Roshni Senthilkumar^{1,2}, Sai Man Cheung^{2}, Kwok-Shing Chan^{3}, and Jiabao He^{2}

^{1}Radiology Physics, University Hospital Coventry and Warwickshire, Coventry, United Kingdom, ^{2}Institute of Medical Sciences, School of Medicine, Medical Sciences and Nutrition, University of Aberdeen, Fosterhill, Aberdeen, Scotland, ^{3}Donders Institute for Brain, Cognition and Behaviour, AJ Nijmegen, Germany

MR relaxation properties of T1 and T2 are well known to alter in cancer, reflecting diseased tissue micro-environment. Multiple compartment models have been developed to better approximate tissue classes within an imaging voxel, allowing more accurate estimation of disease load for more precise treatment planning and monitoring. However, multiple compartment models is more sensitive to noise and suffers from potential overfitting, due to from significantly increased number of variables for fitting exponential functions and consequently more complex cost function. We therefore conducted numerical simulation to establish, the first in the literature, applicability condition of multiple compartment model in breast cancer.

The authors would like to thank Prof Andy Welch and Dr Hugh Seton for managerial support, and Ms Eleanor Hutcheon for administrative support.

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After numerical simulation
from three simulations in mono-exponential and bi-exponential fitting on
single/two compartment tissue model, the mean and standard deviation (mean ±
SD) of fitted T1 and T2 relaxation distribution at SNR = 300, (W1=W2=0.5) is
displayed. Two compartment tissues contain adipose and malignant lesion for T1
and fibrogandular and malignant
for T2.
In mono-exponential fitting, the SD increases as the T1 and T2 rises. In
bi-exponential fitting the SD is larger than mono-exponential. However, the
mean T1 and T2 resemble the actual tissue relaxation time.

A) Mean signal graph of all the tissues. B) T1
distribution of each of the tissues with corresponding mean and standard
deviation. (10,000 runs) The estimated
T1 values are less precise (higher standard deviation) for tissues with long T1
because the complete magnetization relaxation is much longer than the timeframe
of the inversion time. Moreover, in T1 fitting, the null point is crucial for
accurate fitting. For accurate estimation of T1, the TR is typically greater
than 5 times the longest T1 (5×T1<TR).

(A) Mean and error bar of MR signal from
4 tissues. (B) T2 distribution histogram is plotted for each tissue which follows Gaussian distribution as seen from skewness and the
Anderson-Darling test (H=1) so the original dataset is preserved. 10,000 runs). The estimated
T2 values showed high variability for tissues with longer T2. The estimation of
T2 values becomes less accurate for tissues with long T2 because of the slow
exponential decay in the signal. The short effective echo time negatively impacted
the determination of long T2 components after fitting.

Simulation
results in two compartments with mono-exponential fitting (A&B) and in
bi-exponential fitting in (C&D)T1 and (E&F)T2. Changing SNR from 100 to 1500, the SD reduced drastically from 25.4 to 1.54
for T1 and 4.18 to 0.32 for T2 in mono-exponential. In bi-exponential SD
reduced from 220.3 to 9.4 (W1=0.1,W2=0.9) and 15.0 to 0.7 (W1=0.9,W2=0.1) in T1S and from 41.1 to 1.9 (W1=0.1,W2=0.9) and 6707 to 53.0 (W1=0.9, W2=0.1) in T1L. Whereas 37.0 to 2.5 (W1=0.1,W2=0.9) and 7.2 to 0.3 (W1=0.9, W2=0.1) in T2S and 6.4 to 0.8 at (W1=0.1,
W2=0.9) and 27.9 to 2.4 in (W1=0.9, W2=0.1) in T2L.

Accuracy
in the estimation of T1 and T2 with respect to SNR. A+B) T1 probability
distribution, C+D) T2 probability distribution. In bi-exponential fitting, as
the SNR was increased from 100 to 1500, the estimated T1s and T2s in both
compartments converge to a narrower range at a weighting factor of 0.5. This
shows that utilizing higher SNR is beneficial in obtaining accurate T1/T2
distribution.

DOI: https://doi.org/10.58530/2022/0615