Simultaneous estimation of physiological parameters and the input function--in vivo PET data

Non-invasive [15O]H2O PET measurements of cerebral perfusion and cerebrovascular reactivity using an additional heart scan

Obtaining the arterial input function (AIF) is essential for quantitative regional cerebral perfusion (rCBF) measurements using [15O]H2O PET. However, arterial blood sampling is invasive and complicates the scanning procedure. We propose a new non-invasive dual scan technique with an image derived input function (IDIF) from an additional heart scan. Six patients and two healthy subjects underwent [15O]H2O PET imaging of 1) heart and brain during baseline, and 2) heart and brain after infusion of acetazolamide. The IDIF was extracted from the left ventricle of the heart and compared to the AIF. The rCBF was compared for six bilateral cortical regions. AIFs and IDIFs showed strong agreement. rCBF with AIF and IDIF showed strong correlation for both baseline rCBF (R2 = 0.99, slope = 0.89 CI: [0.87; 0.91], p < 0.0001) and acetazolamide rCBF (R2 = 0.98, slope = 0.93, CI:[0.90;0.97], p < 0.0001) but showed a positive bias of 0.047 mL/(g·min) [-0.025; +0.119] for baseline and 0.024 [-1.04, +1.53] mL/(g·min) for acetazolamide. In conclusion, the invasive arterial cannulation can be replaced by an additional scan of the heart with a minor bias of rCBF estimation. The method is applicable to all scanner systems.

Exact parameter identification in PET pharmacokinetic modeling using the irreversible two tissue compartment model. Phys Med Biol 2024;69:165008. [PMID: 38830366 PMCID: PMC11288174 DOI: 10.1088/1361-6560/ad539e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Objective.In quantitative dynamic positron emission tomography (PET), time series of images, reflecting the tissue response to the arterial tracer supply, are reconstructed. This response is described by kinetic parameters, which are commonly determined on basis of the tracer concentration in tissue and the arterial input function. In clinical routine the latter is estimated by arterial blood sampling and analysis, which is a challenging process and thus, attempted to be derived directly from reconstructed PET images. However, a mathematical analysis about the necessity of measurements of the common arterial whole blood activity concentration, and the concentration of free non-metabolized tracer in the arterial plasma, for a successful kinetic parameter identification does not exist. Here we aim to address this problem mathematically.Approach.We consider the identification problem in simultaneous pharmacokinetic modeling of multiple regions of interests of dynamic PET data using the irreversible two-tissue compartment model analytically. In addition to this consideration, the situation of noisy measurements is addressed using Tikhonov regularization. Furthermore, numerical simulations with a regularization approach are carried out to illustrate the analytical results in a synthetic application example.Main results.We provide mathematical proofs showing that, under reasonable assumptions, all metabolic tissue parameters can be uniquely identified without requiring additional blood samples to measure the arterial input function. A connection to noisy measurement data is made via a consistency result, showing that exact reconstruction of the ground-truth tissue parameters is stably maintained in the vanishing noise limit. Furthermore, our numerical experiments suggest that an approximate reconstruction of kinetic parameters according to our analytic results is also possible in practice for moderate noise levels.Significance.The analytical result, which holds in the idealized, noiseless scenario, suggests that for irreversible tracers, fully quantitative dynamic PET imaging is in principle possible without costly arterial blood sampling and metabolite analysis.

Non-Invasive Quantification of the Brain [¹⁸F]FDG-PET Using Inferred Blood Input Function Learned From Total-Body Data With Physical Constraint

Full quantification of brain PET requires the blood input function (IF), which is traditionally achieved through an invasive and time-consuming arterial catheter procedure, making it unfeasible for clinical routine. This study presents a deep learning based method to estimate the input function (DLIF) for a dynamic brain FDG scan. A long short-term memory combined with a fully connected network was used. The dataset for training was generated from 85 total-body dynamic scans obtained on a uEXPLORER scanner. Time-activity curves from 8 brain regions and the carotid served as the input of the model, and labelled IF was generated from the ascending aorta defined on CT image. We emphasize the goodness-of-fitting of kinetic modeling as an additional physical loss to reduce the bias and the need for large training samples. DLIF was evaluated together with existing methods in terms of RMSE, area under the curve, regional and parametric image quantifications. The results revealed that the proposed model can generate IFs that closer to the reference ones in terms of shape and amplitude compared with the IFs generated using existing methods. All regional kinetic parameters calculated using DLIF agreed with reference values, with the correlation coefficient being 0.961 (0.913) and relative bias being 1.68±8.74% (0.37±4.93%) for [Formula: see text] ( [Formula: see text]. In terms of the visual appearance and quantification, parametric images were also highly identical to the reference images. In conclusion, our experiments indicate that a trained model can infer an image-derived IF from dynamic brain PET data, which enables subsequent reliable kinetic modeling.

Deep-learning-derived input function in dynamic [18F]FDG PET imaging of mice

Dynamic positron emission tomography and kinetic modeling play a critical role in tracer development research using small animals. Kinetic modeling from dynamic PET imaging requires accurate knowledge of an input function, ideally determined through arterial blood sampling. Arterial cannulation in mice, however, requires complex, time-consuming and terminal surgery, meaning that longitudinal studies are impossible. The aim of the current work was to develop and evaluate a non-invasive, deep-learning-based prediction model (DLIF) that directly takes the PET data as input to predict a usable input function. We first trained and evaluated the DLIF model on 68 [18F]Fluorodeoxyglucose mouse scans with image-derived targets using cross validation. Subsequently, we evaluated the performance of a trained DLIF model on an external dataset consisting of 8 mouse scans where the input function was measured by continuous arterial blood sampling. The results showed that the predicted DLIF and image-derived targets were similar, and the net influx rate constants following from Patlak modeling using DLIF as input function were strongly correlated to the corresponding values obtained using the image-derived input function. There were somewhat larger discrepancies when evaluating the model on the external dataset, which could be attributed to systematic differences in the experimental setup between the two datasets. In conclusion, our non-invasive DLIF prediction method may be a viable alternative to arterial blood sampling in small animal [18F]FDG imaging. With further validation, DLIF could overcome the need for arterial cannulation and allow fully quantitative and longitudinal experiments in PET imaging studies of mice.

Kinetic Modeling of Brain [18-F]FDG Positron Emission Tomography Time Activity Curves with Input Function Recovery (IR) Method

Accurate positron emission tomography (PET) data quantification relies on high-quality input plasma curves, but venous blood sampling may yield poor-quality data, jeopardizing modeling outcomes. In this study, we aimed to recover sub-optimal input functions by using information from the tail (5th-100th min) of curves obtained through the frequent sampling protocol and an input recovery (IR) model trained with reference curves of optimal shape. Initially, we included 170 plasma input curves from eight published studies with clamp [18F]-fluorodeoxyglucose PET exams. Model validation involved 78 brain PET studies for which compartmental model (CM) analysis was feasible (reference (ref) + training sets). Recovered curves were compared with original curves using area under curve (AUC), max peak standardized uptake value (maxSUV). CM parameters (ref + training sets) and fractional uptake rate (FUR) (all sets) were computed. Original and recovered curves from the ref set had comparable AUC (d = 0.02, not significant (NS)), maxSUV (d = 0.05, NS) and comparable brain CM results (NS). Recovered curves from the training set were different from the original according to maxSUV (d = 3) and biologically plausible according to the max theoretical K1 (53//56). Brain CM results were different in the training set (p < 0.05 for all CM parameters and brain regions) but not in the ref set. FUR showed reductions similarly in the recovered curves of the training and test sets compared to the original curves (p < 0.05 for all regions for both sets). The IR method successfully recovered the plasma inputs of poor quality, rescuing cases otherwise excluded from the kinetic modeling results. The validation approach proved useful and can be applied to different tracers and metabolic conditions.

Simultaneous estimation of a model-derived input function for quantifying cerebral glucose metabolism with [18F]FDG PET

BACKGROUND

Quantification of the cerebral metabolic rate of glucose (CMRGlu) by dynamic [18F]FDG PET requires invasive arterial sampling. Alternatives to using an arterial input function (AIF) include the simultaneous estimation (SIME) approach, which models the image-derived input function (IDIF) by a series of exponentials with coefficients obtained by fitting time activity curves (TACs) from multiple volumes-of-interest. A limitation of SIME is the assumption that the input function can be modelled accurately by a series of exponentials. Alternatively, we propose a SIME approach based on the two-tissue compartment model to extract a high signal-to-noise ratio (SNR) model-derived input function (MDIF) from the whole-brain TAC. The purpose of this study is to present the MDIF approach and its implementation in the analysis of animal and human data.

METHODS

Simulations were performed to assess the accuracy of the MDIF approach. Animal experiments were conducted to compare derived MDIFs to measured AIFs (n = 5). Using dynamic [18F]FDG PET data from neurologically healthy volunteers (n = 18), the MDIF method was compared to the original SIME-IDIF. Lastly, the feasibility of extracting parametric images was investigated by implementing a variational Bayesian parameter estimation approach.

RESULTS

Simulations demonstrated that the MDIF can be accurately extracted from a whole-brain TAC. Good agreement between MDIFs and measured AIFs was found in the animal experiments. Similarly, the MDIF-to-IDIF area-under-the-curve ratio from the human data was 1.02 ± 0.08, resulting in good agreement in grey matter CMRGlu: 24.5 ± 3.6 and 23.9 ± 3.2 mL/100 g/min for MDIF and IDIF, respectively. The MDIF method proved superior in characterizing the first pass of [18F]FDG. Groupwise parametric images obtained with the MDIF showed the expected spatial patterns.

CONCLUSIONS

A model-driven SIME method was proposed to derive high SNR input functions. Its potential was demonstrated by the good agreement between MDIFs and AIFs in animal experiments. In addition, CMRGlu estimates obtained in the human study agreed to literature values. The MDIF approach requires fewer fitting parameters than the original SIME method and has the advantage that it can model the shape of any input function. In turn, the high SNR of the MDIFs has the potential to facilitate the extraction of voxelwise parameters when combined with robust parameter estimation methods such as the variational Bayesian approach.

Current and Future Use of Long Axial Field-of-View Positron Emission Tomography/Computed Tomography Scanners in Clinical Oncology

The latest technical development in the field of positron emission tomography/computed tomography (PET/CT) imaging has been the extension of the PET axial field-of-view. As a result of the increased number of detectors, the long axial field-of-view (LAFOV) PET systems are not only characterized by a larger anatomical coverage but also by a substantially improved sensitivity, compared with conventional short axial field-of-view PET systems. In clinical practice, this innovation has led to the following optimization: (1) improved overall image quality, (2) decreased duration of PET examinations, (3) decreased amount of radioactivity administered to the patient, or (4) a combination of any of the above. In this review, novel applications of LAFOV PET in oncology are highlighted and future directions are discussed.

Quantitation of dynamic total-body PET imaging: recent developments and future perspectives

BACKGROUND

Positron emission tomography (PET) scanning is an important diagnostic imaging technique used in disease diagnosis, therapy planning, treatment monitoring, and medical research. The standardized uptake value (SUV) obtained at a single time frame has been widely employed in clinical practice. Well beyond this simple static measure, more detailed metabolic information can be recovered from dynamic PET scans, followed by the recovery of arterial input function and application of appropriate tracer kinetic models. Many efforts have been devoted to the development of quantitative techniques over the last couple of decades.

CHALLENGES

The advent of new-generation total-body PET scanners characterized by ultra-high sensitivity and long axial field of view, i.e., uEXPLORER (United Imaging Healthcare), PennPET Explorer (University of Pennsylvania), and Biograph Vision Quadra (Siemens Healthineers), further stimulates valuable inspiration to derive kinetics for multiple organs simultaneously. But some emerging issues also need to be addressed, e.g., the large-scale data size and organ-specific physiology. The direct implementation of classical methods for total-body PET imaging without proper validation may lead to less accurate results.

CONCLUSIONS

In this contribution, the published dynamic total-body PET datasets are outlined, and several challenges/opportunities for quantitation of such types of studies are presented. An overview of the basic equation, calculation of input function (based on blood sampling, image, population or mathematical model), and kinetic analysis encompassing parametric (compartmental model, graphical plot and spectral analysis) and non-parametric (B-spline and piece-wise basis elements) approaches is provided. The discussion mainly focuses on the feasibilities, recent developments, and future perspectives of these methodologies for a diverse-tissue environment.

PET AIF estimation when available ROI data is impacted by dispersive and/or background effects

Objective.Blood pool region of interest (ROI) data extracted from the field of view of a PET scanner can be impacted by both dispersive and background effects. This circumstance compromises the ability to correctly extract the arterial input function (AIF) signal. The paper explores a novel approach to addressing this difficulty.Approach.The method involves representing the AIF in terms of the whole-body impulse response (IR) to the injection profile. Analysis of a collection/population of directly sampled arterial data sets allows the statistical behaviour of the tracer's impulse response to be evaluated. It is proposed that this information be used to develop a penalty term for construction of a data-adaptive method of regularisation estimator of the AIF when dispersive and/or background effects maybe impacting the blood pool ROI data.Main results.Computational efficiency of the approach derives from the linearity of the impulse response representation of the AIF and the ability to substantially rely on quadratic programming techniques for numerical implementation. Data from eight different tracers, used in PET cancer imaging studies, are considered. Sample image-based AIF extractions for brain studies with:18F-labeled fluoro-deoxyglucose and fluoro-thymidine (FLT),11C-labeled carbon dioxide (CO2) and15O-labeled water (H2O) are presented. Results are compared to the true AIF based on direct arterial sampling. Formal numerical simulations are used to evaluate the performance of the AIF extraction method when the ROI data has varying amounts of contamination, in comparison to a direct approach that ignores such effects. It is found that even with quite small amounts of contamination, the mean squared error of the regularised AIF is significantly better than the error associated with direct use of the ROI data.Significance.The proposed IR-based AIF extraction scheme offers a practical methodological approach for situations where the available image ROI data may be contaminated by background and/or dispersion effects.

Non-invasive kinetic modelling approaches for quantitative analysis of brain PET studies

Pharmacokinetic modelling with arterial sampling is the gold standard for analysing dynamic PET data of the brain. However, the invasive character of arterial sampling prevents its widespread clinical application. Several methods have been developed to avoid arterial sampling, in particular reference region methods. Unfortunately, for some tracers or diseases, no suitable reference region can be defined. For these cases, other potentially non-invasive approaches have been proposed: (1) a population based input function (PBIF), (2) an image derived input function (IDIF), or (3) simultaneous estimation of the input function (SIME). This systematic review aims to assess the correspondence of these non-invasive methods with the gold standard. Studies comparing non-invasive pharmacokinetic modelling methods with the current gold standard methods using an input function derived from arterial blood samples were retrieved from PubMed/MEDLINE (until December 2021). Correlation measurements were extracted from the studies. The search yielded 30 studies that correlated outcome parameters (V_T, DVR, or BP_ND for reversible tracers; K_i or CMR_glu for irreversible tracers) from a potentially non-invasive method with those obtained from modelling using an arterial input function. Some studies provided similar results for PBIF, IDIF, and SIME-based methods as for modelling with an arterial input function (R² = 0.59-1.00, R² = 0.71-1.00, R² = 0.56-0.96, respectively), if the non-invasive input curve was calibrated with arterial blood samples. Even when the non-invasive input curve was calibrated with venous blood samples or when no calibration was applied, moderate to good correlations were reported, especially for the IDIF and SIME (R² = 0.71-1.00 and R² = 0.36-0.96, respectively). Overall, this systematic review illustrates that non-invasive methods to generate an input function are still in their infancy. Yet, IDIF and SIME performed well, not only with arterial blood calibration, but also with venous or no blood calibration, especially for some tracers without plasma metabolites, which would potentially make these methods better suited for clinical application. However, these methods should still be properly validated for each individual tracer and application before implementation.

Development of a minimally invasive simultaneous estimation method for quantifying translocator protein binding with [18F]FEPPA positron emission tomography

BACKGROUND

The purpose of this study was to assess the feasibility of using a minimally invasive simultaneous estimation method (SIME) to quantify the binding of the 18-kDa translocator protein tracer [¹⁸F]FEPPA. Arterial sampling was avoided by extracting an image-derived input function (IDIF) that was metabolite-corrected using venous blood samples. The possibility of reducing scan duration to 90 min from the recommended 2-3 h was investigated by assuming a uniform non-displaceable distribution volume (V_ND) to simplify the SIME fitting.

RESULTS

SIME was applied to retrospective data from healthy volunteers and was comprised of both high-affinity binders (HABs) and mixed-affinity binders (MABs). Estimates of global V_ND and regional total distribution volume (V_T) from SIME were not significantly different from values obtained using a two-tissue compartment model (2CTM). Regional V_T estimates were greater for HABs compared to MABs for both the 2TCM and SIME, while the SIME estimates had lower inter-subject variability (41 ± 17% reduction). Binding potential (BP_ND) values calculated from regional V_T and brain-wide V_ND estimates were also greater for HABs, and reducing the scan time from 120 to 90 min had no significant effect on BP_ND. The feasibility of using venous metabolite correction was evaluated in a large animal model involving a simultaneous collection of arterial and venous samples. Strong linear correlations were found between venous and arterial measurements of the blood-to-plasma ratio and the remaining [¹⁸F]FEPPA fraction. Lastly, estimates of BP_ND and the specific distribution volume (i.e., V_S = V_T - V_ND) from a separate group of healthy volunteers (90 min scan time, venous-scaled IDIFs) agreed with estimates from the retrospective data for both genotypes.

CONCLUSIONS

The results of this study demonstrate that accurate estimates of regional V_T, BP_ND and V_S can be obtained by applying SIME to [¹⁸F]FEPPA data. Furthermore, the application of SIME enabled the scan time to be reduced to 90 min, and the approach worked well with IDIFs that were scaled and metabolite-corrected using venous blood samples.

Source-to-Target Automatic Rotating Estimation (STARE) - a publicly-available, blood-free quantification approach for PET tracers with irreversible kinetics: Theoretical framework and validation for [18F]FDG

INTRODUCTION

Full quantification of positron emission tomography (PET) data requires an input function. This generally means arterial blood sampling, which is invasive, labor-intensive and burdensome. There is no current, standardized method to fully quantify PET radiotracers with irreversible kinetics in the absence of blood data. Here, we present Source-to-Target Automatic Rotating Estimation (STARE), a novel, data-driven approach to quantify the net influx rate (K_i) of irreversible PET radiotracers, that requires only individual-level PET data and no blood data. We validate STARE with human [¹⁸F]FDG PET scans and assess its performance using simulations.

METHODS

STARE builds upon a source-to-target tissue model, where the tracer time activity curves (TACs) in multiple "target" regions are expressed at once as a function of a "source" region, based on the two-tissue irreversible compartment model, and separates target region K_i from source K_i by fitting the source-to-target model across all target regions simultaneously. To ensure identifiability, data-driven, subject-specific anchoring is used in the STARE minimization, which takes advantage of the PET signal in a vasculature cluster in the field of view (FOV) that is automatically extracted and partial volume-corrected. To avoid the need for any a priori determination of a single source region, each of the considered regions acts in turn as the source, and a final K_i is estimated in each region by averaging the estimates obtained in each source rotation.

RESULTS

In a large dataset of human [¹⁸F]FDG scans (N=69), STARE K_i estimates were correlated with corresponding arterial blood-based K_i estimates (r=0.80), with an overall regression slope of 0.88, and were precisely estimated, as assessed by comparing STARE K_i estimates across several runs of the algorithm (coefficient of variation across runs=6.74 ± 2.48%). In simulations, STARE K_i estimates were largely robust to factors that influence the individualized anchoring used within its algorithm.

CONCLUSION

Through simulations and application to [¹⁸F]FDG PET data, feasibility is demonstrated for STARE blood-free, data-driven quantification of K_i. Future work will include applying STARE to PET data obtained with a portable PET camera and to other irreversible radiotracers.

Cerebral blood flow measurements with 15O-water PET using a non-invasive machine-learning-derived arterial input function

Cerebral blood flow (CBF) can be measured with dynamic positron emission tomography (PET) of 15O-labeled water by using tracer kinetic modelling. However, for quantification of regional CBF, an arterial input function (AIF), obtained from arterial blood sampling, is required. In this work we evaluated a novel, non-invasive approach for input function prediction based on machine learning (MLIF), against AIF for CBF PET measurements in human subjects.Twenty-five subjects underwent two 10 min dynamic 15O-water brain PET scans with continuous arterial blood sampling, before (baseline) and following acetazolamide medication. Three different image-derived time-activity curves were automatically segmented from the carotid arteries and used as input into a Gaussian process-based AIF prediction model, considering both baseline and acetazolamide scans as training data. The MLIF approach was evaluated by comparing AIF and MLIF curves, as well as whole-brain grey matter CBF values estimated by kinetic modelling derived with either AIF or MLIF.The results showed that AIF and MLIF curves were similar and that corresponding CBF values were highly correlated and successfully differentiated before and after acetazolamide medication. In conclusion, our non-invasive MLIF method shows potential to replace the AIF obtained from blood sampling for CBF measurements using 15O-water PET and kinetic modelling.

Substitution of venous for arterial blood sampling in the determination of regional rates of cerebral protein synthesis with L-[1-11C]leucine PET: A validation study

We developed and validated a method to estimate input functions for determination of regional rates of cerebral protein synthesis (rCPS) with L-[1-¹¹C]leucine PET without arterial sampling. The method is based on a population-derived input function (PDIF) approach, with venous samples for calibration. Population input functions were constructed from arterial blood data measured in 25 healthy 18-24-year-old males who underwent L-[1-¹¹C]leucine PET scans while awake. To validate the approach, three additional groups of 18-27-year-old males underwent L-[1-¹¹C]leucine PET scans with both arterial and venous blood sampling: 13 awake healthy volunteers, 10 sedated healthy volunteers, and 5 sedated subjects with fragile X syndrome. Rate constants of the L-[1-¹¹C]leucine kinetic model were estimated voxel-wise with measured arterial input functions and with venous-calibrated PDIFs. Venous plasma leucine measurements were used with venous-calibrated PDIFs for rCPS computation. rCPS determined with PDIFs calibrated with 30-60 min venous samples had small errors (RMSE: 4-9%), and no statistically significant differences were found in any group when compared to rCPS determined with arterial input functions. We conclude that in young adult males, PDIFs calibrated with 30-60 min venous samples can be used in place of arterial input functions for determination of rCPS with L-[1-¹¹C]leucine PET.

Non-invasive kinetic modelling of PET tracers with radiometabolites using a constrained simultaneous estimation method: evaluation with 11C-SB201745

Background

Kinetic analysis of dynamic PET data requires an accurate knowledge of available PET tracer concentration within blood plasma over time, known as the arterial input function (AIF). The gold standard method used to measure the AIF requires serial arterial blood sampling over the course of the PET scan, which is an invasive procedure and makes this method less practical in clinical settings. Traditional image-derived methods are limited to specific tracers and are not accurate if metabolites are present in the plasma.

Results

In this work, we utilise an image-derived whole blood curve measurement to reduce the computational complexity of the simultaneous estimation method (SIME), which is capable of estimating the AIF directly from tissue time activity curves (TACs). This method was applied to data obtained from a serotonin receptor study (¹¹C-SB207145) and estimated parameter results are compared to results obtained using the original SIME and gold standard AIFs derived from arterial samples. Reproducibility of the method was assessed using test-retest data. It was shown that the incorporation of image-derived information increased the accuracy of total volume of distribution (V _T) estimates, averaged across all regions, by 40% and non-displaceable binding potential (BP _ND) estimates by 16% compared to the original SIME. Particular improvements were observed in K₁ parameter estimates. BP _ND estimates, based on the proposed method and the gold standard arterial sample-derived AIF, were not significantly different (P=0.7).

Conclusions

The results of this work indicate that the proposed method with prior AIF information obtained from a partial volume corrected image-derived whole blood curve, and modelled parent fraction, has the potential to be used as an alternative non-invasive method to perform kinetic analysis of tracers with metabolite products.

A hybrid deconvolution approach for estimation of in vivo non-displaceable binding for brain PET targets without a reference region

BACKGROUND AND AIM

Estimation of a PET tracer's non-displaceable distribution volume (VND) is required for quantification of specific binding to its target of interest. VND is generally assumed to be comparable brain-wide and is determined either from a reference region devoid of the target, often not available for many tracers and targets, or by imaging each subject before and after blocking the target with another molecule that has high affinity for the target, which is cumbersome and involves additional radiation exposure. Here we propose, and validate for the tracers [11C]DASB and [11C]CUMI-101, a new data-driven hybrid deconvolution approach (HYDECA) that determines VND at the individual level without requiring either a reference region or a blocking study.

METHODS

HYDECA requires the tracer metabolite-corrected concentration curve in blood plasma and uses a singular value decomposition to estimate the impulse response function across several brain regions from measured time activity curves. HYDECA decomposes each region's impulse response function into the sum of a parametric non-displaceable component, which is a function of VND, assumed common across regions, and a nonparametric specific component. These two components differentially contribute to each impulse response function. Different regions show different contributions of the two components, and HYDECA examines data across regions to find a suitable common VND. HYDECA implementation requires determination of two tuning parameters, and we propose two strategies for objectively selecting these parameters for a given tracer: using data from blocking studies, and realistic simulations of the tracer. Using available test-retest data, we compare HYDECA estimates of VND and binding potentials to those obtained based on VND estimated using a purported reference region.

RESULTS

For [11C]DASB and [11C]CUMI-101, we find that regardless of the strategy used to optimize the tuning parameters, HYDECA provides considerably less biased estimates of VND than those obtained, as is commonly done, using a non-ideal reference region. HYDECA test-retest reproducibility is comparable to that obtained using a VND determined from a non-ideal reference region, when considering the binding potentials BPP and BPND.

CONCLUSIONS

HYDECA can provide subject-specific estimates of VND without requiring a blocking study for tracers and targets for which a valid reference region does not exist.

Improved simultaneous estimation of tracer kinetic models with artificial immune network based optimization method

Tracer kinetic modeling (TKM) is a promising quantitative method for physiological and biochemical processes in vivo. In this paper, we investigated the applications of an immune-inspired method to better address the issues of Simultaneous Estimation (SIME) of TKM with multimodal optimization. Experiments of dynamic FDG PET imaging experiments and simulation studies were carried out. The proposed artificial immune network (TKM_AIN) shows more scalable and effective when compared with the gradient-based Marquardt-Levenberg algorithm and the scholastic-based simulated annealing method.

Improved derivation of input function in dynamic mouse [18F]FDG PET using bladder radioactivity kinetics

PURPOSE

Accurate determination of the plasma input function (IF) is essential for absolute quantification of physiological parameters in positron emission tomography (PET). However, it requires an invasive and tedious procedure of arterial blood sampling that is challenging in mice because of the limited blood volume. In this study, a hybrid modeling approach is proposed to estimate the plasma IF of 2-deoxy-2-[18F]fluoro-D-glucose ([18F]FDG) in mice using accumulated radioactivity in urinary bladder together with a single late-time blood sample measurement.

METHODS

Dynamic PET scans were performed on nine isoflurane-anesthetized male C57BL/6 mice after a bolus injection of [18F]FDG at the lateral caudal vein. During a 60- or 90-min scan, serial blood samples were taken from the femoral artery. Image data were reconstructed using filtered backprojection with computed tomography-based attenuation correction. Total accumulated radioactivity in the urinary bladder at late times was fitted to a renal compartmental model with the last blood sample and a one-exponential function that described the [18F]FDG clearance in blood. Multiple late-time blood sample estimates were calculated by the blood [18F]FDG clearance equation. A sum of four-exponentials was assumed for the plasma IF that served as a forcing function to all tissues. The estimated plasma IF was obtained by simultaneously fitting the [18F]FDG model to the time-activity curves (TACs) of liver and muscle and the forcing function to early (0-1 min) left-ventricle data (corrected for delay, dispersion, partial-volume effects, and erythrocyte uptake) and the late-time blood estimates. Using only the blood sample collected at the end of the study to estimate the IF and the use of liver TAC as an alternative IF were also investigated.

RESULTS

The area under the plasma IFs calculated for all studies using the hybrid approach was not significantly different from that using all blood samples. [18F]FDG uptake constants in brain, myocardium, skeletal muscle, and liver computed by the Patlak analysis using estimated and measured plasma IFs were in excellent agreement (slope∼1; R2>0.983). The IF estimated using only the last blood sample drawn at the end of the study and the use of liver TAC as the plasma IF provided less reliable results.

CONCLUSIONS

The estimated plasma IFs obtained with the hybrid method agreed well with those derived from arterial blood sampling. Importantly, the proposed method obviates the need of arterial catheterization, making it possible to perform repeated dynamic [18F]FDG PET studies on the same animal. Liver TAC is unsuitable as an input function for absolute quantification of [18F]FDG PET data.

Estimation of input functions from dynamic [18F]FLT PET studies of the head and neck with correction for partial volume effects

BACKGROUND

We present a method for extracting arterial input functions from dynamic [18F]FLT PET images of the head and neck, directly accounting for the partial volume effect. The method uses two blood samples, for which the optimum collection times are assessed.

METHODS

Six datasets comprising dynamic PET images, co-registered computed tomography (CT) scans and blood-sampled input functions were collected from four patients with head and neck tumours. In each PET image set, a region was identified that comprised the carotid artery (outlined on CT images) and surrounding tissue within the voxels containing the artery. The time course of activity in the region was modelled as the sum of the blood-sampled input function and a compartmental model of tracer uptake in the surrounding tissue.The time course of arterial activity was described by a mathematical function with seven parameters. The parameters of the function and the compartmental model were simultaneously estimated, aiming to achieve the best match between the modelled and imaged time course of regional activity and the best match of the estimated blood activity to between 0 and 3 samples. The normalised root-mean-square (RMSnorm) differences and errors in areas under the curves (AUCs) between the measured and estimated input functions were assessed.

RESULTS

A one-compartment model of tracer movement to and from the artery best described uptake in the tissue surrounding the artery, so the final model of the input function and tissue kinetics has nine parameters to be estimated. The estimated and blood-sampled input functions agreed well when two blood samples, obtained at times between 2 and 8 min and between 8 and 60 min, were used in the estimation process (RMSnorm values of 1.1 ± 0.5 and AUC errors for the peak and tail region of the curves of 15% ± 9% and 10% ± 8%, respectively). A third blood sample did not significantly improve the accuracy of the estimated input functions.

CONCLUSIONS

Input functions for FLT-PET studies of the head and neck can be estimated well using a one-compartment model of tracer movement and TWO blood samples obtained after the peak in arterial activity.

Extraction of time activity curves from gated FDG-PET images for small animals' heart studies

We introduce a new approach to extract the input function and the tissue time activity curve from dynamic ECG-gated (18)F-FDG PET images. These curves are mandatory to model the myocardium metabolic rate of glucose for heart studies. The proposed method utilizes coupled active contours to track the myocardium and the blood pool deformations. Furthermore, a statistical approach is developed to model the blood and tissue activities and to correct for spillovers. The developed algorithm offers a reliable alternative to serial blood sampling for small animal cardiac PET studies. Indeed, the calculated MMRG value differs by 1.54% only from the reference value.

Image-derived input function for brain PET studies: many challenges and few opportunities

Quantitative positron emission tomography (PET) brain studies often require that the input function be measured, typically via arterial cannulation. Image-derived input function (IDIF) is an elegant and attractive noninvasive alternative to arterial sampling. However, IDIF is also a very challenging technique associated with several problems that must be overcome before it can be successfully implemented in clinical practice. As a result, IDIF is rarely used as a tool to reduce invasiveness in patients. The aim of the present review was to identify the methodological problems that hinder widespread use of IDIF in PET brain studies. We conclude that IDIF can be successfully implemented only with a minority of PET tracers. Even in those cases, it only rarely translates into a less-invasive procedure for the patient. Finally, we discuss some possible alternative methods for obtaining less-invasive input function.

A robust state-space kinetics-guided framework for dynamic PET image reconstruction

Dynamic PET image reconstruction is a challenging issue due to the low SNR and the large quantity of spatio-temporal data. We propose a robust state-space image reconstruction (SSIR) framework for activity reconstruction in dynamic PET. Unlike statistically-based frame-by-frame methods, tracer kinetic modeling is incorporated to provide physiological guidance for the reconstruction, harnessing the temporal information of the dynamic data. Dynamic reconstruction is formulated in a state-space representation, where a compartmental model describes the kinetic processes in a continuous-time system equation, and the imaging data are expressed in a discrete measurement equation. Tracer activity concentrations are treated as the state variables, and are estimated from the dynamic data. Sampled-data H(∞) filtering is adopted for robust estimation. H(∞) filtering makes no assumptions on the system and measurement statistics, and guarantees bounded estimation error for finite-energy disturbances, leading to robust performance for dynamic data with low SNR and/or errors. This alternative reconstruction approach could help us to deal with unpredictable situations in imaging (e.g. data corruption from failed detector blocks) or inaccurate noise models. Experiments on synthetic phantom and patient PET data are performed to demonstrate feasibility of the SSIR framework, and to explore its potential advantages over frame-by-frame statistical reconstruction approaches.

Propagation of Blood Function Errors to the Estimates of Kinetic Parameters with Dynamic PET

Dynamic PET, in contrast to static PET, can identify temporal variations in the radiotracer concentration. Mathematical modeling of the tissue of interest in dynamic PET can be simplified using compartment models as a linear system where the time activity curve of a specific tissue is the convolution of the tracer concentration in the plasma and the impulse response of the tissue containing kinetic parameters. Since the arterial sampling of blood to acquire the value of tracer concentration is invasive, blind methods to estimate both blood input function and kinetic parameters have recently drawn attention. Several methods have been developed, but the effect of accuracy of the estimated blood function on the estimation of the kinetic parameters is not studied. In this paper, we present a method to compute the error in the kinetic parameter estimates caused by the error in the blood input function. Computer simulations show that analytical expressions we derive are sufficiently close to results obtained from numerical methods. Our findings are important to observe the effect of the blood function on kinetic parameter estimation, but also useful to evaluate various blind methods and observe the dependence of kinetic parameter estimates to certain parts of the blood function.

Sensitivity analysis for biomedical models

This article discusses the application of sensitivity analysis (SA) in biomedical models. Sensitivity analysis is widely applied in physics, chemistry, economics, social sciences and other areas where models are developed. By assigning a prior probability distribution to each model variable, the SA framework appeals to the posterior probabilities of the model to evaluate the relative importance of these variables on the output distribution based on the principle of general variance decomposition. Within this framework, the SA paradigm serves as an objective platform to quantify the contributions of each model factor relative to their empirical range. We present statistical derivations of variance-based SA in this context and discuss its detailed properties through some practical examples. Our emphasis is on the application of SA in the biomedical field. As we show, it may provide a useful tool for model quality assessment, model reduction and factor prioritization, and improve our understanding of the model structure and underlying mechanisms. When usual approaches for calculating sensitivity index involve the employment of Monte Carlo analysis, which is computationally expensive in the large-sampling paradigm, we develop two effective numerical approximate methods for quick SA evaluations based on the unscented transformation (UT) that utilize a deterministic sampling approach in place of random sampling to calculate posterior statistics. We show that these methods achieve an excellent compromise between computational burden and calculation precision. In addition, a clear guideline is absent to evaluate the importance of variable for model reduction, we also present an objective statistical criterion to quantitatively decide whether or not a descriptive parameter is nominal and may be discarded in ensuing model-based analysis without significant loss of information on model behavior.

A hybrid clustering method for ROI delineation in small-animal dynamic PET images: application to the automatic estimation of FDG input functions

Tracer kinetic modeling with dynamic positron emission tomography (PET) requires a plasma time-activity curve (PTAC) as an input function. Several image-derived input function (IDIF) methods that rely on drawing the region of interest (ROI) in large vascular structures have been proposed to overcome the problems caused by the invasive approach for obtaining the PTAC, especially for small-animal studies. However, the manual placement of ROIs for estimating IDIF is subjective and labor-intensive, making it an undesirable and unreliable process. In this paper, we propose a novel hybrid clustering method (HCM) that objectively delineates ROIs in dynamic PET images for the estimation of IDIFs, and demonstrate its application to the mouse PET studies acquired with [ (18)F]Fluoro-2-deoxy-2-D-glucose (FDG). We begin our HCM using k-means clustering for background removal. We then model the time-activity curves using polynomial regression mixture models in curve clustering for heart structure detection. The hierarchical clustering is finally applied for ROI refinements. The HCM achieved accurate ROI delineation in both computer simulations and experimental mouse studies. In the mouse studies, the predicted IDIF had a high correlation with the gold standard, the PTAC derived from the invasive blood samples. The results indicate that the proposed HCM has a great potential in ROI delineation for automatic estimation of IDIF in dynamic FDG-PET studies.

A model-constrained Monte Carlo method for blind arterial input function estimation in dynamic contrast-enhanced MRI: I. Simulations

Widespread adoption of quantitative pharmacokinetic modeling methods in conjunction with dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has led to increased recognition of the importance of obtaining accurate patient-specific arterial input function (AIF) measurements. Ideally, DCE-MRI studies use an AIF directly measured in an artery local to the tissue of interest, along with measured tissue concentration curves, to quantitatively determine pharmacokinetic parameters. However, the numerous technical and practical difficulties associated with AIF measurement have made the use of population-averaged AIF data a popular, if sub-optimal, alternative to AIF measurement. In this work, we present and characterize a new algorithm for determining the AIF solely from the measured tissue concentration curves. This Monte Carlo blind estimation (MCBE) algorithm estimates the AIF from the subsets of D concentration-time curves drawn from a larger pool of M candidate curves via nonlinear optimization, doing so for multiple (Q) subsets and statistically averaging these repeated estimates. The MCBE algorithm can be viewed as a generalization of previously published methods that employ clustering of concentration-time curves and only estimate the AIF once. Extensive computer simulations were performed over physiologically and experimentally realistic ranges of imaging and tissue parameters, and the impact of choosing different values of D and Q was investigated. We found the algorithm to be robust, computationally efficient and capable of accurately estimating the AIF even for relatively high noise levels, long sampling intervals and low diversity of tissue curves. With the incorporation of bootstrapping initialization, we further demonstrated the ability to blindly estimate AIFs that deviate substantially in shape from the population-averaged initial guess. Pharmacokinetic parameter estimates for K(trans), k(ep), v(p) and v(e) all showed relative biases and uncertainties of less than 10% for measurements having a temporal sampling rate of 4 s and a concentration measurement noise level of sigma = 0.04 mM. A companion paper discusses the application of the MCBE algorithm to DCE-MRI data acquired in eight patients with malignant brain tumors.

Simultaneous estimation of input functions: an empirical study

In neuroreceptor mapping, methods for the estimation of distribution volume require determination of a metabolite-corrected arterial input function. In application, this may be accomplished by collecting arterial blood samples during scanning, adjusting these measurements according to a separate metabolite analysis, and then modeling the resulting concentration data. Although many groups do this routinely, it is invasive and requires considerable effort. Furthermore, both the plasma and the metabolite data are noisy, and thus estimation of kinetic parameters can be affected by this variability. One promising alternative to full-input function modeling is the simultaneous estimation (SIME) approach, in which kinetic parameters and common input function parameters are estimated using results obtained from several regions at once. We investigate the performance of this approach on data from four different radioligands, using various kinetic models, comparing the results with those obtained by estimation using full-input function modeling. Results indicate that SIME provides a promising alternative for all the radioligands considered.

Model-based blind estimation of kinetic parameters in dynamic contrast enhanced (DCE)-MRI

A method to simultaneously estimate the arterial input function (AIF) and pharmacokinetic model parameters from dynamic contrast-enhanced (DCE)-MRI data was developed. This algorithm uses a parameterized functional form to model the AIF and k-means clustering to classify tissue time-concentration measurements into a set of characteristic curves. An iterative blind estimation algorithm alternately estimated parameters for the input function and the pharmacokinetic model. Computer simulations were used to investigate the algorithm's sensitivity to noise and initial estimates. In 12 patients with sarcomas, pharmacokinetic parameter estimates were compared with "truth" obtained from model regression using a measured AIF. When arterial voxels were included in the blind estimation algorithm, the resulting AIF was similar to the measured input function. The "true" K(trans) values in tumor regions were not significantly different than the estimated values, 0.99 +/- 0.41 and 0.86 +/- 0.40 min(-1), respectively, P = 0.27. "True" k(ep) values also matched closely, 0.70 +/- 0.24 and 0.65 +/- 0.25 min(-1), P = 0.08. When only tissue curves free of significant vascular contribution are used (v(p) < 0.05), the resulting AIF showed substantial delay and dispersion consistent with a more local AIF such as has been observed in dynamic susceptibility contrast imaging in the brain.

Single-input-dual-output modeling of image-based input function estimation

PURPOSE

Quantification of small-animal positron emission tomography (PET) images necessitates knowledge of the plasma input function (PIF). We propose and validate a simplified hybrid single-input-dual-output (HSIDO) algorithm to estimate the PIF.

PROCEDURES

The HSIDO algorithm integrates the peak of the input function from two region-of-interest time-activity curves with a tail segment expressed by a sum of two exponentials. Partial volume parameters are optimized simultaneously. The algorithm is validated using both simulated and real small-animal PET images. In addition, the algorithm is compared to existing techniques in terms of area under curve (AUC) error, bias, and precision of compartmental model micro-parameters.

RESULTS

In general, the HSIDO method generated PIF with significantly (P < 0.05) less AUC error, lower bias, and improved precision of kinetic estimates in comparison to the reference method.

CONCLUSIONS

HSIDO is an improved modeling-based PIF estimation method. This method can be applied for quantitative analysis of small-animal dynamic PET studies.

Quantitative analysis of [18F]FDDNP PET using subcortical white matter as reference region

Purpose

Subcortical white matter is known to be relatively unaffected by amyloid deposition in Alzheimer’s disease (AD). We investigated the use of subcortical white matter as a reference region to quantify [¹⁸F]FDDNP binding in the human brain.

Methods

Dynamic [¹⁸F]FDDNP PET studies were performed on 7 control subjects and 12 AD patients. Population efflux rate constants (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {k\prime_2} $$\end{document}) from subcortical white matter (centrum semiovale) and cerebellar cortex were derived by a simplified reference tissue modeling approach incorporating physiological constraints. Regional distribution volume ratio (DVR) estimates were derived using Logan and simplified reference tissue approaches, with either subcortical white matter or cerebellum as reference input. Discriminant analysis with cross-validation was performed to classify control subjects and AD patients.

Results

The population estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {k\prime_2} $$\end{document} in subcortical white matter did not differ significantly between control subjects and AD patients but the variability of individual estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {k\prime_2} $$\end{document} determined in white matter was lower than that in cerebellum. Logan DVR showed dependence on the efflux rate constant in white matter. The DVR estimates in the frontal, parietal, posterior cingulate, and temporal cortices were significantly higher in the AD group (p<0.01). Incorporating all these regional DVR estimates as predictor variables in discriminant analysis yielded accurate classification of control subjects and AD patients with high sensitivity and specificity, and the results agreed well with those using the cerebellum as the reference region.

Conclusion

Subcortical white matter can be used as a reference region for quantitative analysis of [¹⁸F]FDDNP with the Logan method which allows more accurate and less biased binding estimates, but a population efflux rate constant has to be determined a priori.

Kinetic modelling in small animal imaging with PET

Small animal imaging with positron emission tomography has undergone a major evolution. This has been driven by technical improvements and the development of dedicated PET camera's for small animals. The focus has shifted from detection of tracer uptake and visualization of the tracer distribution towards the quantification of the physiological parameters necessary to use this technique for kinetic modelling of tracers. At the moment there are still several issues which need further research and evaluation before we can fully employ the possibilities of PET as an in-vivo measurement of underlying molecular biology. These issues relate to improved quantification of measurements, improved image reconstruction and processing, and the use of blood plasma data in combination with kinetic models. Besides the more technical issues, there are two more issues which need further clarification: the effect of the anaesthesia, and the effect of radiation on the experiment itself. In this review, we will give an overview of how the technique can be used but we will also discuss the issues mentioned above. The focus will be on the three major parts of the imaging procedure: acquisition, reconstruction of images, and kinetic modelling of the data.

Clustering dynamic PET images on the Gaussian distributed sinogram domain

Segmentation of dynamic PET images is an important preprocessing step for kinetic parameter estimation. The time activity curve (TAC) of individual pixels has very low signal-to-noise ratio (SNR). Therefore, the kinetic parameters estimated from the TAC of an individual pixel may not be accurate, and these estimations may have very high spatial variance. To alleviate this problem, pixels with similar kinetic characteristics are clustered into regions, and TACs of pixels within each region are averaged to increase SNR. It has recently been shown that clustering dynamic PET images in the sinogram domain is better than clustering them in the reconstructed image domain [M.E. Kamasak, B. Bayraktar, Clustering dynamic PET images on the projection domain, IEEE Trans. Nucl. Sci. 54 (3) (June 2007) 496-503.]. In that study, the sinograms are assumed to have Poisson distribution. The clusters and TACs of the clusters are then chosen to maximize the posterior probability of the measured sinograms. Although the raw sinogram data are Poisson distributed, the sinogram data corrected for scatter, randoms, attenuation etc. are not Poisson distributed anymore. In this paper, we describe how to cluster dynamic PET images on the sinogram domain when the sinograms are Gaussian distributed.

An activity-subspace approach for estimating the integrated input function and relative distribution volume in PET parametric imaging

Dynamic positron emission tomography (PET) imaging technique enables the measurement of neuroreceptor distributions corresponding to anatomic structures, and thus, allows image-wide quantification of physiological and biochemical parameters. Accurate quantification of the concentration of neuroreceptor has been the objective of many research efforts. Compartment modeling is the most widely used approach for receptor binding studies. However, current compartment-model-based methods often either require intrusive collection of accurate arterial blood measurements as the input function, or assume the existence of a reference region. To obviate the need for the input function or a reference region, in this paper, we propose to estimate the input function. We propose a novel concept of activity subspace, and estimate the input function by the analysis of the intersection of the activity subspaces. Then, the input function and the distribution volume (DV) parameter are refined and estimated iteratively. Thus, the underlying parametric image of the total DV is obtained. The proposed method is compared with a blind estimation method, iterative quadratic maximum-likelihood (IQML) via simulation, and the proposed method outperforms IQML. The proposed method is also evaluated in a brain PET dataset.

A Factor-Image Framework to Quantification of Brain Receptor Dynamic PET Studies

The positron emission tomography (PET) imaging technique enables the measurement of receptor distribution or neurotransmitter release in the living brain and the changes of the distribution with time and thus allows quantification of binding sites as well as the affinity of a radioligand. However, quantification of receptor binding studies obtained with PET is complicated by tissue heterogeneity in the sampling image elements (i.e., voxels, pixels). This effect is caused by a limited spatial resolution of the PET scanner. Spatial heterogeneity is often essential in understanding the underlying receptor binding process. Tracer kinetic modeling also often requires an intrusive collection of arterial blood samples. In this paper, we propose a likelihood-based framework in the voxel domain for quantitative imaging with or without the blood sampling of the input function. Radioligand kinetic parameters are estimated together with the input function. The parameters are initialized by a subspace-based algorithm and further refined by an iterative likelihood-based estimation procedure. The performance of the proposed scheme is examined by simulations. The results show that the proposed scheme provides reliable estimation of factor time-activity curves (TACs) and the underlying parametric images. A good match is noted between the result of the proposed approach and that of the Logan plot. Real brain PET data are also examined, and good performance is observed in determining the TACs and the underlying factor images.

Novel reference region model reveals increased microglial and reduced vascular binding of 11C-(R)-PK11195 in patients with Alzheimer's disease

11C-(R)-PK11195 is a PET radiotracer for the quantification of peripheral benzodiazepine binding sites (PBBSs). The PBBS is a consistent marker of activated microglia, and 11C-(R)-PK11195 has been used to image microglial activity in the diseased brain and in neoplasia. However, the PBBS is also expressed in the brain vasculature (endothelium and smooth muscles), and no evidence, to our knowledge, exists of a change in the vascular PBBS in pathologic brains or of such a change having an effect on the quantification of 11C-(R)-PK11195 binding. To investigate this issue, we have used a modified reference-tissue model (SRTMV) that accounts for tracer vascular activity both in reference and target tissues and applied it for the estimation of binding potential (BP) in a cohort of patients with Alzheimer's disease (AD).

METHODS

A total of 10 patients with AD and 10 age-matched healthy subjects who underwent a 11C-(R)-PK11195 scan were considered in the analysis. The time-activity curves of 11 regions of interest were extracted using the Hammersmith maximum probability atlas. BPs were first estimated using the standard simplified reference-tissue model (SRTM) with the reference tissue computed with a supervised selection algorithm. Subsequently, we applied an SRTMV that models PBBS vascular activity using an additional linear term for both target (VbT) and reference (VbR) regions accounting for vascular tracer activity (C(B)), whereas C(B) was extracted directly from the images. VbR was fixed to 5%, and R1, k2, BP, and VbT were estimated. PBBS density in the vasculature was also assessed by immunocytochemistry on a separate cohort of young and elderly controls and 3 AD postmortem brains.

RESULTS

The inclusion of a vascular component in the SRTM increased BPs in all subjects, but the amount of the increase was different (about 11.9% in controls and 16.8% in patients with AD). In addition, average VbT values derived using the SRTMV were 4.22% for controls but only 2.87% in patients with AD. Immunochemistry showed reduced PBBS expression in AD due to vascular fibrosis.

CONCLUSION

The reduction of VbT in AD can be interpreted as a consequence of 2 independent but concurring phenomena. The vascular fibrosis in the AD brain causes the well-documented decrease of the size of lumens and the reduction of blood volume. At the same time, the fibrotic process determines the loss of vascular PBBS, particularly in smooth muscles, as here documented by immunochemistry. The inclusion of the additional vascular component in the SRTM effectively models these 2 concurrent processes and amplifies the BP in AD more than in controls because of the decrease in tracer binding to the vasculature in the disease cohort.

Spillover and partial-volume correction for image-derived input functions for small-animal 18F-FDG PET studies

We present and validate a method to obtain an input function from dynamic image data and 0 or 1 blood sample for small-animal 18F-FDG PET studies. The method accounts for spillover and partial-volume effects via a physiologic model to yield a model-corrected input function (MCIF).

METHODS

Image-derived input functions (IDIFs) from heart ventricles and myocardial time-activity curves were obtained from 14 Sprague-Dawley rats and 17 C57BL/6 mice. Each MCIF was expressed as a mathematic equation with 7 parameters, which were estimated simultaneously with the myocardial model parameters by fitting the IDIFs and myocardium curves to a dual-output compartment model. Zero or 1 late blood sample was used in the simultaneous estimation. MCIF was validated by comparison with input measured from blood samples. Validation included computing errors in the areas under the curves (AUCs) and in the 18F-FDG influx constant Ki in 3 types of tissue.

RESULTS

For the rat data, the AUC error was 5.3% +/- 19.0% in the 0-sample MCIF and -2.3% +/- 14.8% in the 1-sample MCIF. When the MCIF was used to calculate the Ki of the myocardium, brain, and muscle, the overall errors were -6.3% +/- 27.0% in the 0-sample method (correlation coefficient r = 0.967) and 3.1% +/- 20.6% in the 1-sample method (r = 0.970). The t test failed to detect a significant difference (P > 0.05) in the Ki estimates from both the 0-sample and the 1-sample MCIF. For the mouse data, AUC errors were 4.3% +/- 25.5% in the 0-sample MCIF and -1.7% +/- 20.9% in the 1-sample MCIF. Ki errors averaged -8.0% +/- 27.6% for the 0-sample method (r = 0.955) and -2.8% +/- 22.7% for the 1-sample method (r = 0.971). The t test detected significant differences in the brain and muscle in the Ki for the 0-sample method but no significant differences with the 1-sample method. In both rat and mouse, 0-sample and 1-sample MCIFs both showed at least a 10-fold reduction in AUC and Ki errors compared with uncorrected IDIFs.

CONCLUSION

MCIF provides a reliable, noninvasive estimate of the input function that can be used to accurately quantify the glucose metabolic rate in small-animal 18F-FDG PET studies.

An input function estimation method for FDG-PET human brain studies

BACKGROUND

A new model of an input function for human [(18)F]-2-Deoxy-2-fluoro-d-glucose fluoro (FDG) positron emission tomography (PET) brain studies with bolus injection is presented.

METHODS

Input data for early time, roughly up to 0.6 min, were obtained noninvasively from the time-activity curve (TAC) measured from a carotid artery region of interest. Representative tissue TACs were obtained by clustering the output curves to a limited number of dominant clusters. Three venous plasma samples at a later time were used to fit the functional form of the input function in conjunction with obtaining kinetic rate parameters of the dominant clusters, K(1), k(2) and k(3), using the compartmental model for FDG-PET. Experiments to test the approach used data from 18 healthy subjects.

RESULTS

The model provides an effective means to recover the input function in FDG-PET studies. Weighted nonlinear least squares parameter estimation using the recovered input function, as contrasted with use of plasma samples, yielded highly correlated values of K=K(1)k(3)/(k(2)+k(3)) for simulated data, a correlation coefficient of 0.99780, a slope of 1.019 and an intercept of almost zero. The estimates of K for real data by graphical Patlak analysis using the recovered input function were almost identical to those obtained using arterial plasma samples, with correlation coefficients greater than 0.9976, regression slopes between 0.958 and 1.091 and intercepts that are virtually zero.

CONCLUSIONS

A reliable semiautomated alternative for input function estimation that uses image-derived data augmented with three plasma samples is presented and evaluated for FDG-PET human brain studies.

Tracer kinetics guided dynamic PET reconstruction

Dynamic PET reconstruction is a challenging issue due to the spatio-temporal nature and the complexity of the data. Conventional frame-by-frame approaches fail to explore the temporal information of dynamic PET data, and may lead to inaccurate results due to the low SNR of data. Due to the ill-conditioning of image reconstruction, proper prior knowledge should be incorporated to constrain the reconstruction. In this paper, we propose a tracer kinetics guided reconstruction framework for dynamic PET imaging. The dynamic reconstruction problem is formulated in a state-space representation, where compartment model serves as a continuous-time system equation to describe the tracer kinetic processes, and the imaging data is expressed as discrete sampling of the system states in a measurement equation. The reconstruction problem has therefore become a state estimation problem in a continuous-discrete hybrid paradigm, and sampled-data Hinfinity filtering is applied to for the estimation. As Hinfinity filtering makes no assumptions on the system and measurement statistics, robust reconstruction results can be obtained for dynamic PET imaging where the statistical properties of measurement data and system uncertainty are not available a priori.

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Blind identification of the kinetic parameters in three-compartment models

Quantified knowledge of tissue kinetic parameters in the regions of the brain and other organs can offer information useful in clinical and research applications. Dynamic medical imaging with injection of radioactive or paramagnetic tracer can be used for this measurement. The kinetics of some widely used tracers such as [18F]2-fluoro-2-deoxy-D-glucose can be described by a three-compartment physiological model. The kinetic parameters of the tissue can be estimated from dynamically acquired images. Feasibility of estimation by blind identification, which does not require knowledge of the blood input, is considered analytically and numerically in this work for the three-compartment type of tissue response. The non-uniqueness of the two-region case for blind identification of kinetic parameters in three-compartment model is shown; at least three regions are needed for the blind identification to be unique. Numerical results for the accuracy of these blind identification methods in different conditions were considered. Both a separable variables least-squares (SLS) approach and an eigenvector-based algorithm for multichannel blind deconvolution approach were used. The latter showed poor accuracy. Modifications for non-uniform time sampling were also developed. Also, another method which uses a model for the blood input was compared. Results for the macroparameter K, which reflects the metabolic rate of glucose usage, using three regions with noise showed comparable accuracy for the separable variables least squares method and for the input model-based method, and slightly worse accuracy for SLS with the non-uniform sampling modification.

Estimating the input function non-invasively for FDG-PET quantification with multiple linear regression analysis: simulation and verification with in vivo data

A novel statistical method, namely Regression-Estimated Input Function (REIF), is proposed in this study for the purpose of non-invasive estimation of the input function for fluorine-18 2-fluoro-2-deoxy- d-glucose positron emission tomography (FDG-PET) quantitative analysis. We collected 44 patients who had undergone a blood sampling procedure during their FDG-PET scans. First, we generated tissue time-activity curves of the grey matter and the whole brain with a segmentation technique for every subject. Summations of different intervals of these two curves were used as a feature vector, which also included the net injection dose. Multiple linear regression analysis was then applied to find the correlation between the input function and the feature vector. After a simulation study with in vivo data, the data of 29 patients were applied to calculate the regression coefficients, which were then used to estimate the input functions of the other 15 subjects. Comparing the estimated input functions with the corresponding real input functions, the averaged error percentages of the area under the curve and the cerebral metabolic rate of glucose (CMRGlc) were 12.13+/-8.85 and 16.60+/-9.61, respectively. Regression analysis of the CMRGlc values derived from the real and estimated input functions revealed a high correlation (r=0.91). No significant difference was found between the real CMRGlc and that derived from our regression-estimated input function (Student's t test, P>0.05). The proposed REIF method demonstrated good abilities for input function and CMRGlc estimation, and represents a reliable replacement for the blood sampling procedures in FDG-PET quantification.

Estimation of kinetic parameters without input functions: analysis of three methods for multichannel blind identification

Compartment modeling of dynamic medical image data implies that the concentration of the tracer over time in a particular region of the organ of interest is well modeled as a convolution of the tissue response with the tracer concentration in the blood stream. The tissue response is different for different tissues while the blood input is assumed to be the same for different tissues. The kinetic parameters characterizing the tissue responses can be estimated by multichannel blind identification methods. These algorithms use the simultaneous measurements of concentration in separate regions of the organ; if the regions have different responses, the measurement of the blood input function may not be required. Three blind identification algorithms are analyzed here to assess their utility in medical imaging: eigenvector-based algorithm for multichannel blind deconvolution; cross relations; and iterative quadratic maximum-likelihood (IQML). Comparisons of accuracy with conventional (not blind) identification techniques where the blood input is known are made as well. Tissue responses corresponding to a physiological two-compartment model are primarily considered. The statistical accuracies of estimation for the three methods are evaluated and compared for multiple parameter sets. The results show that IQML gives more accurate estimates than the other two blind identification methods.