Oxygen Transport in the Microvessel Network

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Oxygen Transport in the Microvessel Network

Kazuo Tanishita

¹

, Kazuto Masamoto

¹

, Tomoko Negishi

¹

, Naosada Takizawa

²

, and Hirosuke Kobayashi

²

Summary. Oxygen delivery in the brain tissue is carried out by a diffusion process principally determined by spatial differences of partial pressure of oxygen (pO

2

). Previous studies identiﬁed inhomogeneous distribution of cerebral tissue pO

2

. This inhomogeneous pO

2

distribution might be related to spatial variations in microvascular structure, because a large amount of oxygen is supplied from microvascular network. In this study, to evaluate the oxygen transport in the cerebral cortex, we focused on regional structure of microvascular network and pO

2

distribution in the rat somatosensory cortex.

To this end, ﬁrstly, we characterized local tissue pO

2

distribution by using an oxygen microelectrode. Secondly, we quantiﬁed three-dimensional micro- vascular structure by combining a traditional method for casting blood capillaries with quantitative analysis by using confocal laser-scanning micro- scope. Finally, the regional variations in oxygen transport were estimated by using numerical simulation of oxygen transport based on these experimen- tal data (i.e., pO

2

distribution and microvascular structure).

Key words: Oxygen transfer, Cerebral cortex, Blood ﬂow, Microvessels, Com- puter simulation

Introduction

The brain is a highly oxidative organ and its consumption rate of oxygen accounts for 20% of that of the whole body. This large consumption rate must be met by continuous supply of oxygen, because lack of oxygen rapidly causes

13

1

Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yoko- hama, Japan

2

School of Allied Health Sciences, Kitasato University, Center of Information Science,

Kitasato University, 1-15-1 Kitasato, Sagamihara, Kanagawa, Japan

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irreversible damage to central nervous system. Acute hypoxic episodes cause a certain pattern of regional damage [1]. The cerebral cortex (e.g., layers III, V, and VI) is one of the most susceptible regions to hypoxia, and damage to sensorimotor function is particularly severe in humans that survive hypoxic/ischemic episodes. However, little is known about whether oxygen transport in intracortical regions relates to such selective vulnerability to hypoxia.

In the cerebral cortex, anatomical, metabolic, and functional variations occur in local regions [2,3], indicating that these spatial variations might be related to the selective damage to hypoxia in the cerebral cortex. Therefore, we need to assess the oxygen transport in the cerebral cortex, and to consider the spatial variations in structure and function of the cerebral cortex.

In the present study, to evaluate the oxygen transport in the cerebral cortex, we ﬁrstly measured pO

2

distribution in the rat somatosensory cortex by using an oxygen microelectrode. Secondly, we quantiﬁed three-dimensional microvascular structure in the rat somatosensory cortex using a confocal laser-scanning microscope (CLSM). Thirdly, regional variations in oxygen transport in the rat somatosensory cortex were estimated by using numerical simulation of oxygen transport based on such experimental values of tissue partial pressure of oxygen (pO

2

) distribution and microvascular structure.

Materials and Methods

Measurement of Tissue pO

₂

Distribution

Six male Wistar rats (9 weeks old) weighing 280–290 g were used for these experiments. The procedure in detail is described in [4]. Animal protocols were approved by the Bio Ethics Committee of the Faculty of the Science and Technology, Keio University.

The oxygen microelectrode was constructed according to the procedure developed by Baumgärtl and Lübbers [5], which is described in detail in [4].

The diameter of the electrode tip ranged from 2 to 10 mm.

Tissue pO

2

was measured perpendicularly from the dorsal surface at depth intervals of a 0.02 mm by positioning the microelectrode with a micro- manipulator (ME-71, Narishige Scientiﬁc Instrument Lab, Tokyo, Japan).

Location for the pO

2

measurement was selected based on a published brain

map [6]. The position at which the microelectrode tip ﬁrst contacted the cere-

bral surface was deﬁned as 0 mm depth. Oxygen current was measured by

using a micro-ammeter (R8340A, Advantest, Tokyo, Japan) with the voltage of

0 .65 V applied. The recorded current was converted into pO

2

values by using

the calibration curve. The average pO

2

is represented here as mean ± SD. Sta-

tistical signiﬁcance was determined by a Student’s t-test and set at P < 0.05.

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Microvascular Density

The reconstructed images of the rat primary somatosensory cortex were sep- arated into four major cortical areas (BF: barrel ﬁeld; FL: forelimb region; Tr:

trunk region; and HL: hindlimb region) and identiﬁed with a published brain map [6]. To calculate microvascular density, we extracted rectangular samples in each cortical area with perpendicular to the brain surface from the recon- structed image. We determined the microvascular density proﬁle in each cor- tical area by calculating the number of black pixels (i.e., the number of vessels) parallel to the brain surface at each depth (each pixel was 1.43 mm) through the entire length of the extracted samples and then dividing the sum of the number of vessels at each depth by the width (in millimeters) of the sample.

Consequently, successive depth proﬁle of the microvascular density (in number of vessels per millimeter) was established at 1.43-mm (one pixel) intervals.

Numerical Simulation of Oxygen Transport

Based on the confocal microscopic images of the cerebral microvascular network, we calculated three-dimensional pO

2

distribution using ﬂow and mass transfer modeling software (FLUENT; Fluent, Lebanon, NH, USA). Flow rate in the arteriole side was assigned in accordance with Poiseuille’s law, the Hill equation was applied to consider the oxyhemoglobin dissociation curve in blood, and the facilitated diffusion coefﬁcient was also incorporated. For the boundary conditions between tissue and vascular wall, equivalent pO

2

and oxygen ﬂux were assigned, as described in Table 1. Figure 1 illustrates the model for superﬁcial and middle layers, and the geometries of arteriole and capillary were determined by microscopic measurements using a confocal laser scanning microscope and micro computed tomography (CT).

Table 1. Assumptions for the calculation

• The oxygen gradient at the edge of module unit is zero

• The oxygen consumption rate is zero in the superﬁcial layer up to 100 mm depth

• Matching ﬂux at the vessel wall

Superﬁcial layer Middle layer

Arteriole inlet Po

2

100 mmHg 85 mmHg

Capillary inlet Po

2

50 mmHg 50 mmHg

CBF (cm

³

/100 g/min) 153 247

CBF, cerebral blood ﬂow

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Results

Depth Proﬁle of Tissue pO

₂

Distribution

Average pO

2

proﬁles of all measurements revealed areal differences in local pO

2

among adjacent cortical areas (HL, FL, and Tr) in rat somatonsensory cor- tex, as shown in Fig. 2. The large error bars at each depth (0.02-mm intervals) indicate spatial variation among single trials in different measurements. In contrast, temporal change of pO

2

in each position was less than about 10% of the average pO

2

at a single position for all three areas. Comparison between HL and FL (Fig. 2A and B) shows that their pO

2

proﬁles were similar, wheaeas the pO

2

proﬁle for the Tr (Fig. 2C) shows a relatively constant yet low average pO

2

. Correspondingly, histological structure did not differ between the HL and FL, whereas the Tr had signiﬁcantly thinner layers IV–VI compared with the same layers in the HL and FL (Fig. 2). Although no sign of tissue hypoxia speciﬁc to the respective layers was observed, comparison of all of the meas- urements reveal that the average pO

2

in the Tr (14 ± 10 torr) signiﬁcantly dif- fered from that in the HL (25 ± 13 torr) and FL (24 ± 13 torr).

Fig. 1. Geometries of arteriole and capillary for superﬁcial and middle layers

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Figure 3 shows a typical profile of average microvascular density at each depth in the BF from all 176 samples. This figure reveals specificity of suc- cessive depth variation in microvascular density in the intracortical region.

Although each individual density proﬁle had many sharp peaks, this average

density proﬁle showed no such peaks because the peaks in microvascular

density (horizontal branches of microvessels) did not depend on speciﬁc

depths. The microvascular density signiﬁcantly increased in layers I–III from

the brain surface toward layer IV, and slightly decreased in layers V–VI to

white matter. The average density proﬁle also showed two characteristic

plateau regions, i.e., at depths of 0.3–0.8 mm and 1.0–1.5 mm. The former

Fig. 2. Depth proﬁles of tissue pO

2

distribution for somatosensory areas hind limb (HL),

fore limb (FL), and trunk (Tr)

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plateau in the middle layers (III–IV) was almost 50% higher in microvascu- lar density than that in the superﬁcial layers (I–II).

Contribution of Arteriole and Capillary to O

₂

Supply

We calculated the oxygen supply from arteriole and capillary. Figure 4 shows the ratio of oxygen supply from capillary S

cap

and from arteriole S

art

as a func- tion of cerebral blood ﬂow (CBF) rate. If S

cap

/S

art

becomes larger, capillary con- tribution becomes larger. In both layers, when only arteriole CBF increased by 30%, S

cap

/S

art

slightly dropped due to the increased supply from arteriole.

However, the S

cap

/S

art

increases with the increase of capillary CBF. Overall, the contribution of capillary was higher in the upper layer than in the middle layer. In contrast, the contribution of arteriole was higher in the middle layer than in the upper layer.

Discussion

Spatial Variations in pO

2

Distribution

Our results of spatial variations in pO

2

distribution reﬂect spatial variations

in microvascular structure [7], microcirculation, and neuronal activity,

because tissue pO

2

is determined by the oxygen content of blood, the rate of

blood ﬂow, and the rate of cellular oxygen consumption [8]. Although local

Fig. 3. Depth proﬁle of capillary density

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pO

2

temporally varied in some measurements, the temporal pO

2

changes were not signiﬁcant because changes in tissue pO

2

during measurements of 10 s at the single position were small (<10% of average pO

²

) in all trials. Such tem- poral changes in pO

2

were possibly caused by spontaneous vasomotion of localized small blood vessels [9]. In relation to the spatial variations in pO

2

distribution, we focused on cytoarchitectural differences between cortical areas because cytoarchitecture is closely related to cerebral function and metabolic activity. Consequently, a close correlation between cytoarchitecture and pO

2

distribution was revealed (Fig. 2). This result suggests that cerebral tissue pO

2

is strongly dependent on anatomical structure in the cerebral cortex.

We also identiﬁed pO

2

change due to the somatosensory stimulation [4] in the rat experiment. The pO

2

on the area of hindlimb and forelimb increased on stimulation, while pO

2

on the area of trunk decreased on stimulation. This may be explained by the regional variation of the balance between the oxygen demand and supply.

We should note the dynamic change of pO

2

for the nervous stimulation. We discovered a biphasic change of pO

2

in the cerebral tissue of hamster [10], and the tissue pO

2

in the activated region initially decreased during the 3 s after the onset of acoustic stimulation and then increased during the successive seconds. This may be explained by the delayed onset of the increase in Fig. 4. Oxygen supply ratio as a function of cerebral blood ﬂow (CBF) in the arteriole and capillary. Total rCBF parameter: (1) control ﬂow; (2) arteriole CBF 30% up; (3) arteriole CBF 30% up + capillary CBF 33% up; (4) arteriole CBF 30% up + capillary CBF 100% up.

Scap, oxygen supply from capillary; Sart, oxygen supply from arteriole

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cerebral blood ﬂow, i.e., the initial decrease in tissue pO

2

is coupled to the induced neural activity and depends on the response time of the local increase in cerebral blood ﬂow.

As we need to know how the blood ﬂow contributes to the supply of oxygen into the cerebral tissue, we performed the computer simulation of oxygen proﬁle. These considerations led us to investigate the role of arteriole and cap- illary networks for the oxygen transfer to tissue. In the middle layer, O

2

supply from arteriole was effective, because penetrating arteriole has some branches at this depth and distributes the blood ﬂow into tissue. On the contrary, oxygen supply from capillary networks in the upper layer comes from the adjacent module or bottom layer.

Therefore, in neuronal activity the cerebral tissue may facilitate the effec- tive O

2

transfer mechanism and necessary oxygen is transported to the local- ized region of high O

2

demand by arteriole, and the upper layer receives the oxygen through capillary networks from the nearby cortex.

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