Model for [15O]H2O PET

The methods to measure perfusion with [15O]H2O (diffusible and inert tracer) are based on the principle of exchange of inert gas between blood and tissues (Kety and Schmidt, 1945; Kety, 1985), and on the Fick's principle:

Venous administration of [15O]H2O can be replaced by inhalation of [15O]CO2, because it is instantly converted to [15O]H2O in the lungs by carbonic anhydrase. Being diffusible and inert, [15O]H2O is an optimal tracer for perfusion assessment, but the relatively even distribution of radioactivity shortly after injection makes it difficult to draw ROIs in the image. It takes ∼ 2 h for water (heavy water, D2O) to fully equilibrate in all body fluids, and arterial and venous concentrations reach the same level at about 40 min (Edelman, 1952).

Since (labelled) water diffuses nearly instantly from capillary blood to extra- and intracellular spaces, and back, the [15O]H2O concentrations in the tissue, CT and in the capillary and venous blood, CV, are in equilibrium (unless perfusion is so high that diffusion becomes partly limiting factor). Tissue-to-blood ratio, the partition coefficient (p) of water, is only dependent on the relative water contents of tissue and blood per volume, which are well known in the literature for normal tissues.

Venous [15O]H2O concentration in Eq (1) can be substituted by CT/p, giving ordinary differential equation (ODE)


This is the formula of a compartmental model with one tissue compartment (i.e. two compartmental model), with K1=f and k2=f/p. It is used to describe mathematically the kinetics of [15O]H2O concentration in the tissue, CT(t), depending on the concentration in arterial blood, CA(t), perfusion or blood flow (f), and the partition coefficient of water, p. This ODE can be solved as usual.

When radioactivity in the volume of interest is measured with PET (CPET(t)), the radioactivity of vascular blood inside the measured volume should also be taken into account; VA is the arterial volume fraction in tissue:

Radioactivity concentration in the local venous blood is, by definition, the same as in the local tissue (or to be precise, CT/p), and venous blood volume thus does not need to be included in the formula. Since major part of blood volume in tissue is venous blood, the tissue concentration CT(t) in previous equation does not necessarily have to be scaled with (1-VA), and certainly not with (1-VB), which is customary in compartmental models for other radiopharmaceuticals, because both VB and the arterial fraction of it are unknown. In practise, tissue volume may contain veins coming from other tissues or tissue vasculature where no or less substrate exchange takes place, leading to increase in apparent blood volume. Otherwise than that, non-nutritive (non-effective) blood flow is not affecting the perfusion estimate obtained using [15O]H2O PET (Lammertsma and Jones, 1983). For the quantification of total vascular volume [15O]CO PET would be more accurate, and could be a useful to combine with radiowater-PET when studying microvascular function.

If a marked proportion of the region of interest or image voxel is non-perfusable tissue or vasculature, that can be included in the model as perfusable tissue fraction (PTF) or α:

If the partition coefficient (p) of water in the perfusable tissue is known, then f, VA, and α can be estimated; this method is routinely used in analysis of myocardial radiowater studies.

Bolus infusion studies can be analyzed with kinetic model fitting or autoradiographic (ARG) method. Both methods are based on the same model, and both can be applied to dynamic PET scan data, but static PET data can only be analyzed with ARG method.

Kinetic model vs. autoradiography (ARG) method

ARG method produces perfusion images that are of better quality (less noise) than images produced by kinetic (dynamic) model with low injected dose, enabling many repeated studies to the same subject. Kinetic technique can also generate reproducible perfusion measurements (de Langen et al., 2008).

ARG method can be applied to static PET images, which reduces the image reconstruction time and file size, and due to better count statistics, may provide better image quality. However, ARG method requires that the partition coefficient of water is known, and that it is uniform in all regions of interest. Dynamic method also avoids the tendency to underestimate the blood flow in the presence of flow heterogeneity within a ROI or pixel (Wells et al., 2003). Therefore, if precise quantitation is required or partition coefficient is of interest, dynamic PET imaging and kinetic modelling is recommended.

Quantitative perfusion estimation requires frequent arterial blood sampling. Blood sampling has been omitted in brain activation studies, where only relative perfusion changes are used, but these have been mostly replaced by MRI. Blood TAC is used instead of plasma TACs, because the permeability of red blood cell membranes is very high for water (Eichling et al., 1974). Venous blood cannot be used as model input because of the very high first-pass extraction of water; however, venous sampling could be used to scale input function derived by measuring the radioactivity of exhaled air (Koeppe et al., 1985). Image-derived, population-based, and model-based input functions are used, when possible, instead of arterial sampling.

Kinetic model analysis

The ordinary differential equation for radiowater can be solved, and model parameters parameters fitted, using variable methods, including non-linear fitting and basis function approach. In addition to the analytic solution with convolution,

, the differential equation for radiowater can also be integrated, assuming that all concentrations are zero at time zero, providing equation

, or, if arterial volume fraction is accounted for,

Tissue concentration can then be calculated via direct numerical approach:

, where Δt is the sample time difference.

The integrated equation can be rearranged into a multilinear form, containing only measured concentrations, from which the parameters can be solved using standard linear algorithms, as suggested by Blomqvist (1984):

In this equation, all concentrations and integrals refer to their means during the PET time frame.

Alternatively, both sides of the first integrated equation (where VA is omitted) can be divided by 0TCA to give equation for the Yokoi plot

Like with other multiple-time graphical analysis methods, including Patlak and Logan plots, line can be fitted to the linear phase of the plotted graph. The slope of the line represents -k2, y axis intercept represents K1, and x axis intercept is the p of radiowater (Yokoi et al., 1993).

In the one-tissue compartment model for radiowater, both rate constants K1 (K1=f or K1=α×f) and k2 (k2=f/p) contain the perfusion term f, and therefore perfusion can be measured using either one of the rate constants. Errors in PET data affect the reliability of parameters differently, and depending on the situation, K1- or k2-based perfusion estimates should be used; for example, k2 is not affected by attenuation and partial tissue effect; the quantification of myocardial perfusion is based on k2.

Computation of blood flow images

Before calculation, make sure that both the blood and PET image are in the same calibration units (preferably kBq/mL or Bq/mL). If necessary, filter the dynamic PET image to reduce the noise level.

To compute the perfusion image (where K1 represents the perfusion), one of the CLI programs imgbfh2o (basis function approach) or imgflow (applying NNLS method to solve the multilinear equation) can be used. Optionally, k2 image can be saved and used to compute perfusion image.

The units in the resulting perfusion image are (ml blood)/(min × ml tissue) by default, but it can be changed to per 100 ml tissue with option -dl.

If perfusion is required in units (ml blood)/(min × 100 g tissue), the perfusion image need to be calculated with options -dl and -density=1.04 (1.04 g/mL is the density of the brain and myocardial tissue; density may be very different in other organs, especially in bone, adipose tissue, and tumours).

The results from parametric images should always be validated against results from regional average curves (Lodge et al., 2000). Noise in dynamic image may lead into biased results with distorted variance. Filtering of dynamic images may be needed to achieve the same quantitative results as in the regional analysis. To prevent artefacts and excessive loss of image resolution, the strength of filtering must not exceed the level that is required to achieve comparable results.

Blood flow analysis from regional TACs

Perfusion model parameters can be estimated in CLI using nonlinear fitting with fit_h2o, or using basis function approach with bfmh2o. Both programs estimate the three radiowater model parameters, blood flow (perfusion), partition coefficient

, and arterial volume fraction. In addition, fit_h2o can optionally estimate and correct also the delay time.

Make sure that both the blood and tissue data are in the same calibration units (preferably kBq/mL or Bq/mL) and that the time unit is sec. You can view the files in text editor, or view and convert the units with tacunit.

Weights should be added to tissue data file using tacweigh. Weights can be calculated based on either SIF or the average tissue curves. If weights are extracted from the SIF, the command could be e.g.:

tacweigh -i=O-15 uo268.dft uo268dy1.img.sif

If SIF file is not available, the command could be:

tacweigh uo268.dft

Note that you may need to change the default lower and upper limits for the model parameters.

Steady-state technique

Many of the first quantitative PET studies using [15O]H2O, or actually [15O]CO2, were performed using steady-state technique (Frackowiak et al., 1980): A static PET scan is performed during continuous inhalation of [15O]CO2 (15O-labelled carbon dioxide), which is the same as continuous intravenous infusion of [15O]H2O. After about 10 min inhalation [15O]H2O concentrations in tissues has reached a dynamic equilibrium ("steady state"), in which the influx from arterial blood into tissue equals the efflux into venous blood and the radioactive decay. PET scan may have been started earlier to verify that the equilibrium has been achieved, but the PET data that is actually used in the analysis is collected from the equilibrium phase.

During the steady state, the radioactivity concentration in the tissue, CT, can be described by equation

, where CA is the radioactivity concentration in arterial blood, p is the partition coefficient of water between tissue and blood, f is the perfusion, and λ is the decay constant for 15O. Radioactivity concentrations are, by way of exception, not corrected for decay in steady-state formulas and computations.

By rearrangement, we get an equation for calculation of the tissue perfusion (Frackowiak et al., 1980; Jones et al., 1985; Ruotsalainen et al., 1997):

Steady-state vs. kinetic method

Performing and analysis of steady-state study is very simple, enabling also computation of parametric perfusion images. Noise level in the data can be decreased simply by extending the PET scan length. However, steady-state technique leads to higher radiation dose.

Steady-state approach has the same disadvantages as the ARG method: partition coefficient of water must be known, and tissue heterogeneity causes underestimation in perfusion estimates.

Whole-body model for [15O]H2O

Comprehensive whole-body pharmacokinetic models for [15O]H2O have been developed for dosimetry (Brihaye et al., 1995) and simulation (Narayana et al., 1997). For describing the [15O]H2O concentration in blood, simplified models with just few compartments have been developed (Bigler et al., 1981; Maguire et al., 2003). The study of Bigler et al. (1981) was mainly aimed at understanding the kinetics of [15O]O2 and its metabolite [15O]H2O in the brain; the model consists of a central compartment (blood water) and water in two reversible tissue compartments, one for slow and the other for rapidly exchanging water. The model is similar to the PK three-compartment model without the clearance term. The model contains four rate constants, and the model was be fitted to the D2O data by Edelman et al (1952).

Maguire et al. (2003) used a rectangular (boxcar) function to represent bolus infusion of the radiowater. The model was applied to arterial blood data from actual [15O]H2O PET studies. Central compartment is the site of tracer administration and the site of sampling; sampled blood is assumed to be delayed and dispersed. The authors tested if one of the tissue compartments could be removed, or assumed irreversible, and, the best model setting was found to be one with irreversible slow tissue compartment.

PK model for radiowater
Pharmacokinetic model for [15O]H2O. Due to short half-life of 15O, study durations are short and k3 can be set to zero. This effectively replaces the slow exchanging component by a clearance term, and is close to two-compartment PK model.

See also:


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Edelman IS. Exchange of water between blood and tissues - characteristics of deuterium oxide equilibration in body water. Am J Physiol. 1952; 171(2): 279-296. doi: 10.1152/ajplegacy.1952.171.2.279.

Eichling JO, Raichle ME, Grubb RL Jr, Ter-Pogossian MM. Evidence of the limitations of water as a freely diffusible tracer in brain of the Rhesus monkey. Circ Res. 1974; 35: 358-364. doi: 10.1161/01.RES.35.3.358.

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Huang S-C, Carson RE, Phelps ME. Measurement of local blood flow and distribution volume with short-lived isotopes: a general input technique. J Cereb Blood Flow Metab. 1982; 2: 99-108. doi: 10.1038/jcbfm.1982.11.

Jones SC, Greenberg JH, Dann R, Robinson GD Jr, Kushner M, Alavi A, Reivich M. Cerebral blood flow with the continuous infusion of oxygen-15-labeled water. J Cereb Blood Flow Metab. 1985; 5: 566-575. doi: 10.1038/jcbfm.1985.85.

Kety SS, Schmidt CF. The determination of cerebral blood flow in man by the use of nitrous oxide in low concentrations. Am J Physiol. 1945; 143: 53-66. doi: 10.1152/ajplegacy.1945.143.1.53.

Kety SS. Regional cerebral blood flow: estimation by means of nonmetabolized diffusible tracers - and overview. Semin Nucl Med. 1985; 15(4): 324-328. doi: 10.1016/S0001-2998(85)80010-6.

Lammertsma AA, Jones T. Correction for the presence of intravascular oxygen-15 in the steady-state technique for measuring regional oxygen extraction ratio in the brain: 1. Description of the method. J Cereb Blood Flow Metab. 1983; 3: 416-424. doi: 10.1038/jcbfm.1983.67.

Lammertsma AA. Quantification of cerebral blood flow. Neuromethods 2012; 71: 99-109. doi: 10.1007/7657_2012_43.

de Langen A, Lubberink M, Boellaard R, Spreeuwenberg MD, Smit EF, Hoekstra OS, Lammertsma AA. Reproducibility of tumor perfusion measurements using 15O-labeled water and PET. J Nucl Med. 2008; 49(11): 1763-1768. doi: 10.2967/jnumed.108.053454.

Lodge MA, Carson RE, Carrasquillo JA, Whatley M, Libutti SK, Bacharach SL. Parametric images of blood flow in oncology PET studies using [15O]water. J Nucl Med. 2000; 41:1784-1792. PMID: 11079484.

Ruotsalainen U, Raitakari M, Nuutila P, Oikonen V, Sipilä H, Teräs M, Knuuti J, Bloomfield PM, Iida H. Quantitative blood flow measurement of skeletal muscle using oxygen-15-water and PET. J Nucl Med. 1997; 38: 314-319. PMID: 9025761.

Ter-Pogossian MM, Eichling JO, Davis DO, Welch MJ, Metzger JM. The determination of regional cerebral blood flow by means of water labeled with radioactive oxygen 15. Radiology 1969; 93(1): 31-40. doi: 10.1148/93.1.31.

van den Hoff J, Burchert W, Müller-Schauenburg W, Meyer G-J, Hundeshagen H. Accurate local blood flow measurements with dynamic PET: fast determination of input function delay and dispersion by multilinear minimization. J Nucl Med. 1993; 34: 1770-1777. PMID: 8410297.

Wells P, Jones T, Price P. Assessment of inter- and intrapatient variability in C15O2 positron emission tomography measurements of blood flow in patients with intra-abdominal cancers. Clin Cancer Res. 2003; 9: 6350-6356. PMID: 14695134.

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Updated at: 2023-07-01
Created at: 2008-03-13
Written by: Vesa Oikonen