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By Karla Sanchez
I was recently invited to present my work on mathematical modelling of renal circulation at the international Artery Conference in Budapest. As honorary visiting researcher at Imperial College I worked with clinical scientists from King’s College London on this project.
The kidneys are the service station of the blood. They perform important functions including ﬁltering, removing unwanted metabolic waste products that ultimately leave the body as urine, reabsorbing substances that are still needed, balancing concentrations in ﬂuid osmolarity, and secretion of hormones and gluconeogenesis.
It is estimated over 3 million people live with chronic kidney disease (CKD) in the UK. A rise in the prevalence of diabetes and hypertension are important contributing factors and involve the gradual loss of kidney function. Transplant and dialysis are the current treatment methods for advanced CKD and kidney failure.
It is estimated there are up to 1 million nephrons per kidney. The nephron is the kidney’s functional unit, and located within it is the glomerulus, a network of small blood vessels. These are in charge of ﬁltering and regulating our blood.
The glomerular ﬁltration rate (GFR) describes the amount of blood ﬁltered by the glomeruli per unit time, and it is a key indicator in kidney function. In CKD, there is a gradual decrease in GFR. If this decrease becomes signiﬁcantly low (typically below 15% of normal function), kidney failure ensues.
However the kidneys have mechanisms to compensate for moderate changes in GFR, but conditions such as excess blood glucose or increased blood pressure can impair them and result in progressive, irreversible damage.
Autoregulation allows blood vessels to constrict or dilate in response to diﬀerent stimuli, e.g. changes in pressure. This means that the kidney can change its own blood ﬂow according to its needs. It is one of only three organs in the body where this ability has been observed, the two others being the heart and the brain. Autoregulation in the kidney has been seen to be impaired in patients with CKD.
Blood vessels also see changes in elasticity with both age and hypertension, but the mechanisms underlying kidney damage are not fully understood. This is partly due to the limited data available describing the dynamic changes in microcirculation, blood ﬂow in the small vasculature.
Mathematical modelling provides a good way to explore the haemodynamic changes involved in CKD. Fellow clinical scientist Dr Nikolaos Fountoulakis from King’s College London and I presented a mathematical model of the renal circulation at the conference, with special focus on the microcirculation, where damage to the glomeruli is known to play a role in CKD.
It consists of two symmetrical branching trees to represent the renal vasculature (arteries and veins) connected to the nephronal compartments. The level of detail in the model allows us to explore fundamental properties of the blood vessels and how these interact with the glomeruli, and thus their eﬀect on glomerular ﬁltration rate. Additionally, we have included an autoregulation function where changes in cross-sectional area are adaptive to changes in pressure. The model can account for the eﬀects of impaired autoregulation to investigate their potential association with CKD.
We showed that, as observed clinically, autoregulation takes place in the small vessels in the kidney. Impaired autoregulation was shown to severely aﬀect glomerular ﬁltration rate and downstream flow.
GFR was shown to be more sensitive to changes in renal blood ﬂow and pressure than to the intrinsic properties of the vessels and glomeruli resistance. We also showed that hypertension and the mechanical properties of the vessels were closely interlinked, with higher sensitivity to higher blood pressure.
Our ﬁndings show that the behaviour of the renal vasculature and the impact of vessel geometry are important factors eﬀecting the renal microcirculation. In turn, changes in GFR are mostly dictated by changes in microcirculation, which implies these factors are of relevance to CKD.
Our research contributes to the wider advances in arterial research that are expanding our knowledge of CKD, through a better understanding of the implications of vessel function in the renal system. We hope that in the future it can also help develop new therapies for patients with CKD.
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