Rapid algorithms for the construction of cerebral blood flow and oxygen utilization images with oxygen-15 and dynamic positron emission tomography

A robust quantitative approach for laser speckle contrast imaging perfusion analysis revealed anomalies in the brain blood flow in offspring mice of preeclampsia

Microcirculation analysis of the brain cortex is challenging because surface perfusion varies rapidly in small space-time regions and is bone protected. The laser speckle contrast imaging (LSCI) technique allows analyzing in vivo brain vascular perfusion generating a large amount of data that requires sophisticated data analytics, making researchers invest much effort in processing. Our research question was whether the reduced placental perfusion model (RUPP) of preeclampsia (PE) was associated with impaired blood perfusion in the offspring's brains. We aimed to develop a robust numerical approach that mainly consisted of applying a signal-processing tool for calculating optimal segmentation and piece-wise fits of the offspring's brain perfusion signals obtained from the LSCI technique. We combined this tool with the usual statistical analysis, implementing both in Matlab software. We performed brain perfusion measurements from offspring (five days postnatal, P5) of control pregnant dams (sham, n = 13) and of RUPP dams (RUPP, n = 7) using the Pericam® PSI-HR system at a basal condition and after thermal stimuli (warm and cold). We found that pups of RUPP mice exhibited significant differences in perfusion and vascular response to thermal stimuli compared to the sham mice. These differences were associated with high data variability in the Sham group, while in the RUPP group, perfusion looks "stiffer." Data also suggest sex-dimorphism in the vascular response since female pups in the Sham group but not male pups showed statistically significant differences in response to the warm stimulus. Again, this sex-related difference was absent in pups of RUPP mice. In conclusion, we present a robust quantitative approach for LSCI measurements that revealed anomalies in the brain blood flow in offspring of the RUPP model of PE.

Fourier domain closed-form formulas for estimation of kinetic parameters in reversible multi-compartment models

Background

Compared with static imaging, dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, providing useful information about molecular disease processes. Dynamic imaging involves estimation of kinetic rate parameters. For multi-compartment models, kinetic parameter estimation can be computationally demanding and problematic with local minima.

Methods

This paper offers a new perspective to the compartment model fitting problem where Fourier linear system theory is applied to derive closed-form formulas for estimating kinetic parameters for the two-compartment model. The proposed Fourier domain estimation method provides a unique solution, and offers very different noise response as compared to traditional non-linear chi-squared minimization techniques.

Results

The unique feature of the proposed Fourier domain method is that only low frequency components are used for kinetic parameter estimation, where the DC (i.e., the zero frequency) component in the data is treated as the most important information, and high frequency components that tend to be corrupted by statistical noise are discarded. Computer simulations show that the proposed method is robust without having to specify the initial condition. The resultant solution can be fine tuned using the traditional iterative method.

Conclusions

The proposed Fourier-domain estimation method has closed-form formulas. The proposed Fourier-domain curve-fitting method does not require an initial condition, it minimizes a quadratic objective function and a closed-form solution can be obtained. The noise is easier to control, simply by discarding the high frequency components, and emphasizing the DC component.

Kinetic parameter estimation using a closed-form expression via integration by parts

Dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, eliciting more information regarding underlying molecular disease processes than is obtained from static imaging. However, estimation of kinetic rate parameters for multi-compartment models can be computationally demanding and problematic due to local minima. A number of techniques for kinetic parameter estimation have been studied and are in use today, generally offering a tradeoff between computation time, robustness of fit and flexibility with differing sets of assumptions. This paper presents a means to eliminate all differential operations by using the integration-by-parts method to provide closed-form formulas, so that the mathematical model is less sensitive to data sampling and noise. A family of closed-form formulas are obtained. Computer simulations show that the proposed method is robust without having to specify the initial condition.

Day-to-day test-retest variability of CBF, CMRO2, and OEF measurements using dynamic 15O PET studies

Purpose

We assessed test–retest variability of cerebral blood flow (CBF), cerebral blood volume (CBV), cerebral metabolic rate of oxygen (CMRO₂), and oxygen extraction fraction (OEF) measurements derived from dynamic ¹⁵O positron emission tomography (PET) scans.

Procedures

In seven healthy volunteers, complete test–retest ¹⁵O PET studies were obtained; test–retest variability and left-to-right ratios of CBF, CBV, OEF, and CMRO₂ in arterial flow territories were calculated.

Results

Whole-brain test–retest coefficients of variation for CBF, CBV, CMRO₂, and OEF were 8.8%, 13.8%, 5.3%, and 9.3%, respectively. Test–retest variability of CBV left-to-right ratios was <7.4% across all territories. Corresponding values for CBF, CMRO₂, and OEF were better, i.e., <4.5%, <4.0%, and <1.4%, respectively.

Conclusions

The test–retest variability of CMRO₂ measurements derived from dynamic ¹⁵O PET scans is comparable to within-session test–retest variability derived from steady-state ¹⁵O PET scans. Excellent regional test–retest variability was observed for CBF, CMRO₂, and OEF. Variability of absolute CBF and OEF measurements is probably affected by physiological day-to-day variability of CBF.

Separation of input function for rapid measurement of quantitative CMRO2and CBF in a single PET scan with a dual tracer administration method

Cerebral metabolic rate of oxygen (CMRO(2)), oxygen extraction fraction (OEF) and cerebral blood flow (CBF) images can be quantified using positron emission tomography (PET) by administrating (15)O-labelled water (H(15)(2)O) and oxygen ((15)O(2)). Conventionally, those images are measured with separate scans for three tracers C(15)O for CBV, H(15)(2)O for CBF and (15)O(2) for CMRO(2), and there are additional waiting times between the scans in order to minimize the influence of the radioactivity from the previous tracers, which results in a relatively long study period. We have proposed a dual tracer autoradiographic (DARG) approach (Kudomi et al 2005), which enabled us to measure CBF, OEF and CMRO(2) rapidly by sequentially administrating H(15)(2)O and (15)O(2) within a short time. Because quantitative CBF and CMRO(2) values are sensitive to arterial input function, it is necessary to obtain accurate input function and a drawback of this approach is to require separation of the measured arterial blood time-activity curve (TAC) into pure water and oxygen input functions under the existence of residual radioactivity from the first injected tracer. For this separation, frequent manual sampling was required. The present paper describes two calculation methods: namely a linear and a model-based method, to separate the measured arterial TAC into its water and oxygen components. In order to validate these methods, we first generated a blood TAC for the DARG approach by combining the water and oxygen input functions obtained in a series of PET studies on normal human subjects. The combined data were then separated into water and oxygen components by the present methods. CBF and CMRO(2) were calculated using those separated input functions and tissue TAC. The quantitative accuracy in the CBF and CMRO(2) values by the DARG approach did not exceed the acceptable range, i.e., errors in those values were within 5%, when the area under the curve in the input function of the second tracer was larger than half of the first one. Bias and deviation in those values were also compatible to that of the conventional method, when noise was imposed on the arterial TAC. We concluded that the present calculation based methods could be of use for quantitatively calculating CBF and CMRO(2) with the DARG approach.

Fast parametric imaging algorithm for dual-input biomedical system parameter estimation

Medical parametric imaging with dynamic positron emission tomography (PET) plays an increasingly potential role in modern biomedical research and clinical diagnosis. The key issue in parametric imaging is to estimate parameters based on sampled data at the pixel-by-pixel level from certain dynamic processes described by valid mathematical models. Classic nonlinear least squares (NLS) algorithm requires a "good" initial guess and the computational time-complexity is high, which is impractical for image-wide parameter estimation. Although a variety of fast parametric imaging techniques have been developed, most of them focus on single input systems, which do not provide an optimal solution for dual-input biomedical system parameter estimation, which is the case of liver metabolism. In this study, a dual-input-generalized linear least squares (D-I-GLLS) algorithm was proposed to identify the model parameters including the parameter in the dual-input function. Monte Carlo simulation was conducted to examine this novel fast algorithm. The results of the quantitative analysis suggested that the proposed technique could provide comparable reliability of the parameter estimation with NLS fitting and accurately identify the parameter in the dual-input function. This method may be potentially applicable to other dual-input biomedical system parameter estimation as well.

Rapid quantitative measurement of CMRO(2) and CBF by dual administration of (15)O-labeled oxygen and water during a single PET scan-a validation study and error analysis in anesthetized monkeys

Cerebral blood flow (CBF) and rate of oxygen metabolism (CMRO(2)) may be quantified using positron emission tomography (PET) with (15)O-tracers, but the conventional three-step technique requires a relatively long study period, attributed to the need for separate acquisition for each of (15)O(2), H(2)(15)O, and C(15)O tracers, which makes the multiple measurements at different physiologic conditions difficult. In this study, we present a novel, faster technique that provides a pixel-by-pixel calculation of CBF and CMRO(2) from a single PET acquisition with a sequential administration of (15)O(2) and H(2)(15)O. Experiments were performed on six anesthetized monkeys to validate this technique. The global CBF, oxygen extraction fraction (OEF), and CMRO(2) obtained by the present technique at rest were not significantly different from those obtained with three-step method. The global OEF (gOEF) also agreed with that determined by simultaneous arterio-sinus blood sampling (gOEF(A-V)) for a physiologically wide range when changing the arterial PaCO(2) (gOEF=1.03gOEF(A-V)+0.01, P<0.001). The regional values, as well as the image quality were identical between the present technique and three-step method for CBF, OEF, and CMRO(2). In addition, a simulation study showed that error sensitivity of the present technique to delay or dispersion of the input function, and the error in the partition coefficient was equivalent to that observed for three-step method. Error sensitivity to cerebral blood volume (CBV) was also identical to that in the three-step and reasonably small, suggesting that a single CBV assessment is sufficient for repeated measures of CBF/CMRO(2). These results show that this fast technique has an ability for accurate assessment of CBF/CMRO(2) and also allows multiple assessment at different physiologic conditions.

Evaluation of Basis Function and Linear Least Squares Methods for Generating Parametric Blood Flow Images Using 15O-Water and Positron Emission Tomography

PURPOSE

Parametric analysis of (15)O-water positron emission tomography (PET) studies allows determination of blood flow (BF), perfusable tissue fraction (PTF), and volume of distribution (V (d)) with high spatial resolution. In this paper the performance of basis function and linear least squares methods for generating parametric flow data were evaluated.

PROCEDURES

Monte Carlo simulations were performed using typical perfusion values for brain, tumor, and heart. Clinical evaluation was performed using seven cerebral and 10 myocardial (15)O-water PET studies. Basis function (BFM), linear least squares (LLS), and generalized linear least squares (GLLS) methods were used to calculate BF, PTF, or V(d).

RESULTS

Monte Carlo simulations and human studies showed that, for low BF values (<1 ml/min(-1)ml(-1), BF, PTF, and V(d) were calculated with accuracies better than 5% for all methods tested. For high BF (>2 ml/min(-1)ml(-1)), use of BFM provided more accurate V(d) compared with (G)LLS.

CONCLUSIONS

In general, BFM provided the most accurate estimates of BF, PTF, and V(d).

Single-photon emission computed tomography and positron-emission tomography assays for tissue oxygenation

Radiotherapy prescription can now be customized to target the major mechanism(s) of resistance of individual tumors. In that regard, functional imaging techniques should be exploited to identify the dominant mechanism(s). Tumor biology research has identified several mechanisms of tumor resistance that may be unique to radiation treatments. These fall into 3 broad areas associated with (1) tumor hypoxic fraction, (2) tumor growth rate, (3) and the intrinsic radiosensitivity of tumor clonogens. Imaging research has markers in various stages of development for quantifying relevant information about each of these mechanisms, and those that measure tumor oxygenation and predict for radioresistance are the most advanced. Positron-emission tomography (PET) measurement of oxygen 15 has yielded important information, particularly about brain tissue perfusion, metabolism, and function. Indirect markers of tumor hypoxia have exploited the covalent binding of bioreductive intermediates of azomycin-containing compounds whose uptakes are inversely proportional to intracellular oxygen concentrations. Pilot clinical studies with single-photon emission computed tomography (SPECT) and PET detection of radiolabeled markers to tumor hypoxia have been reported. Recently, other studies have attempted to exploit the reduction properties of both technetium and copper chelates for the selective deposition of radioactive metals in hypoxic tissues. A growing number of potentially useful isotopes are now available for labeling several novel chemicals that could have the appropriate specificity and sensitivity. Preclinical studies with "microSPECT" and "microPET" will be important to define the optimal radiodiagnostic(s) for measuring tissue oxygenation and for determining the time after their administration for optimal hypoxic signal acquisition. Radiolabeled markers of growth kinetics and intrinsic radiosensitivity of cells in solid tumors are also being developed. We conclude that radiation oncology is uniquely positioned to benefit from functional imaging markers that identify important mechanisms of tumor radioresistance, since several strategies for overcoming these individual mechanisms have already been identified.

New method for the analysis of multiple positron emission tomography dynamic datasets: an example applied to the estimation of the cerebral metabolic rate of oxygen

Positron emission tomography (PET) provides the ability to extract useful quantitative information not available through other radiological techniques. In certain studies, the physiological parameters of interest cannot be determined from the data obtained from a single PET experiment alone. In this case, multiple experiments are required. At present, the methods used to analyse measurements acquired from multiple experiments often involve considering them separately during the modelling procedures. These methods of analysis may cause errors to be propagated through successive modelling procedures and do not fully utilise the information content provided by the PET measurements. A new method is presented, based on linear least squares for the analysis of PET dynamic data acquired from multiple experiments. This method simultaneously considers the complete set of measurements obtained and provides reliable parameter estimates. The efficient use of the information content provided by multiple experiments is considered and the propagation of errors is discussed. To facilitate our discussion, we apply this new method to the estimation of the cerebral metabolic rate of oxygen and the parameters of the oxygen utilisation model as a practical example. The results demonstrate a significant improvement in the reliability and estimation accuracy of the estimates for this new method. Furthermore, this method reduced the likelihood of errors being propagated. Therefore, the proposed method is suitable for the analysis of multiple PET dynamic datasets.