improved only

when blood oxygen concentration is preserved. This is true

with the autoregulation mechanisms that increase blood flow

and maintains hematocrit, and consequently improves tissue

perfusion to vital organs. When crystalloid and colloid fluids

are used they dilute blood and decrease hematocrit.

Consequently, capillary oxygen concentration decreases.

Simulation results showed that the hemodynamic pathway of

hematocrit-capillary flow generated by fluid therapy, causes

a continuous decrease of in tissue. This fact is due to the

sensitivity of oxygen diffusion between capillary and tissue

to oxygen concentration. Therefore, fluid therapy with

solutions that do not include oxygen carrier will restore the

circulation, but without maintaining oxygen partial pressure

in the blood, oxygen supply to the tissue will deteriorate.

V. CONCLUSIONS

Fluid therapy with crystalloid and colloid fluid is useful to

restore hemodynamic stability and increase oxygen delivery

in blood. However, fluid therapy with fluids that do not

include oxygen carriers dilute the blood. This results in

lower oxygen transport to the tissue despite the increase in

blood flow.

VI. REFERENCES

[1] American College of Surgeons, Advanced Trauma Life

Support for Doctors, 8thed, American College of

Surgeons, 2008..

[2] National Institute for Clinical Excellence Excellence

therapy in trauma, issue 2004, National Institute for

Clinical Excellence, 2007.

[3] J. Siam, et al., "Optimization of Oxygen Delivery in

Fluid Resuscitation for Hemorrhagic Shock: A

Figure 5. Mean values of oxygen partial pressure in a tissue segment

for different combinations of capillary flow and Hct. The black circles depict the specific combinations shown in Fig 4 during infusion

following class II hemorrhage.

Figure 6. Effects of Hct and capillary flow on mean oxygen partial pressure of a tissue segment.

198

Computer Simulation Study" Cardiovascular

Engineering and Technology , Vols.

DOI10.1007/s13239-013-0169-z, 2013.

[4] J. Boldt and C. Ince, "The impact of fluid therapy on

microcirculation and tissue oxygenation in

hypovolemic patients: a review," Intensive Care Med,

vol. 36, p. 1299 1308, 2010.

[5] A. Dubin, et al., "Systemic and microcirculatory

responses to progressive hemorrhage," Intensive Care

Med , vol. 35, p. 556 564, 2009 ..

[6] J. Elmer, et al. "Hemoglobin-based oxygen carriers for

hemorrhagic shock," Resuscitation, vol. 83, pp. 285-

292, 2012.

[7] T. Moschandreou,et al., "Influence of tissue metabolism

and capillary oxygen supply on arteriolar oxygen

transport: A computational model," Mathematical

Biosciences , vol. 232, p. 1 10, 2011.

[8] T. Tatara,et al., "Crystalloid infusion rate during fluid

resuscitation from acute haemorrhage," British Journal

of Anaesthesia , vol. 99, no. 2, p. 212 217, 2007.

[9] P. Perel, et al., "Colloids versus crystalloids for fluid

resuscitation in critically ill patients (Review)," The

Cochrane Collaboration. Published by JohnWiley &

Sons, Ltd., no. Issue 2, 2013.

[10] S. Gundersen, et al., "Mathematical model of NO and

O2 transport in an arteriole facilitated by hemoglobin

based O2 carriers," Biophys. Chem., vol. 143, no. 1,

2009.

[11] H. Santry and H. Alam, "Fluid resuscitation: past,

present, and the future," Shock, vol. 33, pp. 229-241,

2010..

[12] S. Simpson et al., "A computer model of major

haemorrhage and resuscitation," Med. Eng. Phys., vol.

18, no. 4, pp. 339-343, 1996.

[13] C. Gyenge et al., "Transport of fluid and solutes in the

body I.Formulation of a mathematical model," Am J

Physiol Heart Circ Physiol, vol. 277, pp. 215-227,

1999.

[14] C. Gyenge et al., "Transport of fluid and solutes in the

body II. validation and implications," Am J Physiol

Heart Circ Physiol, vol. 277, pp. 1228-1240, 1999.

[15] A. Hedlund et al., "Computer Methods and Programs in

Biomedicine," Elsevier, vol. 27, pp. 7-21, 1988.

[16] Barnea O. and Sheffer N., "A computer model for

analysis of fluid resuscitation," Computers in Biology

and Medicine, vol. 23, no. 6, 1993.

[17] M. Mazzoni et al., "Dynamic fluid redistribution in

hyperosmotic resuscitation of hypovolumic

hemorrhage," AM J Physiol, vol. 255, pp. 629-637,

1988.

[18] N. Safaeian and T. David, "A computational model of

oxygen transport in the cerebrocapillary levels for

normal and pathologic brain function," Journal of

Cerebral Blood Flow & Metabolism, vol. 33, p. 1633

1641, 2013.

[19] C. Beynon, et al., "Brain Tissue Oxygen Monitoring

and Hyperoxic Treatment in Patients with Traumatic

Brain Injury," JOURNAL OF NEUROTRAUMA , vol.

29, p. 2109 2123, 2012.

[20] J. Spires, et al., "Model analysis of the relationship

between intracellular PO2 and energy demand in

skeletal muscle," Am J Physiol Regul Integr Comp

Physiol, vol. 303, pp. 1110-1126, 2012.

[21] D. Goldman, " A mathematical model of oxygen

transport in intact muscle with imposed surface

oscillations," Math. Biosc, vol. 213, 2008..

[22] K. Masamoto and K. Tanishita, "Oxygen transport in

brain tissue," J Biomech Eng , vol. 131, no. 074002,

2009.

[23] D. Goldman, " Theoretical models of microvascular

oxygen transport to tissue," Microcirculation, pp. 15(8):

795-811, 2008.

[24] A. Popel, " Theory of oxygen transport to tissue," Crit

Rev Biomed Eng, pp. 17(3):257-321, 1989.

[25] A. Krogh, " The number and distribution of capillaries

in muscles with calculations of the oxygen pressure

head necessary for supplying the tissue," . J Physiol,,

pp. 52(6):409-15, 1991.

[26] B. McGuire and T. Secomb., " Estimation on capillary

density in human skeletal muscle based on maximal

oxygen consumption rates," Am J. Physiol. Heart Circ.

Physiol., p. 285:2382 2391, 2003.

[27] J. Blum, " Concentration profiles in and around

capillaries," Am J Physiol., pp. 198: 991-998, 1960.

[28] J. Whiteley et al., " Mathematical modelling of oxygen

transport to tissue," J Math Biol, pp. 44(6): 503-522 ,

2002.

[29] D. Reneau et al., "A mathematical simulation of

release, diffusion, and consumption in the capillaries

and tissue of the human brain," Chemical Engineering

in Medicine and Biology, p. 135, 1967.

[30] D. Reneau et al., "A digital simulation of transient

oxygen transport in capillary-tissue systems (cerebral

gray matter). Development of a numerical method for

solution of transport equations describing coupled

convection-diffusion systems," AIChE J, p. 15: 916,

1969.

199