^{1}

^{2}

^{3}

Purpose: To optimize contrast to noise ratio (CNR) in magnetic resonance imaging (MRI) of prostate cancer using at 3T. Methods: CNR was expressed as a difference in MR signals of two samples. Amulti-echo spin-echo (MESE) pulse sequence was used. The theoretical value of the maximum CNR was obtained using the derivative of CNR with echo time (TE) as a variable. The T_{1} relaxation time was ignored as repetition time (TR) was assumed to be very long (TR >> T_{1}). The theoretical calculations were confirmed with in vitro and in vivo experiments. For in vitro experiments we used samples with different T_{2} values using various concentrations of super paramagnetic iron oxide (SPIO) and for in vivo experiments we used an animal model of prostate cancer. Results: CNR was maximized by selecting the optimum TE for a multi-echo spin-echo (MESE) pulse sequence based on theoretical predictions. MR images of prostate cancer at 3T were obtained and showed maximum CNR at the predicted TE. Conclusions: It was possible to maximize CNR of prostate tumour by selecting the optimal TE based on simple theoretical calculations. The proposed method can be applied to other pulse sequences and tissues. It can be applied to any MRI system at any magnetic field. However the method requires knowledge of T_{2} relaxation times.

Magnetic Resonance Imaging (MRI) has high spatial resolution and the best soft tissue contrast among in vivo imaging modalities [_{1} or T_{2}-weighted MRI, [

MR signal of a tissue is a function of its spin density and relaxation times [

Optimization of MRI pulse sequence parameters has been a field of interest since the beginning of MRI [_{1}, T_{2} and proton density (PD) weighted imaging would increase or decrease CNR for hepatic lesions among patients. They concluded that although short-TE T_{1}-weighted pulse sequences with multiple excitations has the best signal to noise ratio and anatomic resolution at 0.6T, their described technique is limited by relatively inferior contrast discrimination and artifact suppression at 1.5T resulting in a necessary change in imaging strategy when performing hepatic MR imaging at 1.5T [_{2}. Furthermore, the method does not require absolute values of proton density. Instead we worked with relative values of proton densities between tissues with a method suggested by [_{1}-weighted spoiled gradient echo imaging [_{efficiency} for MR-guided interventional procedures [

The solution presented in this work maximizes CNR by optimizing TE in the spin-echo pulse sequence. Using a formula for MR signal obtained with the spin-echo pulse sequence and knowing T_{2}s of the samples we calculated TE^{max} that provided the maximum CNR for in vitro phantoms and in vivo for prostate and surrounding tissues at 3T.

For the calculations of CNR we used an equation providing a relationship between CNR and pulse parameters. We have assumed T_{2} relaxation times are known and T_{1}relaxation can be neglected. Nine samples with different T_{2} relaxation times were made using different water concentrations of superparamagnetic iron oxide (SPIO). CNR as a function of TE was calculated for all sample pairs. The theoretical results were compared to the MRI experiments in vitro and in vivo using the animal model of prostate cancer at 3T.

Contrast in MR imaging can be defined as the difference in signals from two samples [

where SNR_{1} and SNR_{2} are the signal to noise ratios of two samples.

The MR signals from two samples (S_{1} and S_{2}) using spin-echo pulse sequence can be described as: [

where κ_{1}, κ_{2} are the proportionality constants, ρ_{1}, ρ_{2} are the spin densities,

tudinal and transversal relaxation times of the sample 1 and 2 respectively; TR is the repetition time and TE is the echo time. Each signal for samples is divided by the standard deviation, σ, in the image to obtain SNR.

Subtracting (2) from (3) we obtain CNR for the samples 1 and 2:

Assuming TR is sufficiently long (

As seen from Equation (5), TE^{max} depends only on the T_{2} relaxation times of the samples thus it can be calculated to provide the maximum CNR if only T_{2}s are known.

The results of the calculation for different samples pairs are presented in _{2} value and each sample pair has a corresponding TE^{max}.

Molday ION Rhodamine Carboxyl, a commonly used SPIO, (MIRB, Cat #: CL-50Q02-6C-50, BioPAL, Inc, Worcester, MA, USA) was diluted in de-ionized water to prepare nine samples (0.0019, 0.0022, 0.0029, 0.0042, 0.0061, 0.0071, 0.0083, 0.0121, and 0.0263 μg/μL).The samples were placed in standard 5-mm NMR tubes (Wilmad NMR tubes, Cat#: Z566411-5EA, Sigma Aldrich, St. Louis, MO, USA) and arranged in a grid pattern to allow simultaneous imaging of all samples.

MR imaging was performed using a 3T MRI scanner (Achieva, Philips, The Netherlands). Data was acquired using an 8-channel head RF coil. The spin echo pulse sequence with the following parameters was used: 32 echoes, ΔTE = 20 ms, TR = 5000 ms, FOV = 100 mm × 100 mm, 3 mm slice thickness, 224 × 224 matrix size, NEX = 4. The images were transferred to an external workstation and processed with custom MATLAB scripts (MATLAB and Statistics Toolbox Release R2012a, The MathWorks, Inc., Natick, Massachusetts, United States). A region of interest (ROI) was automatically selected for each sample as a circular area within the sample for in vitro data. The ROI was determined by a mask with a pre-determined threshold in order to make ROIs determination quick and without human error.Single exponential fitting of the echo train was used to calculate T_{T}s according to the formula:

where M_{z} is the signal intensity at the echo time TE; A, B and T_{2} are the fitting parameters.8

To induce prostate tumours, 5 × 106 LNcaP cells suspended in 100 μL of PBS were subcutaneously injected in the flank of 8 male athymic nude mice (Charles River, Wilmington, MA, USA). The mice were anesthetized with isoflurane (Baxter International Inc., Deerfield, IL, USA) during MR imaging and euthanized immediately after.MR imaging of mice was performed once tumours reached a diameter of 5mmusing calipers according to our approved protocol (Lakehead University Animal Care Committee).

Data was acquired using the MESE pulse sequence with an 8-channel wrist RF coil with the following parameters: 30 echoes, ΔTE = 8 ms, TR = 1396 ms, FOV = 240 mm × 240 mm, slice thickness = 3 mm, 156 × 156 matrix, NEX = 4. Processing was performed similarly to in vitro experiments but ROIs were manually determined for the tumour, muscle, and kidney.

CNR was calculated from the MESE image sets for various echo times. Signal intensity of each sample was normalized to the signal intensity of the first echo for each sample for in vitro data and we assumed κ_{1}ρ_{1} = κ_{2}ρ_{2}. For CNR calculations in vivo, ρ and κ constants were found using the method described by Tofts et al. [

A series of CNR curves as a function of TE were calculated and drawn for all the sample pairs using Equation (5) and cross correlation was used to determine the similarity between the theoretical and the experimental CNR curves.

In order to compare the theoretical and the experimental results of CNR, two parameters were defined. The first parameter

where TE_{Exp} is the experimental TE value at which the maximum CNR occurred and TE_{Th} is the theoretical TE value at which the maximum CNR was predicted to occur.

The second parameter

where

T_{2}-weighted MR image of the 9 samples used for analysis is shown in _{2} values are shown in

The calculated TE values providing maximum CNR for each sample pair are shown in

_{2} = 96 and 26 ms, 193 and 53 ms, 193 and 123 ms, and 679 and 86 ms. The corresponding TE^{max} values are 46.6, 60.2, 133.4 and 146.6 ms respectively.

The theoretical curves for these samples are superimposed on the experimental results. The mean cross correlation value between the experimental and theoretical curves was r = 0.98 ± 0.02.

The mean percent difference between the theoretical and experimental TEs at which the maximum (

Sample | |
---|---|

1 2 3 4 5 6 7 8 9 | 679 ± 32 363 ± 28 268 ± 23 193 ± 10 123 ± 6 96 ± 4 86 ± 5 53 ± 3 26 ± 1 |

T_{2} (ms) of Samples | Predicted TE value at which maximum CNR would occur for samples | |||||||
---|---|---|---|---|---|---|---|---|

679 | 363 | 268 | 193 | 123 | 96 | 86 | 53 | |

363 | 488.4 | 411.6 | 339.2 | 256.6 | 218.7 | 203.5 | 146.6 | 88.2 |

268 | 310.7 | 260.3 | 201.3 | 173.6 | 162.3 | 119.4 | 73.8 | |

193 | 226.4 | 177.1 | 153.6 | 143.9 | 107.1 | 67.2 | ||

123 | 152.8 | 133.4 | 125.4 | 94.4 | 60.2 | |||

96 | 108.4 | 102.3 | 78.4 | 51.2 | ||||

86 | 90.8 | 70.3 | 46.6 | |||||

53 | 66.9 | 44.6 | ||||||

26 | 36.3 |

_{2} of the tumor and normal tissue was found to be 55.8 ± 8.8 ms and 32.9 ± 2.4 ms for all 8 mice respectively. Based on the calculations maximum CNR between muscle and tumour tissue was found to occur at 55.2 ms. Typical T_{2}-weighted images of human prostate cancer use an echo time of around 96 ms [

The results have shown that it was possible to maximize CNR by selecting the proper TE for SE pulse sequences when T_{2} relaxation times of the samples are known. The experiments showed that the theory indeed provides the parameters allowing maximum CNR. The cross correlation function showed the theoretical values closely emulated experimental data.

For in vitro calculations we assumed

As it can be seen in _{2} component. In this case where tissues have large differences in proton densities, acquiring a proton density image at short TE could result in an image of higher CNR. This may require the use of very short TE which may not be feasible with some current MRI hardware [

One deficiency of Equation (5) is the possibility of resulting in a negative value of the optimal TE. In some cases, where T_{2} values are close and there are large differences in proton density, assuming κ is the same, the equation results in a negative TE value. For example, if the T_{2} values are 32.9 and 55.8 ms for tumour and muscle tissue respectively, and ρ_{1} is half of ρ_{2}, the resulting optimal TE^{max} is −13.2 ms. This result has no physical meaning so for these cases choosing the smallest TE value possible should result in the best possible CNR.

The experimental values showed CNR can be maximized between prostate cancer and muscle tissues when their T_{2} values differed by about 15 ms. However, in clinical practice, the difference in MRI parameters between malignant prostate cancer and healthy prostate tissue is much lower [

thod has the ability to maximize CNR between healthy and malignant tissue, further work with patients is needed to investigate the differentiation of healthy prostate tissue from malignant tissue in humans and compare with biopsy [

The results have implication in many areas of MRI. Throughout the last few decades, numerous papers have been published regarding advances in MRI. Most of those involve some form of contrast enhancement [

Further work will include performing similar experiments at different magnetic field strengths. The theoretical derivation shown exemplifies the spin echo sequence CNR optimization for T_{2} weighted images.

The work presented showed it is possible to maximize the CNR by selecting proper TE in a SE pulse sequence. This was validated by in vivo experiments in prostate cancer tumours. The work derived here has wide implications as the ability to increase CNR and differentiate between tissues is essential in many aspects of MR imaging. Our future work will incorporate T_{1}-weighted images, including TR values, into the CNR equation thus making it a partial derivative to obtain the maximum CNR. We will also compare CNR at different field strengths in order to show the potential of low field MRI to have an equal or even greater CNR compared to higher field strengths. Our end goal is to develop a robust program which can be used to calculate optimal TE, TR and other user defined MRI parameters in order to obtain an MR image with the highest CNR between two tissues of interest based on intrinsic parameters.

Work funded by NSERC Discovery.

Christopher Brian Abraham,Boguslaw Tomanek,Laura Curiel, (2016) Contrast Optimization for an Animal Model of Prostate Cancer MRI at 3T. Journal of Modern Physics,07,819-826. doi: 10.4236/jmp.2016.78075