Transverse section imaging of mean clearance time

Cerebral oxygen delivery by liposome-encapsulated hemoglobin: a positron-emission tomographic evaluation in a rat model of hemorrhagic shock

Liposome-encapsulated Hb (LEH) is being developed as an artificially assembled, low-toxicity, and spatially isolated Hb-based oxygen carrier (HBOC). Standard methods of evaluating oxygen carriers are based on surrogate indicators of physiology in animal models of shock. Assessment of actual delivery of oxygen by HBOCs and resultant improvement in oxygen metabolism at the tissue level has been a technical challenge. In this work, we report our findings from 15O-positron emission tomographic (15O-PET) evaluation of LEH in a rat model of 40% hypovolemic shock. In vitro studies showed that PEGylated LEH formulation containing approximately 7.5% Hb and consisting of neutral lipids (distearoylphosphatidylcholine:cholesterol:alpha-tocopherol, 51.4:46.4:2.2) efficiently picks up 15O-labeled oxygen gas. The final preparation of LEH contained 5% human serum albumin to provide oncotic pressure. Cerebral PET images of anesthetized rats inhaling 15O-labeled O2 gas showed efficient oxygen-carrying and delivery capacity of LEH formulation. From the PET images, we determined cerebral metabolic rate of oxygen (CMR(O2)) as a direct indicator of oxygen-carrying capacity of LEH as well as oxygen delivery and metabolism in rat brain. Compared with control fluids [saline and 5% human serum albumin (HSA)], LEH significantly improved CMR(O2) to approximately 80% of baseline level. Saline and HSA resuscitation could not improve hypovolemia-induced decrease in CMR(O2). On the other hand, resuscitation of shed blood was the most efficient in restoring oxygen metabolism. The results suggest that 15O-PET technology can be successfully employed to evaluate potential oxygen carriers and blood substitutes and that LEH resuscitation in hemorrhage enhances oxygen delivery to the cerebral tissue and improves oxygen metabolism in brain.

Accurate determination of metabolic rates from dynamic positron emission tomography data with very-low temporal resolution

PURPOSE

The graphical approach is widely used for the pixelwise determination of local metabolic rate of glucose from dynamic positron emission tomography (PET) data. In its conventional implementation, measured integrals over time frames are used to approximate instantaneous tracer concentrations at midframe times ("midframe approach"). This is justified in case of high temporal resolution of the PET measurement; that is, if scan protocols with a large number of short frames are used. This requires fast data handling and large amounts of memory. Cardiac gating and three-dimensional (3D) acquisition of dynamic studies is hardly possible with this approach. Therefore, a new variant of the graphical method is proposed which can be used with a very low number of rather long frames.

METHODS

An operational equation of the graphical method was derived which uses measured time integrals only and, thus, avoids the systematic errors of the midframe approximation. This "integral approach" was evaluated in computer simulations based on experimental data.

RESULTS

The integral approach enables the use of protocols with 3 frames only without compromising accuracy of the derived metabolic rates whereas the midframe approach leads to bias of about 10% to 20% for these protocols. Furthermore, test-retest stability can significantly be improved when using the integral approach.

CONCLUSION

The integral approach to the graphical evaluation of dynamic PET data yields accurate and precise results using scan protocols with down to only 3 frames. This can be relevant to gating and/or 3D acquisition of dynamic studies. The integral approach is applied most naturally whenever the input function is derived from the dynamic PET data.

Variance in parametric images: direct estimation from parametric projections

Recent work has shown that it is possible to apply linear kinetic models to dynamic projection data in PET in order to calculate parameter projections. These can subsequently be back-projected to form parametric images--maps of parameters of physiological interest. Critical to the application of these maps, to test for significant changes between normal and pathophysiology, is an assessment of the statistical uncertainty. In this context, parametric images also include simple integral images from, e.g., [O-15]-water used to calculate statistical parametric maps (SPMs). This paper revisits the concept of parameter projections and presents a more general formulation of the parameter projection derivation as well as a method to estimate parameter variance in projection space, showing which analysis methods (models) can be used. Using simulated pharmacokinetic image data we show that a method based on an analysis in projection space inherently calculates the mathematically rigorous pixel variance. This results in an estimation which is as accurate as either estimating variance in image space during model fitting, or estimation by comparison across sets of parametric images--as might be done between individuals in a group pharmacokinetic PET study. The method based on projections has, however, a higher computational efficiency, and is also shown to be more precise, as reflected in smooth variance distribution images when compared to the other methods.

Dynamic imaging and tracer kinetic modeling for emission tomography using rotating detectors

When performing dynamic studies using emission tomography the tracer distribution changes during acquisition of a single set of projections. This is particularly true for some positron emission tomography (PET) systems which, like single photon emission computed tomography (SPECT), acquire data over a limited angle at any time, with full projections obtained by rotation of the detectors. In this paper, an approach is proposed for processing data from these systems, applicable to either PET or SPECT. A method of interpolation, based on overlapped parabolas, is used to obtain an estimate of the total counts in each pixel of the projections for each required frame-interval, which is the total time to acquire a single complete set of projections necessary for reconstruction. The resultant projections are reconstructed using traditional filtered backprojection (FBP) and tracer kinetic parameters are estimated using a method which relies on counts integrated over the frame-interval rather than instantaneous values. Simulated data were used to illustrate the technique's capabilities with noise levels typical of those encountered in either PET or SPECT. Dynamic datasets were constructed, based on kinetic parameters for fluoro-deoxy-glucose (FDG) and use of either a full ring detector or rotating detector acquisition. For the rotating detector, use of the interpolation scheme provided reconstructed dynamic images with reduced artefacts compared to unprocessed data or use of linear interpolation. Estimates for the metabolic rate of glucose had similar bias to those obtained from a full ring detector.

Parametric image reconstruction using spectral analysis of PET projection data

Spectral analysis is a general modelling approach that enables calculation of parametric images from reconstructed tracer kinetic data independent of an assumed compartmental structure. We investigated the validity of applying spectral analysis directly to projection data motivated by the advantages that: (i) the number of reconstructions is reduced by an order of magnitude and (ii) iterative reconstruction becomes practical which may improve signal-to-noise ratio (SNR). A dynamic software phantom with typical 2-[11C]thymidine kinetics was used to compare projection-based and image-based methods and to assess bias-variance trade-offs using iterative expectation maximization (EM) reconstruction. We found that the two approaches are not exactly equivalent due to properties of the non-negative least-squares algorithm. However, the differences are small (< 5%) and mainly affect parameters related to early and late time points on the impulse response function (K1 and, to a lesser extent, VD). The optimal number of EM iteration was 15-30 with up to a two-fold improvement in SNR over filtered back projection. We conclude that projection-based spectral analysis with EM reconstruction yields accurate parametric images with high SNR and has potential application to a wide range of positron emission tomography ligands.

An investigation of multiple time/graphical analysis applied to projection data: theory and validation

PURPOSE

The determination of tissue time-activity course and pharmokinetics in PET is normally performed by region-of-interest analysis of reconstructed images. However, in some cases, the same analysis may equally well be performed on the data in projections before reconstruction, avoiding the reconstruction of large time sequence data sets. This is especially important in 3D mode.

METHOD

We present a theory that shows why multiple time/graphical analysis can be applied equally well to image or projection data. The method is validated using FDG uptake data from five healthy normal volunteers, by applying the technique to determine regional cerebral metabolic rate for glucose (rCMRglu) and the partition coefficient-related parameter P using various time ranges for the analysis.

RESULTS

The method is shown to be identical to analysis of image data. Variation with time range of the calculated values for regional cerebral glucose metabolism and the partition coefficient of tissue against plasma is shown to be due to the estimation methodology rather than the choice of analysis on projections or on images.

CONCLUSION

The theory presented is shown to be valid for FDG determination of regional cerebral glucose metabolism. The absolute values of the rCMRglu and P are similar to those shown previously.

A new approach of weighted integration technique based on accumulated images using dynamic PET and H2(15)O

We developed a new technique of weighted integration for the measurement of local cerebral blood flow (LCBF) and the blood-tissue partition coefficient (p) using dynamic positron emission tomography (PET) and H2(15)O. The weighted integration in the new technique is carried out on the equation of the first time integration of the Kety-Schmidt differential equation. Practically, serially accumulated images with sequentially prolonged accumulation times are weighted by two arbitrary functions. The weighting functions do not have to be differentiated because of the exclusion of the differential term in the starting equation. Consequently, the method does not require data at the end of the scan. The technique was applied to H2(15)O dynamic PET performed on four normal subjects, and was verified to provide a better signal-to-noise ratio than the previously developed integrated projection (IP) technique. Computer simulations were carried out to investigate the effects of statistical noise, tissue heterogeneity, and time delay and dispersion in arterial input function. The simulation showed that the new technique provided about a 1.4 times lower statistical error in both LCBF and p at 50 ml 100 g-1 min-1 compared to the IP technique, and it should be noted that the new technique was less sensitive to the shape of the weighting functions. The new technique provides a new strategy with respect to the statistical error for estimation of LCBF and p.

A study of the single compartment tracer kinetic model for the measurement of local cerebral blood flow using 15O-water and positron emission tomography

The effects of varying the data collection time on the calculation of cerebral blood flow and distribution volume via the integrated projection technique were studied in four human subjects. The significance of these results in terms of the limitations of the single compartment model for 15O-water was explored using computer simulations. The simulations helped to account for causes for the variations seen in blood flow and distribution volume as a function of the data collection time. Two different compartmental models were explored for better quantitation of blood flow and distribution volume.

Weighted integration method for local cerebral blood flow measurements with positron emission tomography

A new technique called the weighted integration method for the measurement of local CBF (LCBF) in humans with positron emission tomography (PET) is presented. LCBF is calculated from weighted time integrals of the blood and tissue radioactivity curves. This method is computationally efficient and achieves nearly optimal statistical estimation of LCBF. The predicted root mean squared error of the weighted integration method is verified by simulation studies and is only 1-2% larger than the minimum possible error that can be achieved by an ideal estimation algorithm. For LCBF of greater than 30 ml/min/100 g, the weighted integration method provides reduced noise compared with the integrated projection technique, the PET autoradiographic method, and the steady-state technique. In addition, an error analysis is performed to study the sensitivity of the weighted integration method to tissue mixtures, blood sample timing errors, and changes in LCBF during the data collection period.

Performance comparison of parameter estimation techniques for the quantitation of local cerebral blood flow by dynamic positron computed tomography

Local CBF (LCBF) can be quantitated from positron computed tomographic (PCT) data and physiologically based mathematical models by several general methods. Those using a dynamic sequence of PCT scans allow the simultaneous estimation of both LCBF and p, the indicator's tissue-blood partition coefficient. This article presents a comparison of three rapid estimation techniques for use with inert diffusible radioindicators and serial PCT, each of which is based on the original Kety model. One method, developed in our laboratory, involves minimizing the mean squared discrepancy between measured data and model predictions, whereas the other two methods, recently reported in the literature, are weighted integration techniques that involve multiplying the measured data by time-dependent weighting functions. Simulation studies of noise propagation and other sources of error were performed under a variety of simulated conditions. Functional images of LCBF and p were calculated using each method for both phantom and human subject data. Errors can differ by as much as a factor of 2-3 between methods, with each having its own unique advantages and disadvantages.

Positron emission tomography

One of the most exciting new techniques introduced in the last ten years is positron emission tomography (PET). PET provides quantitative, three-dimensional images for the study of specific biochemical and physiological processes in the human body. This approach is analogous to quantitative in vivo autoradiography but has the added advantage of permitting non-invasive in vivo studies. PET scanning requires a small cyclotron to produce short-lived positron emitting isotopes such as oxygen-15, carbon-11, nitrogen-13 and fluorine-18. Proper radiochemical facilities and advanced computer equipment are also needed. Most important, PET requires a multidisciplinary scientific team of physicists, radiochemists, mathematicians, biochemists and physicians. This review analyses the most recent trends in imaging technology, radiochemistry, methodology, and clinical applications of positron emission tomography.

On the construction of functional maps in positron emission tomography

A linear algorithm for the rapid calculation of local rate constants is proposed. The method is applicable to the three-compartment models currently used in the analysis of positron camera measurements with [11C]methionine, [11C]deoxyglucose, and [11C]glucose. The same technique can also be used for the regional measurement of local blood flow with the aid of a freely diffusible tracer. The algorithm was applied to measurements on humans with [11C]glucose. As a comparison, the same data were also analyzed with a standard nonlinear technique. Good agreement between the two methods was obtained.

Measurement of cerebral blood flow using bolus inhalation of C15O2 and positron emission tomography: description of the method and its comparison with the C15O2 continuous inhalation method

This article describes a rapid method for the regional measurement of cerebral blood flow using a single breath of C15O2 and positron emission tomography. The technique is based on the bolus distribution principle and utilises a reference table for the calculation of flow. Seven subjects were studied using both this method and the C15O2 continuous inhalation steady-state technique. The single-breath method gave flow values 20% higher than those obtained using the steady-state method. A simulation study was performed in an attempt to define the reasons for the difference between the two techniques. Estimations were made of identified sources of error in the measurement of regional cerebral blood flow using the single-breath technique and compared with results from a similar study previously described for the steady-state technique. However, further comparative studies will be necessary to satisfactorily explain the difference between both techniques.

Strategy for the measurement of regional cerebral blood flow using short-lived tracers and emission tomography

This report describes a strategy for measurement of regional CBF that rigorously accounts for differing tracer partition coefficients and recirculation, and is convenient for use with positron emission tomography. Based on the Kety model, the measured tissue concentration can be expressed in terms of the arterial concentration, the rate constant K, and the blood flow f. The local partition coefficient may be computed as p = f/K. In our approach, maps of K and f are computed from two transverse section reconstructions. The reconstructions are based on weighted sums of projection data measured frequently during the observation period. Theoretical studies of noise propagation in the estimates of K and f were carried out as a function of tomographic count rate, total measurement time, and tracer half-life for varying input functions. These calculations predict that statistical errors in f of between 5 and 10% at a resolution of 1 cm full width at half maximum can be obtained with existing tomographs following i.v. injection. To compare theory and experiment, a series of flow studies were carried out in phantoms using a positron tomograph. These measurements demonstrate close agreement between computed flow and noise estimates and those measured in a controlled situation. This close agreement between theory and experiment as well as the low statistical errors observed suggest that this approach may be a useful tool in clinical investigation.

Quantitative measurement of local cerebral blood flow in humans by positron computed tomography and 15O-water

A noninvasive method that employs 15O-water and positron-computed tomography (PCT) was used to measure quantitative local cerebral blood flow (lCBF) in man. 15O-Water (about 30-50 mCi) was introduced through a single-breath inhalation of 15O-carbon dioxide or through an intravenous bolus injection of 15O-water. A sequence of five 2-min PCT scans was initiated at the time of tracer administration. A series of 15-20 blood samples (1 ml each) was withdrawn from the radial artery of the subject over a period of 10 min. Oxygen-15 radioactivities in the blood samples were immediately counted in a well counter to give an input function, which together with the projection data collected by PCT were processed to provide images of 1CBF and local water distribution volume. The method was found to be convenient to use and gave good-quality images of 1CBF. Quantitative values of 1CBF in images were 59 +/- 11 and 20 +/- 4 ml/min/100 g for gray and white matter, respectively, with a gray-to-white matter ratio of 2.93 and a global flow value of 42 +/- 8 ml/min/100 g. Distribution volume of water was 0.85 +/- 0.03, 0.76 +/- 0.03, and 0.81 +/- 0.02 ml/g respectively, for gray matter, white matter, and whole brain.

Measurement of local blood flow and distribution volume with short-lived isotopes: a general input technique

A new technique for measuring local blood flow and distribution volume is proposed. The technique uses short-lived isotopes but is different from the equilibrium method in that no constant input is necessary, and no assumption about distribution volume is needed. The theoretical basis of the technique is developed, and the results of a computer-simulation study are presented to show the potential of the technique. The technique is expected to be easier to perform and to give more accurate flow values than the equilibrium method.