To see the other types of publications on this topic, follow the link: Microcirculation – Mathematical models.
Journal articles on the topic 'Microcirculation – Mathematical models'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 15 journal articles for your research on the topic 'Microcirculation – Mathematical models.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.
1
Farina, Angiolo, Antonio Fasano, and Fabio Rosso. "Mathematical Models for Some Aspects of Blood Microcirculation." Symmetry 13, no. 6 (June 6, 2021): 1020. http://dx.doi.org/10.3390/sym13061020.
Full textAbstract:
Blood rheology is a challenging subject owing to the fact that blood is a mixture of a fluid (plasma) and of cells, among which red blood cells make about 50% of the total volume. It is precisely this circumstance that originates the peculiar behavior of blood flow in small vessels (i.e., roughly speaking, vessel with a diameter less than half a millimeter). In this class we find arterioles, venules, and capillaries. The phenomena taking place in microcirculation are very important in supporting life. Everybody knows the importance of blood filtration in kidneys, but other phenomena, of not less importance, are known only to a small class of physicians. Overviewing such subjects reveals the fascinating complexity of microcirculation.
2
Tsoukias, Nikolaos M. "Nitric Oxide Bioavailability in the Microcirculation: Insights from Mathematical Models." Microcirculation 15, no. 8 (January 2008): 813–34. http://dx.doi.org/10.1080/10739680802010070.
Full text
3
Weinbaum, S. "Interfacial Transport in Large and Small Blood Vessels." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S109—S118. http://dx.doi.org/10.1115/1.3120789.
Full textAbstract:
In this paper we shall review some recent mathematical models which have led to new conceptual views of the ultrastructural pathways by which water, solutes and large molecules cross the endothelial interface between tissue and blood. In particular, we shall show how a sequence of models for the endothelium and underlying tissue in large arteries have finally led to the experimental discovery of the large pore via which LDL and other large molecules enter the artery wall and how a new three-dimensional model for the interendothelial cleft in capillaries might reconcile the several long standing paradoxes relating to the measured filtration and solute permeability coefficients in the transcapillary exchange of water and hydrophilic solutes in the microcirculation.
4
ZHAO, NING, and KEIJI IRAMINA. "A MATHEMATICAL COUPLED MODEL OF OXYGEN TRANSPORT IN THE MICROCIRCULATION: THE EFFECT OF CONVECTION–DIFFUSION ON OXYGEN TRANSPORT." Journal of Mechanics in Medicine and Biology 15, no. 01 (February 2015): 1550003. http://dx.doi.org/10.1142/s0219519415500037.
Full textAbstract:
This paper is aimed at examining the effect of convection–diffusion on oxygen transport at the micro-level. A coupled model of the convection–diffusion and molecular diffusion of oxygen is developed, and the solid deformation resulting from capillary fluctuations and the seepage of tissue fluid are incorporated into this model. The results indicate that (1) the oxygen concentration calculated from this coupled model is higher than that given by molecular diffusion models, both within the capillaries and tissue (maximum difference of 16%); (2) convection–diffusion has the greatest effect in tissue surrounding the middle of the capillary, and enhances the amount of oxygen transported to cells far from the oxygen source; (3) larger permeability coefficients or smaller diffusion coefficients produce a more obvious convection–diffusion effect; (4) a counter-current flow occurs near the inlet and outlet ends of the capillary. This model also provides a foundation for the study of how oxygen affects tumor growth.
5
Parker, R. E., R. J. Roselli, and K. L. Brigham. "Effects of prolonged elevated microvascular pressure on lung fluid balance in sheep." Journal of Applied Physiology 58, no. 3 (March 1, 1985): 869–75. http://dx.doi.org/10.1152/jappl.1985.58.3.869.
Full textAbstract:
Experiments were conducted in seven chronically instrumented unanesthetized sheep to estimate the osmotic reflection coefficient (sigma d) for total proteins and the solvent-drag reflection coefficients (sigma f) for six endogenous protein fractions. We measured the lymph-to-plasma ratio of total proteins (CL/CP) and six protein fractions during base-line conditions and after left atrial pressure elevations of 24–26 h per elevation. We also monitored pulmonary arterial pressure, left atrial pressure, systemic arterial pressure, and lung lymph flow at the various levels of pulmonary microvascular pressure. Our results indicate the CL/CP may require up to 24 h to reach a true steady state. It was found that sigma d is at least 0.89 for total proteins and sigma f is at least 0.84, 0.87, 0.86, 0.92, 0.95, and 0.96 for protein fractions with effective molecular radii of 36, 39.5, 44, 66, 105, and 123 A, respectively. In addition, the sigma f values for various protein fractions obtained from this investigation are compared with the predicted values of various mathematical models of the lung microcirculation.
6
Hartung, Grant, Shoale Badr, Mohammad Moeini, Frédéric Lesage, David Kleinfeld, Ali Alaraj, and Andreas Linninger. "Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex." PLOS Computational Biology 17, no. 1 (January 28, 2021): e1008584. http://dx.doi.org/10.1371/journal.pcbi.1008584.
Full textAbstract:
Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease.
7
Pries, A. R., T. W. Secomb, and P. Gaehtgens. "Structure and hemodynamics of microvascular networks: heterogeneity and correlations." American Journal of Physiology-Heart and Circulatory Physiology 269, no. 5 (November 1, 1995): H1713—H1722. http://dx.doi.org/10.1152/ajpheart.1995.269.5.h1713.
Full textAbstract:
The objective of this study was to quantify the heterogeneity of topological, morphological, and hemodynamic parameters in microvascular networks and to identify functionally relevant correlations among these parameters. Seven networks in the rat mesentery (383-913 vessel segments per network) were examined, and measurements were made of segment generation, diameter, length, and hematocrit in all segments (n = 3,129) and of flow velocity (only in 3 networks, 1,321 segments). In addition, hematocrit, flow rate, and pressure were derived for all segments from a mathematical simulation. All parameters obtained exhibit heterogeneous distributions with coefficients of variation ranging from 0.28 (capillary diameter) to > 1.5 (volume flow and pressure gradient). Several strong correlations exist between parameters, e.g., discharge hematocrit increases with vessel diameter, and shear rate increases with intravascular pressure. Because of such correlations, the extrapolation from average values for "typical vessels" to network properties can lead to substantial errors. For example, the mean network transit time estimated based on averaged quantities is 6.5 s, which is about 60% higher than the true value (4.08 s). Simplified models of the vascular bed may therefore be inadequate to describe functional properties of the microcirculation.
8
Mansoor, Wafaa, Graeme Hocking, and Duncan Farrow. "Modelling of hydrogen diffusion in the retina." ANZIAM Journal 61 (July 7, 2020): C119—C136. http://dx.doi.org/10.21914/anziamj.v61i0.14995.
Full textAbstract:
A simple mathematical model for diffusion of hydrogen within the retina has been developed. The model consists of three, well-mixed, one dimensional layers that exchange hydrogen via a diffusion process. A Fourier series method is applied to compute the hydrogen concentration. The effect of important parameters is examined and discussed. The results may contribute to an understanding of the hydrogen clearance technique to estimate blood flow. A two dimensional numerical method for the hydrogen diffusion is also presented. It is shown that the predominant features of the process are captured quite well by the simpler model. References V. A. Alder, D. Y. Yu, S. J. Cringle and E. N. Su. Experimental approaches to diabetic retinopathy. Asia-Pac. J. Ophthalmol. 4:20–25, 1992. J. C. Arciero, P. Causin and F. Malgoroli. Mathematical methods for modeling the microcirculation. AIMS Biophys. 4:362–399, 2017. doi:10.3934/biophy.2017.3.362 D. E. Farrow, G. C. Hocking, S. J. Cringle and D.-Y. Yu. Modeling Hydrogen clearance from the retina. ANZIAM J. 59:281–292, 2018. doi:10.1017/S1446181117000426 A. B. Friedland. A mathematical model of transmural transport of oxygen to the retina. Bull. Math. Biol. 40:823–837, 2018; doi:10.1007/BF02460609 D. Goldman. Theoretical models of microvascular oxygen transport to tissue. Microcirculation 15:795–811, 2008. doi:10.1080/10739680801938289 A. C. Hindmarsh. ODEPACK, A Systematized Collection of ODE Solvers. In Scientific Computing, R. S. Stepleman, et al., Eds., pp. 55-64. North-Holland, Amsterdam, 1983. S. S. Kety. The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev. 3:1–41, 1951. http://pharmrev.aspetjournals.org/content/3/1/1 B. P. Leonard. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19:59–98, 1979. doi:10.1016/0045-7825(79) 90034-3 S. L. Mitchell. Coupling transport and chemistry: numerics, analysis and applications. PhD thesis, University of Bath, UK, 2003. https://researchportal.bath.ac.uk/en/studentTheses/coupling-transport-and-chemistry-numerics-analysis-and-applicatio G. A. Winchell. Mathematical model of inert gas washout from the retina: evaluation of hydrogen washout as a means of determining retinal blood flow in the cat. Master\textquoteright s Thesis, Northwestern University, Evanston, USA, 1983. https://search.library.northwestern.edu/permalink/f/5c25nc/01NWU_ALMA21563278530002441 D. Y. Yu, V. A. Alder and S. J. Cringle. Measurement of blood flow in rat eyes by hydrogen clearance. Am. J. Physiol. (Heart Circ. Physiol.) 261:H960–H968, 1991. doi:10.1152/ajpheart.1991.261.3.H960 D. Y. Yu, S. J. Cringle, V. A. Alder, E. N. Su, and P. K. Yu, Intraretinal oxygen distribution and choroidal regulation in the avascular retina of guinea pigs. Am. J. Physiol. (Heart Circ. Physiol.) 270:H965-H973, 1996. doi:10.1152/ajpheart.1996.270.3.H965 S. Cringle, D.-Y. Yu, V. Alder, E.-N. Su, and P. Yu. Choroidal regulation of oxygen supply to the guinea pig retina. In A. G. Hudetz, and D. F. Bruley (Eds.), Oxygen Transport to Tissue XX, pp. 385–389. Springer, 1998. doi:10.1007/978-1-4615-4863-8
9
Al-Shammari, Abdullah A., Roger W. P. Kissane, Simon Holbek, Abigail L. Mackey, Thomas R. Andersen, Eamonn A. Gaffney, Michael Kjaer, and Stuart Egginton. "Integrated method for quantitative morphometry and oxygen transport modeling in striated muscle." Journal of Applied Physiology 126, no. 3 (March 1, 2019): 544–57. http://dx.doi.org/10.1152/japplphysiol.00170.2018.
Full textAbstract:
Identifying structural limitations in O2 transport is primarily restricted by current methods employed to characterize the nature of physiological remodeling. Inadequate resolution or breadth of available data has impaired development of routine diagnostic protocols and effective therapeutic strategies. Understanding O2 transport within striated muscle faces major challenges, most notably in quantifying how well individual fibers are supplied by the microcirculation, which has necessitated exploring tissue O2 supply using theoretical modeling of diffusive exchange. With capillary domains identified as a suitable model for the description of local O2 supply and requiring less computation than numerically calculating the trapping regions that are supplied by each capillary via biophysical transport models, we sought to design a high-throughput method for histological analysis. We present an integrated package that identifies optimal protocols for identification of important input elements, processing of digitized images with semiautomated routines, and incorporation of these data into a mathematical modeling framework with computed output visualized as the tissue partial pressure of O2 (Po2) distribution across a biopsy sample. Worked examples are provided using muscle samples from experiments involving rats and humans. NEW & NOTEWORTHY Progress in quantitative morphometry and analytical modeling has tended to develop independently. Real diagnostic power lies in harnessing both disciplines within one user-friendly package. We present a semiautomated, high-throughput tool for determining muscle phenotype from biopsy material, which also provides anatomically relevant input to quantify tissue oxygenation, in a coherent package not previously available to nonspecialist investigators.
10
Винников, Артем Викторович, Александр Владимирович Быков, Николай Алексеевич Кореневский, Людмила Петровна Лазурина, Полина Сергеевна Азарова, and Гулайым Камчибековна Усубалиева. "METHOD FOR PREDICTING FATAL COMPLICATIONS IN THE DEVELOPMENT OF CORONAVIRAL INFECTION ON THE BACKGROUND OF SYSTEMIC LUPUS ERYTHEMATOSUS." СИСТЕМНЫЙ АНАЛИЗ И УПРАВЛЕНИЕ В БИОМЕДИЦИНСКИХ СИСТЕМАХ, no. 2 (July 26, 2021): 63–69. http://dx.doi.org/10.36622/vstu.2021.20.2.008.
Full textAbstract:
Целью исследования является разработка метода прогнозирования возникновения и развития фатальных осложнений, провоцируемых действием на организм человека новой коронавирусной инфекции (COVID-19) на фоне иммунопролиферативных заболеваний, который позволит усовершенствовать лечебно-диагностические мероприятия при данной патологии. В качестве базового математического аппарата была выбрана методология синтеза гибридных нечетких решающих правил, которая хорошо зарекомендовала себя при решении задач с нечётким описанием исследуемых классов и схожим типом неопределенности. Предлагаемый метод прогнозирования позволяет учесть мультипликативный эффект воздействия на организм человека существенных факторов риска, характерных для рассматриваемого заболевания, с учетом его тяжести и скорости развития патологического процесса. В ходе проводимых исследований были синтезированы математические модели прогнозирования возникновения и развития фатальных осложнений. В ходе экспертного оценивания, математического моделирования и статистических испытаний показано, что уверенность в правильном принятии решений по прогнозу появления и развития исследуемого класса фатальных осложнений превышает величину 0,85. В работе получены нечёткие математические модели прогнозирования возникновения и развития фатальных осложнений у людей при развитии коронавирусной инфекции на фоне системной красной волчанки, для которых ведущими факторами риска являются вторичный антифосфолипидный синдром с нарушением микроциркуляции и гипоксемия. В ходе проведенных исследований была показана целесообразность использования полученных результатов в практике работы таких врачей, как иммунологи, инфекционисты, пульмонологи The aim of the study is to develop a method for predicting the occurrence and development of fatal complications provoked by the effect on the human body of a new coronavirus infection (COVID-19) against the background of immunoproliferative diseases, which will improve diagnostic and treatment measures for this pathology. The methodology for the synthesis of hybrid fuzzy decision rules was chosen as the basic mathematical apparatus, which has proven itself well in solving problems with a fuzzy description of the classes under study and a similar type of uncertainty. The proposed forecasting method allows one to take into account the multiplicative effect of exposure to the human body of significant risk factors characteristic of the disease under consideration, taking into account its severity and the rate of development of the pathological process. In the course of the research, mathematical models were synthesized for predicting the occurrence and development of fatal complications. In the course of expert assessment, mathematical modeling and statistical tests, it was shown that confidence in the correct decision-making on the prediction of the appearance and development of the studied class of fatal complications exceeds 0.85, which makes it possible to recommend the results obtained during the study for implementation into the practice of such doctors. as immunologists, infectious disease specialists, pulmonologists. The work obtained fuzzy mathematical models for predicting the occurrence and development of fatal complications in people with the development of coronavirus infection against the background of systemic lupus erythematosus, for which the leading risk factors are secondary antiphospholipid syndrome with microcirculation disorders and hypoxemia. In the course of the studies, the expediency of using the results obtained in the practice of the work of such doctors as immunologists, infectious disease specialists, pulmonologists was shown
11
Antonova, N. M., V. K. Paskova, and I. V. Velcheva. "Blood rheological and electrical properties and relationships with the microvascular tone regulation in patients with diabetes mellitus type 2." Regional blood circulation and microcirculation 20, no. 1 (March 22, 2021): 25–33. http://dx.doi.org/10.24884/1682-6655-2021-20-1-25-33.
Full textAbstract:
Aim. The study aims to evaluate impairment of the rheological and electrical properties of blood, plasma viscosity and blood conductivity in patients with type 2 diabetes mellitus (T2DM) in comparison with the data of the control group of healthy individuals. It also aims to investigate the changes of the skin blood flow responses to cold stress in T2DM patients through wavelet analysis of the peripheral skin temperature pulsations and to estimate their relationships with the blood viscosity and blood conductivity parameters, obtained from the simulation of experimental data with mathematical equations.Materials and methods. The whole blood viscosity was measured by Contraves LS30 viscometer (Switzerland) at a steady flow in 9 healthy individuals and in 13 patients with type 2 diabetes mellitus. Time variation of whole blood conductivity σ under transient flow at rectangular and trapezium shaped Couette viscometric flow and under electric field of 2 kHz was determined. The amplitudes of the skin temperature pulsations (ASTP) were monitored by «Microtest» device («FM-Diagnostics», Russia). To analyze the temperature fluctuations, wavelet transformation analysis of the low amplitude oscillations of skin temperature in accordance with myogenic (0.05–0.14 Hz), neurogenic (0.02–0.05 Hz), and endothelial (0.0095–0.02 Hz) control mechanisms of the vascular tone (WAST method) was applied.Results. Blood viscosity was increased in the T2DM patients’ group, while blood conductivity decreased in comparison to controls. Two sigmoidal equations were applied to describe the kinetics of blood conductivity. Both models include conductivity indices (σ1 , σ2 , σ3 ) and time indices too. The Pearson correlations between these parameters and the ASTP in the frequency ranges, corresponding to the myogenic, neurogenic and endothelial mechanisms of the microcirculation tone regulation were analyzed. The correlation analysis revealed good ASTP–(σ1 , σ2 , σ3 ) relationships in the neurogenic range 3 minutes after the cold test, while the ASTP–(σ1 , σ2 , σ3 ) correlation in the myogenic frequency range before the cold test was negative (r<–0.8, p<0.5).Conclusion. The results complement the studies of the microvascular regulatory mechanisms and endothelial dysfunction in patients with type 2 diabetes mellitus, as well as their relationships with the rheological and electrical properties of blood.
12
Cattaneo, Laura, and Paolo Zunino. "Computational models for fluid exchange between microcirculation and tissue interstitium." Networks & Heterogeneous Media 9, no. 1 (2014): 135–59. http://dx.doi.org/10.3934/nhm.2014.9.135.
Full text
13
Spaan, Jos, Christina Kolyva, Jeroen van den Wijngaard, Rene ter Wee, Pepijn van Horssen, Jan Piek, and Maria Siebes. "Coronary structure and perfusion in health and disease." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1878 (June 17, 2008): 3137–53. http://dx.doi.org/10.1098/rsta.2008.0075.
Full textAbstract:
Blood flow is distributed through the heart muscle via a system of vessels forming the coronary circulation. The perfusion of the myocardium can be hampered by atherosclerosis creating localized obstructions in the epicardial vessels or by microvascular disease. In early stages of the disease, these impediments to blood flow are offset by dilation of the resistance vessels, which normally compensates for a decrease in perfusion pressure or increased metabolism. However, this dilatory reserve can become exhausted, which in general occurs first at the deeper layers of the heart wall where intramural vessels are subjected to compressive forces related to heart contraction. In the catheterization laboratory, guide wires of 0.33 mm diameter are available that are equipped with a pressure and flow velocity sensor at the tip, which can be positioned distal to the stenosis. These signals provide information about the impediment of the stenosis on coronary flow and allow for the evaluation of the status of the microcirculation. However, the interpretation of these signals is strongly model-dependent and therefore it is of paramount importance to develop realistic models reflecting the anatomy and unique physiology of the coronary circulation.
14
Pan, Qing, Ruofan Wang, Bettina Reglin, Guolong Cai, Jing Yan, Axel R. Pries, and Gangmin Ning. "A One-Dimensional Mathematical Model for Studying the Pulsatile Flow in Microvascular Networks." Journal of Biomechanical Engineering 136, no. 1 (December 4, 2013). http://dx.doi.org/10.1115/1.4025879.
Full textAbstract:
Techniques that model microvascular hemodynamics have been developed for decades. While the physiological significance of pressure pulsatility is acknowledged, most of the microcirculatory models use steady flow approaches. To theoretically study the extent and transmission of pulsatility in microcirculation, dynamic models need to be developed. In this paper, we present a one-dimensional model to describe the dynamic behavior of microvascular blood flow. The model is applied to a microvascular network from a rat mesentery. Intravital microscopy was used to record the morphology and flow velocities in individual vessel segments, and boundaries are defined according to the experimental data. The system of governing equations constituting the model is solved numerically using the discontinuous Galerkin method. An implicit integration scheme is adopted to increase computing efficiency. The model allows the simulation of the dynamic properties of blood flow in microcirculatory networks, including the pressure pulsatility (quantified by a pulsatility index) and pulse wave velocity (PWV). From the main input arteriole to the main output venule, the pulsatility index decreases by 66.7%. PWV obtained along arterioles declines with decreasing diameters, with mean values of 77.16, 25.31, and 8.30 cm/s for diameters of 26.84, 17.46, and 13.33 μm, respectively. These results suggest that the 1D model developed is able to simulate the characteristics of pressure pulsatility and wave propagation in complex microvascular networks.
15
Herrera, Arturo Solís, and Oscar Aguilera Madrigal. "The Unsuspected Intrinsic Property of Melanin to Dissociate the Water Molecule, Implications in Pulmonary Biology." Journal of Pulmonology Research & Reports, December 31, 2020, 1–7. http://dx.doi.org/10.47363/jprr/2020(2)108.
Full textAbstract:
Life originated in anoxia, but paradoxically many organisms came to depend upon oxygen for survival, independently evolving diverse respiratory systems for expel CO2 and acquiring oxygen to and from the environment, respectively. Thereby, Oxygen, a vital gas, and a lethal toxin, represents a trade-off with which all organisms have had a conflicted relationship. The study of oxygen movements in the tissues of the human body has been a matter of great interest ever since centuries. In the beginning of the past century, Dr. Christian Bohr and August Krogh’s work on respiratory physiology and capillary modelling using mathematical models to calculate molecular transport in microcirculation, trying to determine the negative impact of lack of oxygen transport to tissues. Supposedly, computer simulation allowed investigation of the dynamic and non-linear characteristics of the systems. But the results have been and are contradictory. In Germany, Dietrich Werner Lubbers (1917-2005) obtained several patents related to designs for the study of gases in tissues. The aim of Dietrich Lübbers’ research was to understand the entire pathway and regulation of oxygen transport from the blood into the mitochondria. Assessment of pO2 histograms on most organs, revealed a remarkable similarity under physiological conditions: a Gaussian distribution always with less than 5% of values less than 5mmHg. Other studies detected changes in the concentrations of oxy- ([HbO2]) deoxy- ([HHb]) and total haemoglobin ([HbT]=[HbO2]þ [HHb]) measured using near infrared spectroscopy (NIRS) [1]. It has been shown that diabetic rats have markedly decreased oxygen availability in the kidney, supposedly resulting from increased oxygen consumption [2]