Sarah Eskreis-Winkler^{1,2}, Natsuko Onishi^{2}, Liangdong Zhou^{3}, Pascal Spincemaille^{1}, Ramin Jafari^{3}, Meredith Sadinski^{2}, Elizabeth J. Sutton^{2}, Elizabeth A. Morris^{2}, and Yi Wang^{1}

Quantitative perfusion imaging is challenging in the breast because the requisite arterial input function (AIF) is difficult to measure given the lack of large-caliber feeding arteries. To overcome this problem, we show that quantitative transport mapping (QTM), a new AIF-free perfusion model, is not only technically feasible in the breast, but has the potential to better distinguish malignant from benign breast lesions compared to conventional perfusion modeling.

This HIPPA-compliant,
IRB-approved retrospective study included 12 consecutive breast lesions that: 1)
were identified on ultrafast-DCE MRI as part of a hybrid protocol with
conventional DCE MRI, 2) subsequently underwent image-guided biopsy to reveal
an invasive cancer or benign pathology, and 3) had a lesion volume greater than 300mm^{3}. All patients underwent MRI examinations on a
3.0T GE MRI system. Ultrafast DCE-MRI using Differential Subsampling with Cartesian Ordering (DISCO) was acquired continuously for 15 phases (16-channel-breast-coil) or
10 phases (8-channel-breast-coil) during the first 60 seconds, starting
at the time of of contrast injection (0.1mmol/kg gadobutrol). Additional
acquisition parameters include: TR/TE=3.8/1.7msec, flip angle=10°, in-plane
spatial resolution=1.6×1.6mm, thickness=1.6mm, temporal resolution=3.0–7.6 seconds,
axial orientation.

For each case, a radiologist with 4 years of experience
selected the axial slice best displaying the lesion. Signal intensity was
converted to relative enhancement, which was taken as tracer concentration,
given the assumed linear relationship between relaxation rate and
concentration.
QTM was implemented on the 4D imaging data using the
Fokker-Planck equation assuming incompressible flow:^{7}

$$\arg\min_{\bf U}\sum_{t}\|\dot{C}(t,{\bf r})+\nabla C(t,{\bf r})\cdot {\bf U}({\bf r})\|_2^2+\lambda\left(\|\nabla u({\bf r})\|_2^2+\|\nabla v({\bf r})\|_2^2+\|\nabla w({\bf r})\|_2^2\right)$$
where
$$${\bf U}({\bf r})=u({\bf r})\hat{\bf x}+v({\bf r})\hat{\bf y}+w({\bf r})\hat{\bf z}$$$
are velocity
components in spatial dimension and $$$\nabla$$$ denotes spatial gradient. A lambda
of 20 was selected. From
U(r), the vector flow, f, into a
voxel was computed:
$$${\bf f}({\bf r})=a_xu({\bf r})\hat{\bf x}+a_yv({\bf r})\hat{\bf y}+a_zw({\bf r})\hat{\bf z}$$$ where a_{x}, a_{y }and a_{z} are
the cross sectional areas of the voxel.

A blood flow map was computed:
$$$f_{QTM}=|{\bf f}|V(100/(\rho\nu))^{2/3}$$$
, with tissue density $$$\rho$$$ taken as 1.08g/ml, blood
volume V taken as 1.2%^{8} and v as voxel
volume (in mm^{3}) . f_{QTM} was compared with f_{Kety},
which was computed using a standard two compartment model:
$$\arg\min_{k_a,k_2}\sum_{t}\|\dot{C}(t)-k_aC_a(t)+k_2C(t)\|_2^2$$
For each lesion, the AIF was measured in the ipsilateral internal
mammary artery.
Breast lesions were semi-automatically segmented by a
radiologist. Mean f_{QTM} and
mean f_{Kety} were
calculated for each lesion. Paired t-tests evaluated whether there was a
significant difference in blood flow between malignant and benign lesions, and
whether there was a significant difference between f_{QTM}
and f_{Kety} across all lesions.

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5. Spincemaille P, Zhang Q, Nguyen TD, Wang Y. Vector Field Perfusion Imaging. Proc. Intl. Soc. Mag. Recon. Med. 25, 2017.

6. Zhou, L, Spincemaille, P. Vector Field Perfusion Imaging: A Validation Study by Using Multiphysics Model. Proc. Intl. Soc. Mag. Reson. Med 26 (2018).

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8. Delille, J, et al. Measurements of Regional Blood Flow and Blood Volume in Breast Cancer With MRI. Proc. Intl. Soc. Mag. Reson. Med 9 (2001)

Row 1: Invasive cancer. A)
DISCO demonstrates an enhancing right breast mass with central necrosis. B)
Velocity vector field components (mm/s). C) QTM and Kety flow maps (ml/100g/min)
show high flow within the mass.
Row 2: Benign lesion. D) DISCO, E) Velocity maps, and
F) QSM and Kety flow maps, in which the lesion is inconspicuous, reflecting
lack of increased blood flow.
Row 3: Invasive cancer. G)
DISCO shows an enhancing left breast mass, H) Velocity maps high velocity in
the z-component(superior-inferior). I) QTM shows high flow within the lesion,
but this is difficult to appreciate on the Kety flow map.

Relative flow measurements
of malignant and benign breast lesions using QTM and Kety models. The mean flow
within each lesion is denoted by a red x.