Radiation Dose Reduction and Image Enhancement in Medical Imaging through Equally-Sloped Tomography

Since its introduction in the 1970s, the X-ray computed tomography scan (commonly referred to as a CT or CAT scan) has become a revolutionary medical tool in the diagnosis of a large number of diseases as well as the visualization of critical interventional procedures. However, a major limitation of CT is the unavoidable radiation dose imparted to the patient. According to the report from the 2003 National Conference on Dose Reduction in CT, CT scanning has grown to be about 15% of the total number of radiological examinations, but it disproportionately accounts for approximately 70% of the cumulative dose in diagnostic examinations [1]. With the growing number of medical CT procedures and whole body scans, radiation dose to the patient has become a very serious issue, especially for pediatric patients [2,3]. We have recently developed a novel imaging technique called equally-sloped tomography (EST) to significantly alleviate the radiation dose problem. By using pseudo-polar fast Fourier transform (PPFFT) and iterative algorithms with constraints, we have showed that EST makes superior 3D reconstruction to conventional tomography, which has intrinsic drawbacks due to the use of equally-angled projections [4]. Based on our computer simulations and preliminary experimental results, we have demonstrated that EST can reduce radiation dose to the patient by at least 50% while producing the same image resolution and signal-to-noise ratio (SNR) as conventional CT [5-7].

Fig. 1 Schematic layout of the iterative EST method. The algorithm iterates back and forth between Fourier and object space. In each iteration, the calculated slices are updated with the measured (experimental) slices in Fourier space and the physical constraints are enforced in object space.

Figure 1 shows the schematic layout of the iterative algorithm, which is initiated by placing the measured projection data onto the frequency domain using the fractional Fourier transform (FrFt). Random values are then assumed for the missing frequency domain data and the iterative process is initiated. The j^th iteration of the algorithm can then be considered in four steps. First, the inverse PPFFT is applied to the frequency data to obtain an object space image f ' _j r . f_j ()

( ) Second, a new object r is obtained through the application of constraints:

f ^' r ^'( )

() if r � S � f r 0

jj

f r =

()

j ' ' (1)

f r f () <

( )-� f ()r if r � S � r 0

j 1 jj

where S represents a support that separates a patient from its surroundings, and the parameter β is usually set to 0.9 [5]. Eq. (1) pushes the negative attenuation coefficients inside the support close to zero and the attenuation coefficients outside the support (i.e. air) to a smaller value. Furthermore, the attenuation coefficients of the CT bed are predetermined values, and are utilized in an additional constraint. Third, the forward PPFFT is applied to the modified image to obtain a set of calculated Fourier slices in the frequency domain. Fourth, the frequency data is updated with the measured Fourier slices. The iterative process is then repeated. The iterations are monitored by an error function, defined as the difference between the measured Fourier slices and corresponding calculated ones. The algorithm is automatically terminated if the error does not reach a minimum after a set number of iterations; in all simulations presented in this paper, the algorithm terminates the iterative process and saves the reconstruction with the lowest error function value when a minimum error is not reached within 10 iterations. It has been shown that specific set of initial random values does not have bearing on the final reconstruction.

We carried out a series of comparative simulations between conventional tomography and equally-sloped tomography [5,7]. The simulations were performed on a slice of the MOBY whole body mouse phantom (Fig. 2a), which was modeled after the MicroCT systems at the UCLA Crump Institute for Molecular Imaging. Statistical noise, corresponding to a flux of 12000 photons for typical scan, was added to the projection data. SNR and Contrast to Noise Ratio (CNR) were used to quantify the noise response and image quality of the reconstructed images. Fig. 2b shows the results of simulations of conventional tomography performed using 64 equal angled projections around a total 180° rotation angle. The image reconstruction was carried out by using the most accurate form of filtered back-projection (FBP) [8]. Exactly the same number of projections was used for the equally-sloped simulations, but instead the projections were taken along the equally-sloped lines. The iterative algorithm automatically terminated after 33 iterations; the results are displayed in Fig. 2c. Quantitatively, Figs. 3d and e demonstrate that EST has both significantly higher SNR and CNR for all tissue types; this is confirmed visually as the EST reconstruction is significantly less noisy than the FBP reconstruction. Fig. 2f shows that Fourier ring correction curve for the EST reconstruction is above the FBP curve for all spatial frequencies indicating that the EST reconstruction has higher resolution. Visually, the increase in resolution can be seen in crisper edge definition of the thoracic bones. Similar results were attained using 32, 96, 128, 256 and 512 projections and photon fluence of 6000 and 9000; in all case the SNR and CNR of EST was higher than FBP for all tissue types and the FRC curves for EST were above that of FBP.

Fig. 2 (a) The 160x160 MOBY test phantom. (b) and (c) FBP and EST reconstruction with 64 projections, respectively. (d) and (e) Comparison of SNR and CNR of different tissues, respectively. (f) Comparison of the Fourier ring correlation.

To experimentally verify image enhancement and dose reduction with EST, we have applied it to 3D image reconstruction of hemocyanin molecule using cryo electron tomography [6]. The molecule consists of a double-layered and hollow barrel complex about 30 nm in diameter and 35 nm in length. The reason that we chose hemocyanin molecule is because it is a radiation sensitive sample and there is a structure model of the molecule that we can perform a quantitative comparison (Fig. 3b) [9]. Purified hemocyanin molecules were plunge-frozen in vitreous ice and imaged using a cryoelectron microscope at Caltech (Prof. Jensen’s group). Data sets were acquired by tilting the specimen from -69.4° to +69.4° with a total of 105 projections. Image reconstruction was carried out using equal slope reconstruction and filtered back projection. To perform a quantitative comparison, we picked up 11 individual hemocyanin molecules of the two reconstructions. The particles were compared with the structure model averaged from hundreds of hemocyanin molecules. Fig. 3a shows the cross-correlation values between the reconstructed particles and the model, which indicates that equal slope reconstruction improved the cross correlation values by about 40-50%. Furthermore, EST reconstructions at half dose have a greater correlation than full dose reconstruction through conventional methods. The iso-surface renderings shown in Fig. 3e further demonstrated that the EST reconstruction at half dose has a higher visual correlation to the model than FBP at full dose.

Fig. 3 (a) Cross-correlation comparison of 11 hemocyanin molecules reconstructed by equal slope reconstruction and IMOD, indicating that equal slope reconstruction improved the cross correlation values by about 40%. (b) High resolution model. (c),(d) Three different views of the iso-surface renderings of the hemocyanin model using EST and FBP at full dose, respectively. (e) EST at half dose.