Renal blood flow using [¹⁵O]H₂O

Renal blood flow (RBF) is very high: kidneys receive 20-25% of the resting cardiac output, but their weight is less than 1% of body mass. Renal perfusion, ∼400 mL/(min*dL), is higher than perfusion in the myocardium, liver, or brain. Cortical blood flow composes ∼80-90% of the total renal blood flow, because the mass and perfusion of medullary tissue is markedly smaller. However, quantitative measurement of regional distribution of blood flow within the kidneys with traditional methods, such as washout method, has been difficult and prone to errors (Grünfeld et al., 1974; Aukland, 1975; Blaufox, 1989). Effective renal plasma flow has been commonly assessed as urinary clearance of para-aminohippurate (PAH); conversion of that into quantitative RBF requires that the extraction ratio of PAH (∼0.9 in healthy men) is known. Without extraction correction, renal clearance provides only the minimum blood flow. ¹³¹I-hippuran has even lower extraction ratio than PAH.

[¹⁵O]H₂O can be used to assess renal perfusion (Peters et al., 1972; Inaba et al., 1989; Nitzsche et al., 1993; Juillard et al., 2000; Alpert et al., 2002; Anderson et al., 2003; Kudomi et al., 2009; Damkjær et al., 2010; Koivuviita et al., 2012; Rahman et al., 2019; Normand et al., 2019), also in transplanted kidney (Päivärinta et al., 2019). Due to the short half-life of ¹⁵O, renal perfusion measurements can be repeated during one imaging session. This enables the assessment of microvascular function of the kidneys by measuring renal perfusion at baseline and after a vasodilator, such as enalapril, and calculating renal flow reserve (RFR) as the difference (Päivärinta et al., 2018).

Sympathetic nerve activity and even mild exercise reduces RBF, especially in heart failure patients (Middlekauff et al., 1997a, 1997b, 2000, 2001). MRI measurement has shown that hand-grip exercise reduced perfusion in renal cortex and medulla, and medullary oxygenation was increased because of decreased GFR (Haddock et al., 2018). Heat and cold stress activates sympathetic system, reducing renal blood flow and increasing renal vascular resistance. Stress during the PET scan should be avoided; Middlekauff et al (1997a) reported that induced mental stress reduced cortical renal blood flow by ∼30%. Sodium and water intake, and medications, must be standardized in renal studies to avoid confounding effects on GFR, perfusion, and oxygen consumption.

Renal perfusion decreases by age, and is higher in subjects on a high sodium intake, but the RBF response to salt intake is blunted in older individuals (Hollenberg et al., 1974).

Renal vasculature

Renal artery branches directly from abdominal aorta, and branches in renal pelvis into interlobal arteries. In 20-30% of normal individuals, additional arteries supply (usually) the lower pole of the kidney. Interlobar arteries branch into arcuate arteries, which reside at the border of cortex and medulla, and practically define the border of cortex and medulla. Arcuate arteries give rise to interlobular arteries that extend through the cortex toward the surface of the kidney. Interlobular arteries branch into afferent arterioles, which lead into glomeruli. A single efferent arteriole directs the blood from each glomerulus to the peritubular capillary network in the cortex and vasa recta in the medulla. Capillary network in the kidney is very dense, especially in the medulla: in mice, capillary density and capillary surface area are 7400/mm² and 1400 cm²/cm³, respectively, in the renal medulla, which are clearly higher than in the mouse heart muscle (5300/mm² and 1000 cm²/cm³) and liver (4200/mm² and 800 cm²/cm³); in renal cortex the values are 4500/mm² and 850 cm²/cm³, respectively (Kety, 1951).

All of the medullary blood flow is derived from the efferent arterioles of the juxtamedullary nephrons. Renal blood flow to the cortical glomeruli (cortical perfusion) and juxtamedullary glomeruli (cortical and medullary perfusion) are differentially regulated (Evans et al., 2004). Juxtamedullary afferent and efferent arterioles are larger than cortical arterioles. The efferent arterioles that descend from the juxtamedullary glomeruli to the medulla have also thicker endothelial layer, and the arterioles descend in parallel, with lateral branches forming capillary plexus. Medullary vasa recta has markedly larger diameter than cortical peritubular capillaries. Descending vasa recta capillaries have contractile smooth muscle-like pericytes, which constrict and dilate the capillaries and regulate medullary perfusion (Kennedy-Lydon et al., 2013). Vasoconstrictors (including angiotensin II, endothelin, and noradrenaline) mainly affect cortical blood flow (Evans et al., 2004). In healthy subjects administration of angiotensin II led to renal hypoxia (Schachinger et al., 2006). Vasodilators (including NO and bradykinin) increase medullary blood flow. Vasopressin reduces, and adenosine and acetylcholine increase medullary blood flow. Increased luminal flow, in physiological range, in medullary thick ascending limbs of Henle leads to increased production of ROS, which diffuse to vasa recta capillaries and reduce medullary blood flow (Cowley Jr et al., 2015).

Medullary venous vessels are larger and more numerous than arterial vessels.

Water transport in kidneys

Kidneys filter ∼100-200 L of fluid each day (or 1.0-1.2 L/min), but normally less than 1% (or ∼1 mL/min) of the filtered water is excreted in urine. About 20% of the plasma is filtered at the glomeruli from blood vessels into the Bowman capsule and proximal tubules. Proximal tubule reabsorbs 60-90% of the water and solutes. Diffusion of water is driven by osmotic pressure gradients, and is facilitated by Aquaporin AQP1 in the proximal tubules and by Aquaporin AQP2 in the connecting and collecting ducts. The osmotic gradient for water reabsorption is formed by active reabsorption of Na⁺, Cl^-, and glucose. Hydrostatic pressure in the proximal tubular tissue, and high protein content in the peritubular capillaries, drives the water into the blood. The loop of Henle reabsorbs ∼15% of the filtered water; the descending limb has AQP1 channels, but the ascending limb is impermeable to water, as is the initial segment of the distal tubule. Since Na⁺, Cl^-, and other solutes are actively reabsorbed in the ascending limb and the distal tubule, the remaining fluid is dilute, as compared to plasma. The late distal tubule and collecting duct cells possess AQP2, AQP3 and AQP4 channels, and reabsorb variable proportion (∼8-17%) of the water. The collecting ducts are responsible for maintaining the water balance of the body, since the osmolality of the tubular fluid that they receive is fairly constant in all conditions, but the produced urine can be very hypo- or hyperosmotic. Vasopressin level regulates the water reabsorption in these segments, as well as the medullary blood flow.

Ascending vasa recta capillaries in the medulla are highly permeable to water, and are responsible for removing the water that is reabsorbed from the tubular fluid in loops of Henle and in collecting ducts.

[¹⁵O]H₂O bolus model

The analysis method of renal blood flow (RBF) is based on one-tissue compartment model. Model parameters for the kidney are RBF, p (ρ, partition coefficient, K₁/k₂), and RBV (renal arterial blood volume). Wash-out of [¹⁵O]H₂O, injected into the renal artery, is mono-exponential during the first 60 s (Inaba et al., 1989). The first [¹⁵O]H₂O kidney study was done using external detectors (Peters et al., 1972), and in that two compartments were detected, with compartmental distributions of 55% for the fast component (cortex) and 45% for the slow component (medulla) with perfusion 370 and 55 mL/(100g * min), respectively (Szabo & Mathews, 2006).

RBF can be estimated from regional time-activity concentration curves (TACs), or from dynamic PET image to produce perfusion image. Further, volumetrically normalized images could be used for statistical parametric mapping (Rahman et al., 2019). Arterial blood curve can be measured from arterial line as model input function, but input could also be measured from the image from ROI placed on ascending aorta.

Inaba et al. (1989) applied the radiowater model to assess renal perfusion from regional data in 8 subjects. They calculated renal plasma flow (RPF) as

, where HCT was the systemic hematocrit, because renal arterial hematocrit is not known. They apparently did not account for the RBV, which causes overestimation of RBF (Kudomi et al., 2009), although they had measured RBV using [¹⁵O]CO. The RPF was 171±61 mL/(min * 100 g); assuming that HCT=0.45, that means that RBF was about 3.1±1.1 mL/(min*g). The apparent partition coefficient (ρ) was 0.66±0.10, and it correlated with RPF. RPF correlated with glomerular filtration rate (Inaba et al., 1989). Nitzsche et al (1993) added RBV parameter to the model, and used it to validate renal perfusion assessment using [¹³N]ammonia; their radiowater results for cortical RBF and RBV were 4.70±0.28 mL/(min*g) and 0.16±0.11 mL/g, respectively. Middlekauff et al (1995) reported that cortical RBF was markedly lower in patients with advanced heart failure (2.4±0.1 mL/(min*mL)) than in healthy controls (4.3±0.2 mL/(min*mL)). Juillard et al (2000) validated the method, assuming K₁/k₂=1, against microspheres in pigs. Microspheres cannot be used to measure medullary blood flow, because they are trapped in the glomeruli (Ericson et al., 1979). Using the same method, Juillard et al. (2002) measured RBF of 2.2±0.2 mL/(min*g) in men with hypertension and moderate CKD; ACE inhibitor quinaprilat increased RBF by ∼20%. Alpert et al. (2002) obtained RBF of 3.4±0.4 mL/(min*g) in healthy subjects and 2.1±1.1 mL/(min*g) in patients with CKD; probenecid did not affect RBF. Rahman et al (2019) reported lower K₁, k₂, and V_A in patients with chronic renal failure than in healthy subjects. Normand et al (2019) did renal radiowater PET in order to validate [1-¹¹C]acetate for assessing renal perfusion in human subjects; delay and blood volume were accounted for in the model, and the measured cortical perfusion was 3.29±0.65 (range 2.00-4.70) mL/(g*min); after protein load, RBF increased ∼20%. The test-retest reproducibility of K₁ in healthy subjects was 0.36 with an ICC of 0.64 (Normand et al., 2019).

Nalin et al (2014) reported renal perfusion values ∼2.3 mL/(mL*min) in healthy pigs and ∼1.3 mL/(mL*min) in diabetic pigs.

Alpert et al (2002) applied linearized method for calculation of RBF image, but ignored RBV; in our implementation of the linear method (see below) RBV can be included in the analysis. Not accounting for RBV causes overestimation of RBF Also time delay between arterial input and tissue TACs must be corrected, if it exceeds 2 s (Kudomi et al., 2009). Basis functions method is another option for computation of parametric RBF images (Kudomi et al., 2009).

Kötz et al (2009) reported range 0.71-0.82 for partition coefficient of water, and 1.30-1.85 mL/(min mL) for blood flow in the kidneys. Kudomi et al (2009) reported that apparent partition coefficient in healthy subjects was on average 0.35 mL/g and RBV was 0.15 mL/mL. Physiological partition coefficient (p_phys) is 0.94 mL/mL (Kudomi et al., 2009). partial volume effect and tissue heterogeneity additionally cause the apparent p to be lower than p_phys; this has been studied especially in [¹⁵O]H₂O brain studies.

The total renal blood volume, including both arterial and venous volumes, can be measured using [¹⁵O]CO. Yamashita et al (1989) reported that the blood volume in 15 subjects was in the range ∼10-20 mL/100 g, and correlates with GFR. Renal blood volume is reduced markedly in murine models of CKD, already prior to fibrosis (Ehling et al., 2016).

Most of the studies compute RBF from K₁, which is affected by PVE and tissue heterogeneity; Kudomi et al (2009), Koivuviita et al (2012), and Päivärinta et al (2018) estimated RBF based on k₂:

Kudomi et al (2009) used p_phys=0.94. RBF based on k₂ is not affected by PVE and heterogeneity, but it is instead affected by glomerular filtration rate (GFR), estimated to be 9.6% of k₂ (Kudomi et al., 2009). Similarly, RBF based on k₂ will not be reduced by increased fraction of non-perfusing tissue volumes, for example scar tissue, but that will be represented as reduced K₁ and K₁/k₂ (p). For perfusion maps, k₂ is more stable than K₁ (Rahman et al., 2019).

Cortical RBF has usually been the parameter of interest, but Damkjær et al (2010) have shown that calculation of medullary perfusion is feasible. Based on K₁, corrected for extraction fraction 0.85, medullary perfusion was 2.30±0.17 mL/(g*min) at baseline, and 2.97±0.18 and 1.57±0.17 mL/(g*min) during glyceryl nitrate infusion and after L-NMMA bolus, respectively. Cortical perfusion values were 4.67±0.31, 4.66±0.53, and 3.48±0.23 mL/(g*min), respectively (Damkjær et al., 2010).

Due to the relatively low time-resolution of PET, the modelling of fast dynamics of reversible tracer uptake is technically demanding and error-prone.

Perfusion ratio

In animal models of kidney diseases, including renal arterial stenosis, fibrosis, and unilateral ureteral obstruction (UUO), one of the kidneys is affected by the disease model and the other kidney serves as control organ. Because the tissue uptake of radiowater correlates with perfusion (although non-linearly), and arterial input function is the same for both kidneys, tissue uptake ratio between the affected and non-affected kidney provides perfusion ratio without arterial sampling. For the non-affected kidney a perfusion ratio of 1 can be used. For control animals, the ratio between individual kidneys can be calculated.

In the analysis of pig model of renal artery stenosis Xia et al (2008) calculated perfusion ratio from AUCs of renal curves; AUC was limited to the first peak of the tissue curves to achieve better linearity between tissue uptake and perfusion. Stenosis was deemed successful only if reduction in perfusion ratio was ≥10%. The same approach has been used in ischemia-reperfusion pig model (Gulaldi et al., 2013).

Perfusion ratio can be biased, as show in a simulation (Figure 1). However, the method is more robust than traditional compartmental model fitting. In rabbits, perfusion ratio separated UUO animals clearly from sham-operated animals, while there was overlap in the results of model fitting (Figure 2). The bias is mainly caused by the non-linear nature of the relationship between tissue uptake and perfusion; shortening integration time only slightly reduces the bias, and the effect of vascular blood is also relatively small. The effect of vascular volume increases with decreasing perfusion.

Perfusion ratio can be calculated from regional TACs using program perfrat.

Arterial blood data

Blood data from online sampler

Arterial blood data, collected using on-line sampling system, must be calibrated and corrected for physical decay, dispersion, and time delay. It is recommended that regional tissue TAC from kidney is used in time delay correction, because aorta or even the heart, where high radioactivity concentration appears considerably sooner than in the kidneys, is also located in the PET image, preventing the use of count rate or head curve for time delay correction.

1. Draw ROIs on kidneys for delay correction (ROIs need not be accurate) and calculate tissue TACs. Do not save aortic TACs in the same TAC file!
2. On MS Windows PC in TPC network, do the corrections for blood data using water_input script. Alternatively, these corrections can also be done using a series of low-level commands.
3. Verify visually that the corrected blood TAC is fine and that time delay correction has moved it to start to rise at the same time as the tissue TACs. Previous water_input command made a graph of these curves. Alternatively you can create the plot by yourself.

Extraction of arterial blood data from PET image

Instead of using ABSS, blood TAC can be extracted from the dynamic image. With modern PET scanners the image resolution is good enough for using the blood TAC from small ROI drawn into abdominal aorta without any correction for partial volume effect. Rahman et al (2019) used profile fitting method to obtain blood TAC in their kidney radiowater study. Factor analysis could be used to derive the BTAC from ascending aorta and TTAC from cortical tissue (Ahn et al., 2000).

Delay correction is usually not needed for input that is extracted from abdominal aorta, and usually the time difference between it and renal tissue is less than 2 s.

Calculation of RBF image

If you have the PET images in DICOM format, convert them to ECAT format.

with basis function method (BFM):

Option #1

RBF image can be calculated with basis function method (Kudomi et al., 2009; Rahman et al., 2019) using rbf_bfm_h2o, version 0.01 or later, in Solaris terminal window on SUN or PC platform (if the Solaris workstation where this software was installed happens to be working).

For example, if the dynamic PET image file name is us345dy1.v, and the pre-corrected arterial blood curve is us345ab.kbq, you would enter the following command:

rbf_bfm_h2o us345ab.kbq us345dy1.v 1. us345rbf.v us345vd.v us0345va.v 10.

This command will create RBF, p, and RBV images as us345rbf.v, us345vd.v, and us345va.v, respectively. All images of inputs and outputs are ECAT7 format. Unit of RBF is [ml blood * min^-1 * (ml renal tissue)^-1] and unit of RBV is [ml blood * (ml renal tissue)^-1].

Option #2

K₁ image, and optionally k₂, K₁/k₂ and RBV images, can be computed using imgbfh2o in Windows, Linux, or macOS command prompt window. Dynamic image data can be in ECAT, Analyze, or NIfTI format.

For example, if the dynamic PET image file name is us4044dy1.v, and the TAC from abdominal aorta is in file us4044aorta.tac, and you wish to calculate RBF from k₂, with 240 s fit time, you would enter the following commands:

imgbfh2o -k2=us4044k2.v -k2max=8 -pmin=0.1 us4044aorta.tac us4044dy1.v 240 us4044k1.v
imgcalc us4044k2.v x 0.94 us4044rbf.v

These commands will create an RBF image us4044rbf.v, where the unit of RBF is [ml blood * min^-1 * (ml renal tissue)^-1]. These parametric images can be processed further as needed.

BFM is based on a list curves calculated with a set of k₂ values. Program imgbfh2o can calculated the range of k₂s based on optional flow and p limits, or k₂ limits can be set directly using options -k2min and -k2max.

BFM will also be implemented in future release of Carimas; please ask Chunlei Han about the status of this project.

with linearized model:

RBF image can be calculated using imgflow in Windows, Linux, or macOS command prompt window. Dynamic image data can be in ECAT, Analyze, or NIfTI format.

For example, if the dynamic PET image file name is us345dy1.img, and the pre-corrected arterial blood curve is us345ab.kbq, you would enter the following command:

imgflow -va=us345rbv.img us345ab.kbq us345dy1.img 180 us345rbf.img

This command will create an RBF image (based on K₁) us345rbf.img and RBV image us345rbv.img. Unit of RBF is [ml blood * min^-1 * (ml renal tissue)^-1] and unit of RBV is [ml blood * (ml renal tissue)^-1]. These parametric images can be processed further as needed. RBF image based on k₂ could be calculated with option -k2 as in a previous example.

Calculation of regional RBF

with traditional non-linear model fitting

After ROIs have have been drawn and average time-activity concentration curves have been calculated from dynamic PET images, the regional RBF can be assessed using fit_h2o in Windows, Linux, or macOS command prompt window.

For example, if the renal TAC file name is us345dy1.dft, and the corrected arterial blood curve is us345ab.kbq, you would enter the following command:

fit_h2o -ml us345ab.kbq us345dy1.dft 240 us345rbf.res

This command will create a result file us345rbf.res, which contains regional RBF, p, and RBV values. If you remembered to put the option -ml to the command line, the unit of RBF is [ml blood * min^-1 * (ml renal tissue)^-1], otherwise [ml blood * min^-1 * (dl renal tissue)^-1].

Sometimes you may need to specify lower and upper limits for the parameters. For this purpose a parameter file needs to be created. It is a text file, which has to be created/edited only once, using for example Notepad in MS Windows or from the command line with command:

fit_h2o -lim=rbf.lim

Suitable contents for RBF calculation are:

K1_lower := 0
K1_upper := 600
K1k2_lower := 0.2
K1k2_upper := 1.2
Va_lower := 0
Va_upper := 40
Delay_lower := 0
Delay_upper := 0

After this, the program is called with following command:

fit_h2o -lim=rbf.lim -ml us345ab.kbq us345dy1.dft 240 us345rbf.res

with basis functions method (BFM):

BFM can be applied to estimate regional RBF using bfmh2o in Windows, Linux, or macOS command prompt window.

For example, if the renal TAC file name is us345dy1.dft, and the corrected arterial blood curve is us345ab.kbq, you would enter the following command:

bfmh2o -ml us345ab.kbq us345dy1.dft 240 us345rbf.res

See also:

• Radiowater model
• ARG method
• Perfusion
• Fick's principle
• Kidneys
• Pancreatic blood flow
• [¹⁵O]CO₂

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Tags: Perfusion, Radiowater, Kidney

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Updated at: 2022-02-02
Created at: 2008-03-18
Written by: Vesa Oikonen