Statistical properties of cerebral CT perfusion imaging systems. Part I. Cerebral blood volume maps generated from nondeconvolution-based systems

[Nonlocal low-rank and sparse matrix decomposition for low-dose cerebral perfusion CT image restoration]

OBJECTIVE

To present a nonlocal low-rank and sparse matrix decomposition (NLSMD) method for low-dose cerebral perfusion CT image restoration.

METHODS

Low-dose cerebral perfusion CT images were first partitioned into a matrix, and the low- rank and sparse matrix decomposition model was constructed to obtain high-quality low-dose cerebral perfusion CT images. The cerebral hemodynamic parameters were calculated from the restored high-quality CT images.

RESULTS

In the phantom study, the average structured similarity (SSIM) value of the sequential images obtained by filtered back-projection (FBP) algorithm was 0.9438, which was increased to 0.9765 using the proposed algorithm; the SSIM values of cerebral blood flow (CBF) and cerebral blood volume (CBV) map obtained by FBP algorithm were 0.7005 and 0.6856, respectively, which were increased using the proposed algorithm to 0.7871 and 0.7972, respectively.

CONCLUSION

The proposed method can effectively suppress noises in low-dose cerebral perfusion CT images to obtain accurate cerebral hemodynamic parameters.

[Low-dose cerebral perfusion CT image restoration using prior image constrained diffusion tensor]

OBJECTIVE

We propose an efficient method to reduce the noise in low-dose cerebral perfusion CT images using prior image constrained diffusion tensor to reduce the radiation dose in brain CT examination.

METHODS

By utilizing the redundant information in cerebral perfusion CT images, we embedded the complementary structure information in prior images into lowdose cerebral perfusion CT image restoration process to suppress the image noise and artifacts.We first calculated the diffusion tensor for the low-dose cerebral perfusion CT image and prior image separately and then constructed a prior image constrained diffusion tensor (PICDT) to incorporate the structure information from the prior image into low-dose image restoration process.

RESULTS

In experiments with the Shepp-Logan phantom, the SSIM value of CBF map obtained by the proposed algorithm was increased by 63% as compared with that of the FBP algorithm.In analysis of the clinical dataset, the SSIM value of CBF map obtained by the proposed algorithm was increased by 45% as compared with that of FBP algorithm.

CONCLUSION

The proposed method can effectively reduce noises and artifacts of low-dose cerebral perfusion CT images while maintaining the structural details to obtain accurate cerebral hemodynamic maps.

Iterative reconstruction for low-dose cerebral perfusion computed tomography using prior image induced diffusion tensor

Cerebral perfusion computed tomography (CPCT) can depict the functional status of cerebral circulation at the tissue level; hence, it has been increasingly used to diagnose patients with cerebrovascular disease. However, there is a significant concern that CPCT scanning protocol could expose patients to excessive radiation doses. Although reducing the x-ray tube current when acquiring CPCT projection data is an effective method for reducing radiation dose, this technique usually results in degraded image quality. To enhance the image quality of low-dose CPCT, we present a prior image induced diffusion tensor (PIDT) for statistical iterative reconstruction, based on the penalized weighted least-squares (PWLS) criterion, which we referred to as PWLS-PIDT, for simplicity. Specifically, PIDT utilizes the geometric features of pre-contrast scanned high-quality CT image as a structure prior for PWLS reconstruction; therefore, the low-dose CPCT images are enhanced while preserving important features in the target image. An effective alternating minimization algorithm is developed to solve the associated objective function in the PWLS-PIDT reconstruction. We conduct qualitative and quantitative studies to evaluate the PWLS-PIDT reconstruction with a digital brain perfusion phantom and patient data. With this method, the noise in the reconstructed CPCT images is more substantially reduced than that of other competing methods, without sacrificing structural details significantly. Furthermore, the CPCT sequential images reconstructed via the PWLS-PIDT method can derive more accurate hemodynamic parameter maps than those of other competing methods.

Statistical properties of cerebral CT perfusion imaging systems. Part II. Deconvolution-based systems

PURPOSE

The purpose of this work was to develop a theoretical framework to pinpoint the quantitative relationship between input parameters of deconvolution-based cerebral computed tomography perfusion (CTP) imaging systems and statistical properties of the output perfusion maps.

METHODS

Deconvolution-based CTP systems assume that the arterial input function, tissue enhancement curve, and flow-scaled residue function k(t) are related to each other through a convolution model, and thus by reversing the convolution operation, k(t) and the associated perfusion parameters can be estimated. The theoretical analysis started by deriving analytical formulas for the expected value and autocovariance of the residue function estimated using the singular value decomposition-based deconvolution method. Next, it analyzed statistical properties of the "max" and "arg max" operators, based on which the signal and noise properties of cerebral blood flow (CBF) and time-to-max ( t max ) are quantitatively related to the statistical model of the estimated residue function [ k * ( t ) ] and system parameters. To validate the theory, CTP images of a digital head phantom were simulated, from which signal and noise of each perfusion parameter were measured and compared with values calculated using the theoretical model. In addition, an in vivo canine experiment was performed to validate the noise model of cerebral blood volume (CBV).

RESULTS

For the numerical study, the relative root mean squared error between the measured and theoretically calculated value is ≤0.21% for the autocovariance matrix of k * ( t ) , and is ≤0.13% for the expected form of k * ( t ) . A Bland-Altman analysis demonstrated no significant difference between measured and theoretical values for the mean or noise of each perfusion parameter. For the animal study, the theoretical CBV noise fell within the 25th and 75th percentiles of the experimental values. To provide an example of the theory's utility, an expansion of the CBV noise formula was performed to unveil the dominant role of the baseline image noise in deconvolution-based CBV. Correspondingly, data of the three canine subjects used in the Part I paper were retrospectively processed to confirm that preferentially partitioning dose to the baseline frames benefits both nondeconvolution- and deconvolution-based CBV maps.

CONCLUSIONS

Quantitative relationships between the statistical properties of deconvolution-based CTP maps, source image acquisition and reconstruction parameters, contrast injection protocol, and deconvolution parameters are established.