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Jansson L, Barbu A, Bodin B, Drott CJ, Espes D, Gao X, Grapensparr L, Källskog Ö, Lau J, Liljebäck H, Palm F, Quach M, Sandberg M, Strömberg V, Ullsten S, Carlsson PO. Pancreatic islet blood flow and its measurement. Ups J Med Sci 2016; 121:81-95. [PMID: 27124642 PMCID: PMC4900068 DOI: 10.3109/03009734.2016.1164769] [Citation(s) in RCA: 100] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Pancreatic islets are richly vascularized, and islet blood vessels are uniquely adapted to maintain and support the internal milieu of the islets favoring normal endocrine function. Islet blood flow is normally very high compared with that to the exocrine pancreas and is autonomously regulated through complex interactions between the nervous system, metabolites from insulin secreting β-cells, endothelium-derived mediators, and hormones. The islet blood flow is normally coupled to the needs for insulin release and is usually disturbed during glucose intolerance and overt diabetes. The present review provides a brief background on islet vascular function and especially focuses on available techniques to measure islet blood perfusion. The gold standard for islet blood flow measurements in experimental animals is the microsphere technique, and its advantages and disadvantages will be discussed. In humans there are still no methods to measure islet blood flow selectively, but new developments in radiological techniques hold great hopes for the future.
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Affiliation(s)
- Leif Jansson
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
- CONTACT Leif Jansson, Department of Medical Cell Biology, Biomedical Centre, Box 571, Husargatan 3, SE-75123 Uppsala, Sweden
| | - Andreea Barbu
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Birgitta Bodin
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Carl Johan Drott
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Daniel Espes
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
- Department of Medical Sciences, Uppsala University, Uppsala, Sweden
| | - Xiang Gao
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Liza Grapensparr
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Örjan Källskog
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Joey Lau
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Hanna Liljebäck
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Fredrik Palm
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - My Quach
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Monica Sandberg
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | | | - Sara Ullsten
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
| | - Per-Ola Carlsson
- Department of Medical Cell Biology, Uppsala University, Uppsala, Sweden
- Department of Medical Sciences, Uppsala University, Uppsala, Sweden
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Barbu A, Jansson L, Sandberg M, Quach M, Palm F. The use of hydrogen gas clearance for blood flow measurements in single endogenous and transplanted pancreatic islets. Microvasc Res 2014; 97:124-9. [PMID: 25446368 DOI: 10.1016/j.mvr.2014.10.002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2014] [Revised: 10/07/2014] [Accepted: 10/15/2014] [Indexed: 12/20/2022]
Abstract
The blood perfusion of pancreatic islets is regulated independently from that of the exocrine pancreas, and is of importance for multiple aspects of normal islet function, and probably also during impaired glucose tolerance. Single islet blood flow has been difficult to evaluate due to technical limitations. We therefore adapted a hydrogen gas washout technique using microelectrodes to allow such measurements. Platinum micro-electrodes monitored hydrogen gas clearance from individual endogenous and transplanted islets in the pancreas of male Lewis rats and in human and mouse islets implanted under the renal capsule of male athymic mice. Both in the rat endogenous pancreatic islets as well as in the intra-pancreatically transplanted islets, the vascular conductance and blood flow values displayed a highly heterogeneous distribution, varying by factors 6-10 within the same pancreas. The blood flow of human and mouse islet grafts transplanted in athymic mice was approximately 30% lower than that in the surrounding renal parenchyma. The present technique provides unique opportunities to study the islet vascular dysfunction seen after transplantation, but also allows for investigating the effects of genetic and environmental perturbations on islet blood flow at the single islet level in vivo.
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Affiliation(s)
- Andreea Barbu
- Department of Medical Cell Biology, Uppsala University, Sweden; Department of Immunology, Genetics and Pathology, Uppsala University, Sweden.
| | - Leif Jansson
- Department of Medical Cell Biology, Uppsala University, Sweden.
| | - Monica Sandberg
- Department of Medical Cell Biology, Uppsala University, Sweden.
| | - My Quach
- Department of Medical Cell Biology, Uppsala University, Sweden.
| | - Fredrik Palm
- Department of Medical Cell Biology, Uppsala University, Sweden; Department of Medical and Health Sciences, University of Linköping, Sweden.
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Granstam SO, Granstam E. Endothelin-induced changes in blood flow in STZ-diabetic and non-diabetic rats: relation to nitric oxide synthase and cyclooxygenase inhibition. J Physiol Sci 2011; 61:497-505. [PMID: 21881977 PMCID: PMC3204103 DOI: 10.1007/s12576-011-0171-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2011] [Accepted: 08/09/2011] [Indexed: 01/18/2023]
Abstract
In this study, using the microsphere method, the hemodynamic response to endothelin-1 (ET-1) in healthy and streptozotocin (STZ)-diabetic rats was evaluated as well as the influences of inhibition of nitric oxide (NO)-synthase using L-NAME (Nω-nitro-L: -arginine methyl ester) and the cyclooxygenase inhibitor indomethacin. Blood flow (Q) was measured in tissues of interest for vascular complications in diabetes such as kidney, eye, brain, heart and skeletal muscle with the main focus on ophthalmic circulation. Under resting conditions, evidence for renal vasoconstriction was found in diabetic animals. In both groups, administration of L-NAME reduced Q in all investigated tissues indicating a basal NO influence. In the normal rats, ET-1 induced a significant increase in blood pressure and intense vasoconstriction in all tissues except in the choroid of the eye and in the brain, where it induced an increased Q. In the STZ-diabetic rats, effects of ET-1 were less pronounced. Pretreatment with L-NAME, but not the cyclooxygenase inhibitor, abolished the ET-1-induced vasodilation in the choroid of both groups. Administration of ET A receptor antagonist BQ-123 reduced the ET-1-induced vasodilation in the choroid only in diabetic animals. In conclusion, evidence for altered vascular endothelial response to ET-1 in STZ-diabetic animals was found particularly in the ophthalmic circulation. The findings suggest differential involvement of receptors in the response to ET-1 in normal and STZ-diabetic animals.
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Affiliation(s)
- Sven-Olof Granstam
- Department of Medical Sciences, Clinical Physiology, Uppsala University, Uppsala, Sweden.
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Abstract
A number of different qualitative and quantitative techniques have been used to measure inner ear blood flow and all have required that the animal be anesthetized. It is well known that anesthesia can cause a variety of circulatory as well as other systemic changes. In this study, we have employed a technique commonly used for quantifying brain blood flow, the iodo[(14)C]antipyrine technique ([(14)C]IAP). Unlike other techniques, [(14)C]IAP can be used in unanesthetized animals under conditions that are nearly normal, it is non-invasive, it can be used reliably in regions of low local blood flow, and data can be acquired from both the periphery and central nervous system. Results show that blood flow to the lateral wall of the basal turn of the cochlea (387 +/- 19 microl/g/min) is significantly higher (P<0.001) than that of the utricular macula (189 +/- 23 microl/g/min), horizontal (186 +/- 22 microl/g/min), superior (185 +/- 22 microl/g/min), or posterior canal crista (185 +/- 25 microl/g/min). Surprisingly, blood flow to all of the vestibular end-organs is remarkably similar. The use of this technique should allow pharmacological experimentation on inner ear blood flow without the unknown complications of anesthesia or invasive procedures.
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Affiliation(s)
- M J Lyon
- Department of Otolaryngology and Communication Sciences, SUNY Upstate Medical University, Syracuse, NY 13210, USA.
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Granstam E, Granstam SO. Regulation of uveal and retinal blood flow in STZ-diabetic and non-diabetic rats; involvement of nitric oxide. Curr Eye Res 1999; 19:330-7. [PMID: 10520229 DOI: 10.1076/ceyr.19.4.330.5300] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
PURPOSE In experimental and human diabetes mellitus evidence for an impaired function of the vascular endothelial cells has been found. The purpose of the present experiments was to measure uveal and retinal blood flow and vascular resistance at an early stage of experimental diabetes mellitus and to evaluate the effects of acetylcholine and L-arginine in control and L-NAME-pretreated animals. METHOD The radioactively labelled microsphere method was applied to normal Sprague-Dawley rats and rats with STZ-induced diabetes of three weeks duration. RESULTS In the present study, similar blood flow and vascular resistance were observed in the uvea of normal and STZ-diabetic rats. Evidence for a basal vasodilating NO-tone was found both in the uvea and in the retina of both groups. In the normal rats as well as in the diabetic animals, acetylcholine induced choroidal vasodilation. Local blood flow increased from 54 +/- 17 to 142 +/- 32 mg x min(-1) in normal rats and from 57 +/- 18 to 112 +/- 23 mg x min(-1) in diabetic rats (P < 0.05 respectively). No hemodynamic changes were observed in the anterior uvea, demonstrating a difference in reactivity between these vascular beds. In animals pretreated with the NO-synthase inhibitor L-NAME, acetylcholine did not significantly affect local blood flow in the choroid, suggesting NO as a mediator of the vasodilation. CONCLUSION The results indicate a normal action of NO in the ocular vascular beds at this stage of experimental diabetes mellitus in the rat.
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Affiliation(s)
- E Granstam
- Department of Neuroscience/Ophthalmology, University Hospital, Uppsala, Sweden.
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Granstam E, Granstam SO, Fellström B, Lind L. Endothelium-dependent vasodilation in the uvea of hypertensive and normotensive rats. Curr Eye Res 1998; 17:189-96. [PMID: 9523098 DOI: 10.1076/ceyr.17.2.189.5609] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
PURPOSE The effects of endothelium-related substances such as acetylcholine, a stimulator of endogenous NO-production, the NO-synthesis inhibitor L-NMMA, the exogenous NO-donor sodium nitroprusside and the endothelin (ET)A-receptor antagonist BQ123, on uveal blood flow were investigated in normotensive and hypertensive SHR rats. METHOD The radioactively-labelled microsphere method was applied for the measurement of regional blood flow in the uvea. RESULTS Under resting conditions, local blood flow was lower in the hypertensive animals. The increase in choroidal blood flow (145 +/- 50%; P < 0.01) and reduction in vascular resistance (-58 +/- 7%; P < 0.01) observed in the WKY after i.v. infusion of acetylcholine, 2 micrograms x kg bw-1 x min-1, were significantly less pronounced in animals pretreated with L-NMMA, indicating local formation of NO as a vasodilator mechanism. In contrast, acetylcholine did not induce significant vasodilation in the choroid of SHR rats. In the anterior uvea of both strains, acetylcholine did not affect local blood flow. L-NMMA, 20 mg x kg bw-1, alone reduced blood flow in the entire uvea of both strains. Intravenous injection of BQ123, 1 mg x kg bw-1, did not affect regional blood flow in the uvea of WKY or SHR animals. Infusion of acetylcholine following ETA-receptor blockade induced vasodilation in both the choroid and anterior uvea in the WKY but not in the SHR. CONCLUSIONS Acetylcholine-stimulated NO-mediated vasodilation, but not basal NO-formation, was impaired in the choroid of the SHR. Furthermore, an interaction between vasoconstricting ET and acetylcholine was found in the anterior uvea of normotensive but not hypertensive rats.
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Affiliation(s)
- E Granstam
- Department of Ophthalmology, University Hospital of Uppsala, Sweden.
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Granstam SO, Granstam E, Fellström B, Lind L. Effects of acetylcholine and nitroprusside on systemic and regional hemodynamics in hypertensive rats. Clin Exp Hypertens 1998; 20:223-43. [PMID: 9533615 DOI: 10.3109/10641969809053216] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
This study was performed to investigate the in vivo effects of acetylcholine, a stimulator of endogenous NO production, and nitroprusside, an exogenous NO-donor, on hemodynamics in the normotensive (WKY) and the hypertensive (SHR) rat. Anesthetized rats were given microspheres for the measurement of cardiac index (CI), total vascular resistance (TPRI), regional blood flow and vascular resistance. Infusion of acetylcholine (2 microg/kg/min) caused a marked decrease in TPRI by (-35+/-5%, +/-SEM) in the WKY (n=8), whereas in the SHR (n=8) a less pronounced reduction was seen (-14+/-3%, p<0.01 between groups). CI increased by 27+/-9% in the WKY, but was unaltered in the SHR. Blood pressure decreased similarly (17-20%). Acetylcholine significantly increased blood flow by about 40% in the kidneys and the heart in the WKY, but had no significant effect in the SHR. Other tissues, such as skeletal muscle and cerebral tissues, showed no major changes. Infusion of nitroprusside (1 microg/kg/min) reduced blood pressure by 5 to 10% in the strains. The regional effects of nitroprusside did not differ between the strains. In conclusion, the acetylcholine-induced vasodilation in the kidney and the heart was attenuated in the SHR compared to the WKY. These findings might suggest a difference in the endothelial response between the SHR and the WKY in some, but not in all, tissues.
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Affiliation(s)
- S O Granstam
- Department of Internal Medicine, University Hospital of Uppsala, Sweden
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Rarey KE, Ma YL, Gerhardt KJ, Fregly MJ, Garg LC, Rybak LP. Correlative evidence of hypertension and altered cochlear microhomeostasis: electrophysiological changes in the spontaneously hypertensive rat. Hear Res 1996; 102:63-9. [PMID: 8951451 DOI: 10.1016/s0378-5955(96)00148-7] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
The spontaneously hypertensive rat model has been used to show that hypertension is an important pathophysiological risk factor in age-related hearing loss. In the present study, compound action potential (CAP), electrochemical potential (ECP), and potassium concentration (CK+) measurements were taken from the cochlea of genetically predisposed, spontaneously hypertensive rats (SHR) and from normotensive Wistar-Kyoto (WKY) rats. In the SHR model, as the duration of hypertension increased with the animal's age (from 3 to 8 months), CAP thresholds increased, ECP increased in marginal cells only, and CK+ increased in both endolymph and marginal cells. Collectively, the data suggest that ionic alternations of cellular potentials are involved in hearing changes in the hypertensive state. Ultimately, such data may assist in understanding hearing loss in individuals who are diagnosed with hypertension.
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Affiliation(s)
- K E Rarey
- Department of Anatomy and Cell Biology, University of Florida, Gainesville 32610-0235, USA
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Abstract
Vascular change has been proposed as an etiological factor in inner ear aging and in several inner ear disorders. Moreover, some successful medical management of the episodic vertigo and tinnitus associated with Ménière's disease has been directed toward pharmacologically increasing blood flow, changing vascular permeability or ion homeostasis. While there are many studies of cochlear capillary morphology and blood flow, there are very few examining these variables in the vestibular system and none with respect to aging. The purpose of this study was to examine the rat posterior canal ampullary crista for age-related changes in blood flow and capillary morphology. By combining stereological techniques with microsphere injection, we have determined that in the rat posterior canal crista there is a statistically significant age-related decrease in blood flow (75%), mean capillary diameter (31%), and volume fraction of capillary lumen (31%). There is also an overall 18% decrease in the volume of the ampullary crista, a 72% decrease in blood flow/unit volume and a 36% increase in capillary length/unit volume. There were no significant changes in the capillary surface area/unit volume, the absolute capillary length, or the absolute capillary surface area. These data suggest impaired blood flow and degenerative loss of the ampullary crista may be relate to impaired end organ function.
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Affiliation(s)
- M J Lyon
- Department of Otolaryngology and Communication Science, SUNY, Health Science Center, Syracuse 13210
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Hillerdal M, Andersson SE. The effects of calcitonin gene-related peptide (CGRP) on cochlear and mucosal blood flow in the albino rabbit. Hear Res 1991; 52:321-8. [PMID: 2061223 DOI: 10.1016/0378-5955(91)90022-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
The effects of intravenously infused calcitonin gene-related peptide (CGRP) on the regional blood flow of the cochlea, the middle ear and the upper respiratory tract were studied. Two series of experiments were performed without pretreatment on either conscious or pentobarbital anaesthetized animals; in one series the cervical sympathetic chain was severed on one side; in another series anaesthetized animals were subjected to ganglionic blockade with hexamethonium bromide in order to abolish reflexes involving the autonomic nervous system. In still another series conscious animals were pretreated with indomethacin in order to reduce the formation of prostaglandins. In all groups of animals where sympathetic influence was diminished cochlear blood flow increased during the infusion of CGRP. In the mucosa of middle ear and the upper airways, the blood flow increased in all groups. The results indicate that CGRP at these doses causes vasorelaxation in the mucosa of the middle ear and upper airways and does so also in the cochlea if the sympathetic influence is abolished.
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Affiliation(s)
- M Hillerdal
- Department of Physiology and Medical Biophysics, University of Uppsala, Sweden
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Yamamoto K, Kubo T, Matsunaga T. Autoregulation of inner ear blood flow in normal and hydropic guinea pigs. Acta Otolaryngol 1991; 111:312-8. [PMID: 2068917 DOI: 10.3109/00016489109137393] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Inner ear and brainstem blood circulation was measured by three different techniques: the laser Doppler (LD), hydrogen clearance (HC) and oxygen tension (PO2) measurements, while systemic blood pressure (BP) was modulated by norepinephrine infusion or removal of whole blood. Results were as follows: (i) The blood flow (BF) change determined by LD correlated well with that measured by HC and PO2 techniques; (ii) BF in the brainstem was maintained constant in the BP range of 35 to 80 mmHg; however, inner ear BF showed a poor autoregulatory function relative to the change of systemic BP; (iii) although the change of BF was similar for cochlea and semicircular canal the amount of PO2 decrease for lowered BP was significantly less in the cochlea than in the canal; (iv) in guinea pigs with unilaterally obliterated endolymphatic sac and duct, the decrease in cochlear BF was larger on the operated side than on the intact side. This suggests that the autoregulatory function for BF is impaired in the hydropic ear.
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Affiliation(s)
- K Yamamoto
- Department of Otolaryngology, Osaka University Medical School, Japan
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Wanamaker HH, Lyon MJ. Blood flow and capillary surface area of rat posterior canal ampulla. Otolaryngol Head Neck Surg 1990; 103:586-92. [PMID: 2123316 DOI: 10.1177/019459989010300410] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Vascular disorders have often been proposed to explain disorders of the inner ear, in both the cochlear and vestibular systems. While the cochlea has been extensively studied, little work has been done on vestibular blood flow. Existing studies have reported only total vestibular blood flow, using microspheres. By combining the physiologic technique of microsphere injection with new developments in morphologic stereology studies, data on end-organ blood flow (excluding nerve; 0.074 +/- 0.027 microliters/min; 5.99 microliters/min/mm3), capillary surface area (10.87 mm2/mm3), mean capillary diameter (9.64 microns), and end-organ volume (0.013 mm3) was determined for the posterior canal ampulla of young Fischer 344 rats. Results indicate an anatomic basis for increases in blood flow with CO2 breathing, and provide an assessment of appropriate microsphere size for vestibular blood flow studies. By allowing comparison of blood flow and capillary parameters related to surface area and volume, this new method of blood flow study will allow more meaningful data to be collected on the vestibular system.
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Affiliation(s)
- H H Wanamaker
- Department of Otolaryngology and Communication Sciences, State University of New York, Health Science Center, Syracuse 13210
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Hillerdal M, Andersson SE. The effects of calcitonin gene-related peptide on the blood flow of the upper respiratory tract and the middle and inner ear. Acta Otolaryngol 1989; 108:94-100. [PMID: 2788349 DOI: 10.3109/00016488909107398] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
The effects of intravenously infused CGRP on regional blood flows and vascular resistance in the upper respiratory tract, the middle ear, and the inner ear were studied in cats. CGRP caused a pronounced vasodilation and an increase in blood flow of the respiratory mucosa and structures of the middle ear. The substance did not affect the blood flows of the cochlea and the vestibular organ in the inner ear.
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Affiliation(s)
- M Hillerdal
- Department of Physiology and Medical Biophysics, Uppsala University, Sweden
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Abstract
The measurement of inner ear blood flow and other microvascular variables is subject to unique technical problems which are compounded by methodological limitations. As a result, the interpretation of experimental results is often difficult. This report discusses the most important methods currently available for cochlear blood circulation measurements and the technical problems associated with their use. The use of a combination of measurements to resolve problems of interpretation is stressed. An extensive review of the pertinent literature is provided in relation to each method.
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Affiliation(s)
- A L Nuttall
- Kresge Hearing Research Institute, University of Michigan, Ann Arbor 48109-0506
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Hillerdal M, Sperber GO, Bill A. The microsphere method for measuring low blood flows: theory and computer simulations applied to findings in the rat cochlea. ACTA PHYSIOLOGICA SCANDINAVICA 1987; 130:229-35. [PMID: 3604713 DOI: 10.1111/j.1748-1716.1987.tb08132.x] [Citation(s) in RCA: 32] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
When the microsphere method of blood flow measurement is used in small organs, the number of spheres actually recovered may be small. This introduces errors which, however, are not necessarily important as compared with the biological variation. A mathematical model was constructed which allowed estimation of the extra uncertainty caused by the low number of spheres. It was applied to an experimental material of over 100 measurements of cochlear blood flow in the rat, where only about 60 spheres were recovered per cochlea. It was concluded that this paucity of spheres introduced only a small to moderate extra error. Simple approximate formulae were derived allowing easy estimation of the uncertainty caused by low number of spheres under different conditions. In general, there appear to be many situations where fewer microspheres than are commonly used would suffice.
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