Junzhong Xu^{1}, Xiaoyu Jiang^{1}, Sean P Devan^{2}, Lori R Arlinghaus^{1}, Eliot T McKinley^{1}, Jingping Xie^{1}, Zhongliang Zu^{1}, Qing Wang^{3}, A Bapsi Chakravarthy^{1}, Yong Wang^{3}, and John C Gore^{1}

^{1}Vanderbilt University Medical Center, Nashville, TN, United States, ^{2}Vanderbilt University, Nashville, TN, United States, ^{3}Washingon University, St. Louis, MO, United States

Non-invasive mapping of cell size distribution provides a unique means to probe biological tissues. We introduce a diffusion MRI based framework that does not require prior assumptions on distribution functions to provide tissue microstructural properties including non-cell-volume-weighted cell size distributions. We validated this approach, which we call MRI-cytometry, comprehensively using computer simulations in silico, cultured cells in vitro, and animal xenografts in vivo. We then demonstrate the implementation of MRI-cytometry in imaging breast cancer patients using clinical 3T MRI, indicating its potential clinical application such as more specific assessments of tumor status and therapeutic responses.

$$\mathop {}\nolimits_{{w_l} \ge 0}^{\arg \min } \left\{ {\sum\limits_{k = 1}^K {\sum\limits_{l = 1}^{N \times M + P \times Q} {{{\left| {{M_{kl}}{{w'}_l} - {S_k}} \right|}^2} + \xi } } \sum\limits_{l = 1}^{N \times M + P \times Q} {{{\left| {{{w'}_l}} \right|}^2}} } \right\}$$

where $$$\xi$$$ is a regularization factor empirically determined as 0.1. After the fitting, we obtain the cell-volume-weighted cell size distribution $$$P_{vw}(d)$$$ and intracellular volume fraction $$$v_{in}$$$.

Figure 3 shows a comparison of MRI-cytometry and light microscopy derived $$$d$$$ distributions using cultured cells in vitro. The mean cell sizes $$$\bar{d}$$$ obtained using the two methods show good agreement while the standard deviations of cell sizes $$$\sigma_d$$$ show some discrepancies.

Figure 4 shows s comparison of MRI-cytometry and histology-derived cell size distributions of mouse MDA-MB-231 and MCF-7 tumors. The Bland-Altman plots show the agreement of MRI-cytometry and light microscopy derived $$$\bar{d}$$$ and $$$\sigma_d$$$, with limits of agreement (1.96SD) 2.2 μm and 1.4 μm, respectively.

Figure 5 shows the cell size distributions of seven breast tumors obtained in breast cancer patients in vivo. There is a good correlation between the cell-volume-weighted mean cell size $$$d_{vw}$$$ obtained using IMPULSED

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Figure 1 Diagram of two-step MRI-cytometry
fitting of a simulated tissue with a Gaussian cell size distribution

Figure 2 Simulated influence of
noise at different SNR levels on MRI-cytometry fitted distributions of
microstructural parameters. For each SNR, the fittings were repeated 100 times
each with different noise samples but with the same SNR level. The red dashed
lines represent the ground truth, blue solid lines represent the mean fitted
distributions and shaded areas represent standard deviations.

Figure 3 Comparison of MRI-cytometry
and light microscopy derived cell size distributions using cultured cells in
vitro. (a) comparison of distributions of five different cell samples. (b)
correlations of MRI-cytometry and light microscopy derived mean $$$\bar{d}$$$ and standard deviation $$$\sigma_d$$$ of cell sizes.

Figure 4 Comparison of MRI-cytometry
and histology derived cell size distributions of mouse tumors in vivo. (a)
comparison of distributions of five tumors (top: MDA-MB-231. Bottom: MCF-7).
(b) Bland-Altman plots show the agreement of MRI-cytometry and light microscopy
derived mean $$$\bar{d}$$$ and standard deviation $$$\sigma_d$$$ of cell sizes.

Figure 5 (**a**) cell size distributions
of seven breast tumors obtained in cancer patients in vivo. (**b**) The correlation
between cell-volume-weighted mean cell sizes obtained using IMPULSED and MRI-cytometry.