# Automated Cardiac Resting Phase Detection Targeted on the Right Coronary
Artery

Adrian V. Dalca<EMAIL_ADDRESS>
EECS, Massachusetts Institute of Technology, Cambridge, MA, USA Mert R.
Sabuncu https://orcid.org/0000-1111-2222-3333<EMAIL_ADDRESS>
School of Electrical and Computer Engineering, Cornell University, Ithaca, NY,
USA  Seung Su Yoon<EMAIL_ADDRESS>
Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander
University Erlangen-Nuremberg, Erlangen 91058, Germany
Magnetic Resonance, Siemens Healthcare GmbH, Erlangen 91052, Germany Elisabeth
Preuhs<EMAIL_ADDRESS>
Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander
University Erlangen-Nuremberg, Erlangen 91058, Germany Michaela Schmidt
<EMAIL_ADDRESS>
Magnetic Resonance, Siemens Healthcare GmbH, Erlangen 91052, Germany Christoph
Forman<EMAIL_ADDRESS>
Magnetic Resonance, Siemens Healthcare GmbH, Erlangen 91052, Germany Teodora
Chitiboi<EMAIL_ADDRESS>
Siemens Medical Solutions USA, Inc., Princeton, NJ, USA Puneet Sharma
<EMAIL_ADDRESS>
Siemens Medical Solutions USA, Inc., Princeton, NJ, USA Juliano L. Fernandes
<EMAIL_ADDRESS>
Jose Michel Kalaf Research Institute, Sao Paulo, Brazil Christoph Tillmanns
<EMAIL_ADDRESS>
Diagnostikum Berlin, Berlin, Germany Jens Wetzl jens.wetzl@siemens-
healthineers.com
Magnetic Resonance, Siemens Healthcare GmbH, Erlangen 91052, Germany Andreas
Maier<EMAIL_ADDRESS>
Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander
University Erlangen-Nuremberg, Erlangen 91058, Germany

###### Abstract

Static cardiac imaging such as late gadolinium enhancement, mapping, or 3-D
coronary angiography require prior information, e.g., the phase during a
cardiac cycle with least motion, called resting phase (RP). The purpose of
this work is to propose a fully automated framework that allows the detection
of the right coronary artery (RCA) RP within CINE series. The proposed
prototype system consists of three main steps. First, the localization of the
regions of interest (ROI) is performed. Second, the cropped ROI series are
taken for tracking motions over all time points. Third, the output motion
values are used to classify RPs. In this work, we focused on the detection of
the area with the outer edge of the cross-section of the RCA as our target.
The proposed framework was evaluated on 102 clinically acquired dataset at
1.5T and 3T. The automatically classified RPs were compared with the reference
RPs annotated manually by a expert for testing the robustness and feasibility
of the framework. The predicted RCA RPs showed high agreement with the experts
annotated RPs with 92.7% accuracy, 90.5% sensitivity and 95.0% specificity for
the unseen study dataset. The mean absolute difference of the start and end RP
was 13.6 $\pm$ 18.6 ms for the validation study dataset (n=102). In this work,
automated RP detection has been introduced by the proposed framework and
demonstrated feasibility, robustness, and applicability for static imaging
acquisitions.

Keywords: Resting Phase Detection, AI Workflow Automation, Static Cardiac
Imaging

##  1 Introduction

In cardiovascular magnetic resonance (CMR) imaging, static cardiac imaging
techniques, such as late gadolinium enhancement (LGE) (Kellman and Arai, 2012;
Kellman et al., 2002; Akçakaya et al., 2012; Basha et al., 2017), mapping
(Kellman and Hansen, 2014; Messroghli et al., 2017; Aherne et al., 2020), or
three-dimensional (3-D) whole heart coronary angiography (Munoz et al., 2020;
Greil et al., 2017; Cruz et al., 2017; Forman et al., 2014) are increasingly
being performed to qualitatively and quantitatively assess the cardiac anatomy
and function. It is important to acquire the data during the phase of the
cardiac cycle with least motion, called a resting phase (RP), especially mid-
or end-diastolic (ED) phases (Kramer et al., 2020; Isma’eel et al., 2009;
Kramer et al., 2013), or in patients with a fast heart rate during the end-
systolic (ES) phase.
In standardized CMR protocols (Kramer et al., 2020, 2013), the guidelines
recommend using the diastolic RP with a duration of less than 200 ms as the
acquisition window for static cardiac imaging. In certain situations, e.g.,
high heart rate or patients with arrhythmias, especially in terms of mapping
acquisition, the systolic RP is preferably chosen. As outlined in (Kim et al.,
2001; Seifarth et al., 2007; Hofman et al., 1998), electrocardiogram-based
heuristics enable the ED phase selection based on a trigger time at 75% of the
RR interval for most patients, however it can be suboptimal due to the
magnetohydrodynamic effect (Abi-Abdallah et al., 2007), and not generalizable,
especially for patients with high or irregular heart rates. For advanced
applications such as high-resolution angiography, accurate determination of RP
is necessary. As different structures in the heart rest at different times of
the cardiac cycle, ideally a targeted RP for the anatomy of interest should be
determined. For coronary angiography, for example, it is suggested to
accurately determine the RP of the right coronary artery (RCA) (Kramer et al.,
2020, 2013; Shechter et al., 2005; Johnson et al., 2004; Wang et al., 2001).
The selection of the RPs is typically performed based on visual inspection on
a CINE series acquired prior to the static imaging. In current clinical
practice, an expert is required to select either the end-systolic, mid- or
end-diastolic phase for acquisition. To tackle the complex and time-consuming
manual task of RP selection for the static cardiac imaging, some previous
studies have been introduced to perform the RP determination automatically. In
previously conducted studies (Wang et al., 2001; Stuber et al., 1999), a
calibration scan-based approach using navigator echoes has been presented,
however this approach requires significant user experience and interaction in
order to accurately plan the navigator position. A threshold-based clustering
algorithm was proposed to track low-motion periods (Suever et al., 2011).
However to track the RCA area, manual tracking is required. Another approach
(Jahnke et al., 2005) was proposed using image based cross-correlation of CINE
series for the automatic selection of RPs, proving to be advantageous in terms
of image quality. An extension of the previous method (Ustun et al., 2007)
calculates the myocardial displacement from the cross-correlation calculation.
These methods, however, also require user interaction to position the region
of interest (ROI) enclosing the heart. An alternative technique with automated
RCA positioning (Sato et al., 2009) using template matching algorithm was
proposed to automatically select RP based on image intensity differences. The
intensity difference calculation as well as the template matching algorithm
can be sensitive to artifacts. Further, a method attempts to determine the
cardiac motion resolution-independently (Huang et al., 2014) using intensity
standard deviation calculation, and additionally proposed the motion
extraction based on deformable model-based registration. Another idea was
proposed in which the feasibility of motion correction algorithm for
quantifying the rest periods of the coronary arteries is shown (Shechter et
al., 2005). However, the computed RP is based on the entire field-of-view and
do not provide localized RPs for specific anatomies, and the detection is
limited to two RPs due to the two local minima search. In a recent study (Asou
et al., 2018), an automated RP selection algorithm was introduced based on a
motion area map generated from the high-speed component of the motion within a
CINE series, however the high-speed component is not necessarily related to
the anatomical structures.
Deep Learning approaches have the potential to automate clinical workflows,
and the state-of-the-art methods using convolutional neural networks (CNN) are
currently used for image localization and segmentation (Krizhevsky et al.,
2012; Szegedy et al., 2015; Simonyan and Zisserman, 2014; Ronneberger et al.,
2015). The CNN-based models are particularly used for learning the optimal
spatial features from input data, especially images, thus performing a
specific task such as localization or segmentation. Beside the power of CNN
models for learning the spatial information, 3-D convolutional operators are
used to learn spatial and temporal information for capturing features in a 3-D
input data (Ji et al., 2012; Tran et al., 2015). Registration approaches are
commonly used when it comes to motion analysis, object tracking, etc. (Dyke et
al., 2019; Chefd’Hotel et al., 2002; Szeliski and Shum, 1996; Spinei et al.,
1998; Rueckert et al., 1999), by estimating a smooth correspondence function
mapping between the coordinates from a reference image and those in a target
image. These techniques can be used for calculating the motion of a target
with the deformation fields within CINE series quantitatively.

In this work, we propose a fully automated prototype system combining the
advantages of the 3-D CNN and registration algorithms for detecting localized
RPs of the RCA from 4-chamber view (4CH) CINE series. As the CINE series are
time-resolved images, a 3-D CNN based model is trained to perform landmark
detection over the cardiac phases. The proposed system combines the deep
neural network for landmark detection and a registration algorithm. The motion
within a localized anatomy is quantified in order to automatically classifying
the systolic and diastolic RPs of the RCA. The duration of the RPs is
quantified in both cases. To test the robustness and feasibility, the proposed
framework was integrated into the scanner software and validated on patient
data acquired on 1.5T and 3T scanners at multiple centers and different CINE
sequences.

##  2 Methods

###  2.1 System Overview

Figure 1: Overview of the proposed system. Prior to a static imaging, a RP
must be defined to prevent motion artifacts. The automated RP detection system
consists of localization, ROI cropping, motion quantification and RP
classification steps and provides the RPs of the target of interest within a
4CH CINE series.

The proposed prototype system consists of three main steps that are executed
consecutively (Figure 1). The first step is to localize the ROI (see details
in section 2.2) from the input which is a 4CH CINE series. ROI can be chosen
for any anatomical structures, that are of interest displayed in 4CH images,
such as the RCA. The localization can be performed by neural networks trained
for landmark detection tasks. In case of landmark detection, the output can be
pixel coordinates that are used for cropping the image to the localized
anatomy (see details in section 2.3). The cropped series containing the ROI
are used for motion quantification (see details in section 2.4) by performing
the elastic image registration (Chefd’Hotel et al., 2002). By taking the
median of the magnitude of the deformation fields from consecutive frames, the
motion values over time points are calculated. Finally, the RPs are classified
by an absolute threshold, defined based on the correlations of the predicted
RPs by varying the thresholds with the expert annotations (see details in
section 2.5). The frames which have lower motion values than the threshold
value, are selected as RPs. The detected RPs are then used to plan the
subsequent static image acquisition.

###  2.2 Localization

In this work, the landmark detection neural network is built to automatically
detect the location of RCA in a 4CH time-resolved series. The densely
connected neural network (3-D DenseNet) architecture is trained to regress the
x- and y- coordinates of the RCA over time and it is described in detail here.
As a preprocessing step, the 4CH CINE series are interpolated to a fixed
spatial and temporal size of $224\times 224\times 32$ to be independent from
resolution. Further, the min-max pixel intensity normalization was applied to
rescale the different intensity range in [0,1]. The 3-D DenseNet proposed in
(Huang et al., 2017) was trained under supervised learning. The weights of the
network were updated by using the Adam optimizer (Kingma and Ba, 2014) with
$\lambda={10}^{-3}$ and the mean-squared-error loss function (MSE) as follows:

$\displaystyle MSE$
$\displaystyle=\frac{1}{N}\sum_{n=1}^{N}\biggl{(}\frac{1}{T}\left\lVert(\hat{y}_{t,n}-y_{t,n}\right\rVert^{2}\biggr{)}$
(1)

Table 1: The extended 3-D DenseNet built for the RCA detection. Each Conv
consists of the successively executed layers of 3-D batch normalization,
rectified linear unit activation function and 3-D convolutions. For the RCA
detection, the 3-D DenseNet with the total number of 122 convolutional layers
are built as follows: $d=32$, $h,w=224$ and $c_{1,2,3,4}={6,12,24,16}$.

Layers | Output Size | 3-D DenseNet
---|---|---
Convolution | $d\times\frac{h}{2}\times\frac{w}{2}$ |  $3\times 3\times 3$ Conv, $1\times 2\times 2$ stride
Pooling | $\frac{d}{2}\times\frac{h}{4}\times\frac{w}{4}$ |  $3\times 3\times 3$ max-pool, $2\times 2\times 2$ stride
Dense block | $\frac{d}{2}\times\frac{h}{4}\times\frac{w}{4}$ | $\begin{bmatrix}1\times 1\times 1\hskip 2.84544pt\text{Conv}\\\ 3\times 3\times 3\hskip 2.84544pt\text{Conv}\end{bmatrix}\times c_{1}$
Transition block | $\frac{d}{4}\times\frac{h}{8}\times\frac{w}{8}$ |  $1\times 1\times 1$ Conv, $2\times 2\times 2$ avg-pool, $2\times 2\times 2$ stride
Dense block | $\frac{d}{4}\times\frac{h}{8}\times\frac{w}{8}$ | $\begin{bmatrix}1\times 1\times 1\hskip 2.84544pt\text{Conv}\\\ 3\times 3\times 3\hskip 2.84544pt\text{Conv}\end{bmatrix}\times c_{2}$
Transition block | $\frac{d}{8}\times\frac{h}{16}\times\frac{w}{16}$ |  $1\times 1\times 1$ Conv, $2\times 2\times 2$ avg-pool, $2\times 2\times 2$ stride
Dense block | $\frac{d}{8}\times\frac{h}{16}\times\frac{w}{16}$ | $\begin{bmatrix}1\times 1\times 1\hskip 2.84544pt\text{Conv}\\\ 3\times 3\times 3\hskip 2.84544pt\text{Conv}\end{bmatrix}\times c_{3}$
Transition block | $\frac{d}{16}\times\frac{h}{32}\times\frac{w}{32}$ |  $1\times 1\times 1$ Conv, $2\times 2\times 2$ avg-pool, $2\times 2\times 2$ stride
Dense block | $\frac{d}{16}\times\frac{h}{32}\times\frac{w}{32}$ | $\begin{bmatrix}1\times 1\times 1\hskip 2.84544pt\text{Conv}\\\ 3\times 3\times 3\hskip 2.84544pt\text{Conv}\end{bmatrix}\times c_{4}$
Classification block | $d\times 4$ |  3-D adaptive avg-pool, $1\times 1\times 1$ Conv

where $\hat{y}_{t,n}$ is the predicted pixel coordinates at the time $t$ from
$n$ dataset, the $\hat{y}_{t,n}$ ground truth, $T$ the number of frames, and
$N$ the number of the datasets. The ground truth is generated in a semi-
supervised manner, where the RCA pixel coordinates in the first frame are
manually annotated and propagated to the next frames using the deformation
fields describing the displacement between $\hat{y}_{t,n}$ and
$\hat{y}_{t+1,n}$. The deformation field are generated by using the elastic
image registration (Chefd’Hotel et al., 2002). Each frame was then corrected
manually if the propagated coordinates were not accurate. The total number of
convolutional layers (Conv) is 122, and before each Conv a 3-D batch
normalization (BN) (Ioffe and Szegedy, 2015) and rectified linear unit (ReLU)
activation functions (Nair and Hinton, 2010) are applied. After the initial
3-D Conv and max pooling operator, the feature maps were forwarded through 4
concatenated dense blocks (DB) and transition blocks (TB). The number of 4
concatenated DBs are set to 6, 12, 24, 16, in which after each DB, a TB is
applied. In each DB, 2 Convs, each followed by 3-D BN and ReLU operators with
the increase of the feature maps with 12 are applied. Each layer obtains
additional inputs from all preceding layers and forwards the feature maps to
all subsequent layers. In each TB, a Conv with BN and ReLU followed by 3-D
average pooling operator is applied for spatial and temporal down-sampling. As
the last step, a global average pooling and $1\times 1\times 1$ convolutional
operator are used to regress the coordinates from the extracted features maps.
The detailed architectural details can be found in the Table 1.

###  2.3 Cropping

From the output of the localization task, a ROI can be simply selected from
the pixel coordinates. The detected pixel coordinates are transformed back to
the original coordinate system, and then the cropping is performed. Given the
predicted pixel coordinates of RCA by 3-D DenseNet, the bounding box is
defined by taking the minimum and maximum x- and y-coordinates of the points
in the coordinate plane from a time-resolved series and calculating the
average of these x and y-coordinates. The size of the bounding box is selected
based on prior knowledge about the size of the anatomy, chosen as $50\times
50\ mm^{2}$.

###  2.4 Motion Quantification

The motion values are quantitatively determined using elastic image
registration (Chefd’Hotel et al., 2002). Consecutive frames of the CINE
series, $s_{t}(x)$ and $s_{t+1}(x)$ for all timepoints $t$, are registered to
obtain deformation fields $d_{t}(x)$ such that $s_{t+1}(d_{t}(x))$ minimizes
the dissimilarity measure related to $s_{t}(x)$. The motion curve $m(t)$
describing the amount of RCA motion is then computed as the median of the
weighted magnitudes of the deformation fields $\left\lVert
d_{t}(x)\right\rVert$ as follows:

$\displaystyle m(t)$ $\displaystyle=median\\{G_{t}(x)\cdot\left\lVert
d_{t}(x)\right\rVert^{2}\\}$ (2)

where $G_{t}(x)$ is a Gaussian weighting function centered at the midpoint of
the detected location of the RCA between $\hat{y}_{t}$ and ${\hat{y}}_{t+1}$
at the time point t:

$\displaystyle G_{t}(x)$ $\displaystyle=\exp\biggl{(}-\frac{\left\lVert
x-p_{t}\right\rVert^{2}}{\sigma^{2}}\biggr{)}$ (3)

while $p_{t}$ denotes the midpoint of the detected RCA position. This Gaussian
weighting ensures that the motion curve represents mainly the motion of the
RCA, while still being robust to slight imprecisions of the localization
results. The standard deviation was empirically chosen as $\sigma=12$. Figure
2 shows the Gaussian weighting functions overlaid on the anatomical images at
each time point, as well as the weighted deformation fields corresponding to
subsequent image pairs. The quantification of motion can be considered in
different ways, and the detailed analysis of obtaining the RCA motion values
can be found in section 3.2.

Figure 2: An example of RCA ROI overlayed with weighted heatmaps, and below
each two frames the magnitude of the weighted consecutive deformation fields
are illustrated. The upper color bar corresponds to the weighted heatmaps, and
the below one to the magnitude of the deformation vectors. The predicted
systolic resting phase is marked in orange, and the predicted diastolic
resting phase in blue. For the sake of simplicity, the last frame is not
visualized.

###  2.5 Resting Phase Classification

After the motion curve is quantified, a classification is required to obtain
the RP. This classification is performed within a time interval
$T_{valid}=[\alpha,\omega]$, i.e. the first $\alpha$ and the last $\omega$ ms
of a cardiac cycle are excluded. $\alpha$ accounts for the time needed for
preparation pulses before the data acquisition window can start. $\omega$ is a
safety margin at the end of the cardiac cycle to account for heart rate
variability, i.e. the detected resting phase should not be too late in the
cardiac cycle in case subsequent cardiac cycles during the 3-D acquisition are
shorter, which can lead to unstable measurements (Kim et al., 2001; Seifarth
et al., 2007). Based on the ground truth annotation of RPs, the $\alpha$, and
$\omega$ are empirically chosen to be 80 ms. The RPs can be determined with an
absolute threshold from the motion values. The frames with motion values lower
than the absolute threshold value are assigned as RPs which can be described
as follows:

$RP(t)=\begin{cases}1,&m(t)<\tau,t\in T_{valid}\\\ 0,&m(t)\geq\tau,t\in
T_{valid}\end{cases}$

where $\tau$ is the absolute threshold value, and $m(t)$ is the obtained
motion value at trigger time $t$. The threshold value is obtained based on
sensitivity (true positive rate) and specificity (true negative rate) analysis
from manual annotations. The optimal absolute threshold is chosen as the one
achieved with best balanced accuracy.

###  2.6 Data

####  2.6.1 Training and Validation Dataset for the RCA Detection Network

Data used for training and evaluating the RCA detection network was acquired
on 1.5T and 3T clinical MRI scanners (MAGNETOM Aera, Avanto, Prisma, Skyra,
Trio TIM; Siemens Healthcare, Erlangen, Germany) at multiple centers (n=1000).
The dataset was split into 70% training, 15% validation and 15% testing set
for the RCA detection. Details about the datasets used for training,
validating, testing the RCA detection network, and evaluating the classified
resting phases are shown in Table 2. A medical expert with more than 10 years
of cardiac MRI experience manually annotated the RPs on 76 datasets from the
testing set for the analysis of the system.

####  2.6.2 Study Dataset

Data used for evaluating the proposed system was acquired on 1.5T and 3T
clinical MRI scanners (MAGNETOM Aera, Avanto fit, Skyra, Skyra fit, Sola,
Vida; Siemens Healthcare, Erlangen, Germany) at multiple centers (n=102). The
proposed system was integrated into the scanner software and tested online.
The dataset from the study was not used for training, testing the RCA network
or the threshold analysis, and was not mixed with the RCA Detection Network
dataset. The test datasets consist of non-pre-selected patient data with a
minimum heart rate of 35 and a maximum heart rate of 97 who are clinically
referred for coronary assessment. None of the patients have not received beta-
blockers or a target heart rate was determined. Details about the study
datasets are listed in Table 2.

Table 2: Statistics about the data population and acquisition used for
training and testing the RCA detection network, and of the additional unseen
study dataset.

|  RCA Detection
Network Dataset
(Resting Phase
annotation) |  Study Dataset
---|---|---
Number of
patients |  1000
(76) |  102
Age |  55.0 $\pm$ 19.0
(59.0 $\pm$ 17.2) |  39.3 $\pm$ 10.9
Gender |  64 % male
(68% male) |  69% male
Heart Rate
[bpm] |  64.7 $\pm$ 11.6
(68.0 $\pm$ 13.2) |  70.1 $\pm$ 12.3
Field Strength |  $25\,\%\,1.5\,T$, $75\,\%\,3\,T$
($46\,\%\,1.5\,T$, $54\,\%\,3\,T$) |  $22\,\%\,1.5\,T$, $78\,\%\,3\,T$
Spatial Resolution
$[mm^{2}]$ |  1.4 $\pm$ 0.1
(1.5 $\pm$ 0.2) |  1.7 $\pm$ 0.1
Temporal Resolution
$[ms]$ |  33.8 $\pm$ 9.9
(35.8 $\pm$ 6.8) |  37.3 $\pm$ 7.8
FOV
[mm x mm] |  311.3 $\pm$ 30.6
344.4 $\pm$ 26.9
(312.2 $\pm$ 31.7
357.4 $\pm$ 23.6) |  283.5 $\pm$ 9.2
345.9 $\pm$ 8.9
Number of Frames |  25.8 $\pm$ 2.3
(25.6 $\pm$ 1.6) |  26.0 $\pm$ 2.0

###  2.7 Experiments

####  2.7.1 Localization

The RCA detection is validated by calculating the mean and standard deviation
of the Euclidean distance between the predicted pixel coordinates and the
ground truth pixel coordinates.

$\displaystyle\text{Distance
Error}=\frac{1}{N}\sum_{n=1}^{N}\biggl{(}\frac{1}{T}\sum_{t=1}^{T}\left\lVert\hat{p}_{t,n}-p_{t,n}\right\rVert^{2}\biggr{)}$
(4)

where $N$ denotes the number of annotated test dataset, $T$ the number of time
frames in each CINE series and $\hat{p}$ the predicted and $p$ the ground
truth RCA position. The robustness and performance of the network was
qualitatively validated on 12 oblique and diverse oriented 4CH CINE and 9
clinically acquired unseen study dataset with different field strength
scanners. Further, the network was evaluated by a box plot showing the
performance of the prediction at each frame.

####  2.7.2 Motion Quantification

In order to find the best approach to quantify motion values, several
approaches were evaluated on the annotated datasets for quantifying RCA motion
from a cropped CINE series. The first approach is to quantify motion based on
the distance between detected pixel coordinate over each adjacent time point
as follows:

$\displaystyle m_{\text{dist}(t)}$ $\displaystyle=\left\lVert
p_{t}-p_{t+1}\right\rVert$ (5)

The second is to aggregate the magnitudes of the deformation fields within the
ROI without the Gaussian weighting using percentile or mean:

$\displaystyle m_{\text{pct}}(t)$ $\displaystyle=\eta_{n}\\{\left\lVert
d_{t}(x)\right\rVert|\,x\in\text{ROI, or\\}}$ (6) $\displaystyle
m_{\text{mean}}(t)$ $\displaystyle=mean\\{\left\lVert
d_{t}(x)\right\rVert|\,x\in\text{ROI\\}}$ (7)

where $\eta_{n}$ is the $n^{th}$ percentile.
Our last proposed approach is to aggregate the weighted deformation field
magnitudes to calculate the motion values as described in the following:

$\displaystyle m_{\text{wpct}}(t)$
$\displaystyle=\eta_{n}\\{G_{t}(\vec{x})\cdot\left\lVert
d_{t}(x)\right\rVert|\,x\in\text{ROI, or\\}}$ (8) $\displaystyle
m_{\text{wmean}}(t)$ $\displaystyle=mean\\{G_{t}(x)\cdot\left\lVert
d_{t}(x)\right\rVert|\,x\in\text{ROI\\},}$ (9)

where $\left\lVert d_{t}(x)\right\rVert$ is the magnitudes of the deformation
fields. The percentile analysis is performed to quantify motion from the
deformation fields, which is based on calculating the balanced accuracy,
sensitivity and specificity by varying $n$ from 10 to 100 by 10 percentile
steps. Further, the mean value is calculated as well, and compared with the
percentile analysis. In addition, the motion values of the above mentioned 9
clinically acquired dataset are extracted and qualitative validated.

####  2.7.3 Threahold Analysis

The analysis for finding the optimal threshold value to determine the RPs from
the quantified motion value is performed by the binary classification task
with varying the threshold $\tau$ from 0.01 to 1 by 0.01 steps by calculating
the sensitivity and specificity. The analysis is performed separately for 1.5T
and 3T and using the annotated datasets. The performance with the selected
threshold $\tau$ is analyzed based on area under curve (AUC) from the receiver
operating characteristic (ROC) curve (Swets, 1979), and confusion matrices are
evaluated on testing and study datasets. For all different approaches of
motion quantification, the threshold analysis is performed such that each
approach can be fairly compared. Based on thresholding, the accuracy of
classified RPs is evaluated as described in section 2.5.

####  2.7.4 RP Classification

To evaluate the performance of RP classification, the mean absolute error
(MAE) and the standard deviation between the system predicted $\widehat{RP}$
and annotated start and end time points of systolic and diastolic RP are
calculated as follows:

$\displaystyle MAE_{\lambda,\mu_{\text{type}}}$
$\displaystyle=\frac{1}{N}\sum_{n=1}^{N}\bigg{|}\widehat{RP}_{\lambda,\mu_{N,\text{type}}}-RP_{\lambda,\mu_{N,\text{type}}}\bigg{|},$
$\displaystyle\text{where}\,\lambda\in\text{start, end of
RP},\mu\in\text{window, frame}$

The number of RP annotated dataset is denoted as $N$, and the type can be the
classified systolic (sys) or diastolic (dia) RP. The performance was validated
by two different measures, firstly the difference of the time window and
secondly, the number of images between the predicted and ground truth
annotation. The time window specifies the accuracy in milliseconds, whereas
the frame in number of images. The validation was performed on the testing
datasets in which the RPs are manually annotated by a medical expert used for
the threshold analysis. The performance of the system was analyzed based on
Bland-Altmann analysis. The RPs was not counted when it was very short (<30
ms, n=10), i.e., not resolvable by the temporal resolution of the acquisition.
Additionally, the results of the system validation were presented by
sensitivity, specificity and accuracy. To overcome the imbalanced classes (RP,
no RP), the balanced accuracy is calculated based on true positive rate, and
false true negative rate as follows: Accuracy = $\frac{(TPR+TNR)}{2}$, where
TPR is true positive rate, and TNR true negative rate. Further, the ranges of
each annotated RP type and predicted RP type were compared.

To evaluate the robustness of the proposed system, different CINE sequences
(Cartesian segmented, Cartesian segmented with small field-of-view, Cartesian
segmented Compressed Sensing Prototype (CS), Cartesian Real-time CS, Radial
real-time) were acquired and the predicted RPs of each sequence were compared
with each of the expert annotation. Further, the computation time of the
proposed system was measured at the beginning and the end of the proposed
system.

##  3 Results

###  3.1 Localization

The mean and standard deviation error between the prediction and ground truth
of the fully convolutional 3-D DenseNet with 122 layers was 4.6 ± 1.8 mm. The
box plot in Figure 5, shows the Distance Error in mm between the $\hat{p}$ and
the $p$ in each frame. Robustness results for unseen datasets are presented in
two ways, first in Figure 3 which shows the performance on oblique and diverse
oriented cases (n=12) and second in Figure 4, which visualized the worst
cases. The quantitative localization results of a part of the study dataset
(n=9) acquired with breath-hold and free-breathing CINE sequences are shown in
Figure 6 above. The first frame of each CINE series and the corresponding RCA
cropped series are shown. Each case was visualized with the first frame of the
corresponding CINE series marked with a red box showing the position of ROI
defined based on the network prediction and beside it with the cropped series
enclosing the area with the outer edge of the cross-section of the RCA
overlayed with the generated heatmap.

Figure 3: The robustness of the RCA detection network is shown in a subset of
the unseen dataset. For each case, the 4CH input is shown with a bounding box
in red and the cropped image next to it for a total of 12 cases. Figure 4: The
worst cases on the test dataset of the RCA detection network are visualized
(n=4). The blue dot represents the predicted landmark position, the orange
dot, the expert’s annotation and the red box, the ROI defined based on the
predicted landmark positions, respectively. Despite incorrect detection, the
annotation landmark is still invariably included in all ROI windows. Figure 5:
A box plot showing the performance of the 122-layer 3-D DenseNet in each time
point is illustrated. Orange line represents the median value and the green
triangle, the mean value.

Figure 6: Overview of the first frame of 9 different RCA series highlighted
with a generated heatmap, which center point is taken from the predicted
coordinate by the 3-D DenseNet trained for detecting the RCA pixel coordinate
(A). The quantified motion value and classified RPs corresponding to each
dataset are shown below (B). The vertical dashed line represents the window of
interest as described in 2.5. The horizontal dashed line represents the
selected threshold value. The lower the motion value, the less motion exists
in the frame.

###  3.2 Motion Quantification

Table 3: The analysis of motion quantification. Two approaches by using the
Gaussian weighting of the magnitude of the deformation fields, or without any
weighting have been compared for varying the percentile and taking the mean
value.

Metric | Percentile | Accuracy | Sensitivity | Specificity | Threshold [a.u.]
---|---|---|---|---|---
$m_{\text{dist}}$ | - | 71.4 | 50.5 | 92.3 | 0.50
$m_{\text{pct}}$ |  10 | 75.1 | 55.5 | 94.6 | 0.08
$m_{\text{pct}}$ |  20 | 81.5 | 67.3 | 95.8 | 0.13
$m_{\text{pct}}$ |  30 | 84.1 | 72.2 | 96.0 | 0.18
$m_{\text{pct}}$ |  40 | 86.9 | 77.6 | 96.2 | 0.23
$m_{\text{pct}}$ |  50 | 87.2 | 78.1 | 96.4 | 0.28
$m_{\text{pct}}$ |  60 | 87.7 | 80.1 | 95.3 | 0.34
$m_{\text{pct}}$ |  70 | 86.5 | 76.2 | 96.7 | 0.38
$m_{\text{pct}}$ |  80 | 83.2 | 69.0 | 97.5 | 0.42
$m_{\text{pct}}$ |  90 | 81.7 | 65.8 | 97.7 | 0.49
$m_{\text{pct}}$ |  100 | 78.3 | 61.6 | 95.1 | 0.68
$m_{\text{mean}}$ | - | 89.3 | 84.7 | 93.9 | 0.34
$m_{\text{wpct}}$ |  10 | 62.4 | 29.5 | 95.2 | 0.01
$m_{\text{wpct}}$ |  20 | 72.8 | 51.9 | 93.6 | 0.03
$m_{\text{wpct}}$ |  30 | 82.7 | 74.2 | 91.2 | 0.07
$m_{\text{wpct}}$ |  40 | 87.4 | 80.8 | 94.0 | 0.12
$m_{\text{wpct}}$ |  50 | 90.1 | 85.4 | 94.8 | 0.20
$m_{\text{wpct}}$ |  60 | 88.0 | 78.9 | 97.2 | 0.28
$m_{\text{wpct}}$ |  70 | 85.8 | 74.4 | 97.2 | 0.42
$m_{\text{wpct}}$ |  80 | 85.1 | 73.4 | 97.0 | 0.62
$m_{\text{wpct}}$ |  90 | 83.6 | 71.2 | 96.0 | 0.98
$m_{\text{wpct}}$ |  100 | 66.4 | 33.2 | 99.5 | 1.0
$m_{\text{wmean}}$ | - | 86.2 | 76.6 | 95.8 | 0.36

The motion values obtained by calculating the distance between the predicted
pixel coordinates in each adjacent time points achieved 61.1% accuracy for
1.5T, and 52.8% for 3T. As the motion quantification analysis in the Table 3
shows, the 50 percentile/median of Gaussian weighting achieved 90.1% accuracy,
whereas the accuracy was 87.2% without weighting the deformation field. The
median performed 91.0% accuracy for 1.5T and 88.9% for 3T. The best accuracy
achieved by taking the mean metric was 89.3%, without Gaussian weighting. The
motion values quantified based on the median approach with Gaussian weighting
in 9 clinically acquired dataset are shown in Figure 6 bottom.

###  3.3 Threshold Analysis

For each percentile and mean analysis, the threshold $\tau$ selected based on
binary classification task is listed in the right column in the Table 3. From
the motion values obtained by taking the median, the selected $\tau$ was 0.2.
The resulting ROC curve is plotted in Figure 7, and the accuracy over each
threshold step is plotted in Figure 7 in the top row, in which the threshold
$\tau$ is marked by an orange vertical line. On the below row in Figure 7
shows the confusion matrices of each annotated datasets. On the above one, the
performance of the threshold on the testing dataset is shown, while on the
below one the performance of the threshold on the study dataset is displayed.

Figure 7: Upper Left: the ROC curve from the threshold analysis is shown.
Upper Right: the accuracy plot over the threshold values is shown. The best
performed threshold value, 0.2 is marked in orange vertical line. Below Left:
the confusion matrix showing the performance of binary classification task by
taking the best threshold value on testing datasets. Below Right: the
confusion matrix showing the performance by taking the best threshold value on
study datasets. In each measure, the counts and rate in percentage are listed.

###  3.4 RP Classification

Table 4: The results of the system on the unseen study datasets are listed. In
the first row, the difference between the start and end RP and expert
annotations are shown. In the second row, the difference of start and end
systolic and diastolic RPs are shown in frame.

Magnetic Field |  Number datasets |  Threshold |  Start Systolic
RP $[ms]$ |  End Systolic
RP $[ms]$ |  Start Diastolic
RP $[ms]$ |  End Diastolic
RP $[ms]$
---|---|---|---|---|---|---
$1.5\,T$ |  N=22 |  0.20 |  14.4 $\pm$ 19.8 |  15.0 $\pm$ 16.9 |  5.7 $\pm$ 13.1 |  12.2 $\pm$ 16.1
$3\,T$ |  N=80 |  0.20 |  19.7 $\pm$ 22.4 |  12.2 $\pm$ 16.6 |  15.8 $\pm$ 21.3 |  8.9 $\pm$ 15.2
$1.5\,T$ & $3\,T$ |  N=102 |  0.20 |  18.7 $\pm$ 22.1 |  12.7 $\pm$ 16.7 |  13.2 $\pm$ 20.0 |  9.7 $\pm$ 15.5

Magnetic Field |  Number datasets |  Threshold |  Start Systolic
RP $[Frame]$ |  End Systolic
RP $[Frame]$ |  Start Diastolic
RP $[Frame]$ |  End Diastolic
RP $[Frame]$
---|---|---|---|---|---|---
$1.5\,T$ |  N=22 |  0.20 |  0.46 $\pm$ 0.63 |  0.54 $\pm$ 0.63 |  0.16 $\pm$ 0.36 |  0.37 $\pm$ 0.48
$3\,T$ |  N=80 |  0.20 |  0.70 $\pm$ 0.82 |  0.43 $\pm$ 0.59 |  0.49 $\pm$ 0.63 |  0.28 $\pm$ 0.49
$1.5\,T$ & $3\,T$ |  N=102 |  0.20 |  0.66 $\pm$ 0.80 |  0.45 $\pm$ 0.60 |  0.40 $\pm$ 0.59 |  0.31 $\pm$ 0.49

Table 5: Accuracy, sensitive and specificity are listed with the optimally
defined threshold.

Magnetic Field |  Number datasets |  Threshold |  Accuracy |  Sensitivity |  Specificity
---|---|---|---|---|---
$1.5\,T$ |  N=22 |  0.20 |  93.4 |  90.1 |  96.8
$3\,T$ |  N=80 |  0.20 |  92.6 |  90.7 |  94.5
$1.5\,T$ & $3\,T$ |  N=102 |  0.20 |  92.7 |  90.5 |  95.0

The detailed results about the performance of the predicted systolic and
diastolic RP on the study datasets are listed in Table 4, Table 5. The Bland-
Altmann plots showing the performance of start and end detected time point for
each systolic and diastolic RP is shown in Figure 8. $MAE_{start,end\
windo{w/frame}_{sys}}$ and $MAE_{start,end\ windo{w/frame}_{dia}}$ for 1.5T
datasets was 11.8 ± 16.5 ms (0.38 ± 0.53 frame) and 14.2 ± 18.9 ms (0.48 ±
0.63 frame) for 3T datasets. By using the selected $\tau$, the proposed system
resulted in 93.4% accuracy, sensitivity at 90.1% and specificity 96.8% for
1.5T and 92.6%, 90.7% and 94.5% for 3T datasets. $MAE_{start,end\
windo{w/frame}_{sys}}$ and $MAE_{start,end\ windo{w/frame}_{dia}}$ was 13.6 ±
18.6 ms (0.46 ± 0.62 frame) when using the datasets independent from field
strength for analysis. The accuracy, sensitivity and specificity achieved by
the defined absolute $\tau$, <0.2, was 92.7%, 90.5% and 95.0%. The
automatically classified RPs resulted in a mean max error of 30 ms, meaning
that it deviates by roughly one frame.

Figure 8: Top: the difference between the predicted and expert annotations of
start and end systolic RP are shown in Bland-Altmann plot. Bottom: the
difference between the predicted and expert annotations of start and end
diastolic RP are shown. The blue dots represent the exact match between the
predicted and annotation, and the orange dots show when there is one frame
difference. The gray dots represent when the difference is more than 2 frames.

The datasets with RPs with less than 30 ms were discarded (n=9). Further,
there was no systolic RP annotated by the expert in 14 cases, and no diastolic
RP in 12 cases. These phases were excluded from the analysis. The
${{\widehat{RP}}_{start\ window_{sys}}}$ matched with the annotation, or was
off one frame in 93.6%, the ${{\widehat{RP}}_{end\ window_{sys}}}$ in 97.5%,
the ${{\widehat{RP}}_{start\ window_{dia}}}$ in 93.8% and
${{\widehat{RP}}_{end\ window_{dia}}}$ in 96.3%, respectively.
${{\widehat{RP}}_{start\ window_{sys}}}$ was detected earlier/later than the
expert’s annotation in 27.8%/5% and ${{\widehat{RP}}_{start\ window_{dia}}}$
in 20.9%/16.0%. ${{\widehat{RP}}_{end\ window_{sys}}}$ was detected
earlier/later than the expert’s annotation in 11.4%/29.1% and
${{\widehat{RP}}_{end\ window_{end}}}$ in 15.2%/14.8%. In average, the
${\widehat{RP}}_{start\ window}$ was selected earlier than the ground truth in
24.3% of the cases and later in 10.6%. In 10 cases, outliers were present, off
by 2 or more frames. In 10 cases, there were outliers present for the
${\widehat{RP}}_{start\ window}$, off by 2 or more frames. For the
${\widehat{RP}}_{end\ frame}$, it was off by 2 or more frames in 5 cases.
The range of annotated systolic RP was 61.1 ± 24.1 ms and the predicted range
of systolic RP was 75.5 ± 32.9 ms. Further the range of annotated diastolic RP
was 156.0 ± 102.1 ms and the predicted range was 158.2 ± 104.3 ms.

Figure 9: An example of a study case with 6 different CINE sequences. On the
left (A), the first frame of each CINE series and the output of the cropped
series are shown. Each color represents one sequence acquisition. On the top
right (B), the quantified motion values of each RCA cropped series are plotted
over the time points. On the bottom right (C), the classified RPs of each are
shown with the expert’s annotation, which is marked in orange color. The RR
interval of the real-time CINE acquisitions varied from the segmented CINE,
which caused early detection of the RPs.

In Figure 9, the robustness of the proposed system is shown in which the
system was tested in different sequences including a rescan from a single
volunteer. The visualized different CINE outputs are acquired in the order
from top to bottom and with 5min between the first and last acquisition. The
predicted start and end systolic phases were matched with annotation in most
cases, except in one CINE sequence, where the systolic RP was detected by the
system but not by the expert, and in a repeat scan, the end time point was off
one frame. The start diastolic RP was detected one frame earlier in 2 cases,
and end diastolic RP was detected two frames off in real-time sequences. In an
example case, the automatically detected RPs were used for the later 3-D
static cardiac acquisition targeted to the RCA. The 3-D RCA visualization with
the automatically classified RPs showed no residual motion artifacts (Figure
10). The computation time of the proposed system was averaged 1.5 seconds.

Figure 10: An example of a volunteer study illustrated with the main steps of
the framework pipeline. The outputs are generated directly from the scanner
after the proposed system was integrated online. The RCA localization series
is the original CINE series with an RCA position marked by a cross. The ROI
cropping generated the cropped series based on the RCA localization. From
these cropped series, the motion is quantified, from which the RPs are
determined. The series that represent the systolic and diastolic resting phase
are generated as well. Here, the diastolic resting phase window (dark blue
arrow) is applied for the static coronary imaging.

##  4 Discussion

The detection of the RCA ROI is successfully and robustly performed by the 3-D
DenseNet on the testing dataset and on the study cases. The 3-D based Conv
networks leverage the spatial and temporal information from the time-resolved
input, rather than learning only spatial information per time point. The size
of the fixed ROI ($50\times 50$mm2) was sufficient in all cases for depicting
the RCA at each time point. Further, the network was robustly performed on
diverse oriented cases (Figure 3) and different CINE sequences (Figure 9)
which allows the proposed system to be integrated into different clinical
protocols.
In terms of quantifying motion values, the approach of taking the Euclidean
distance from the predicted RCA pixel coordinate over cardiac phases highly
relies on the performance of the network, furthermore, taking the pixel
distance measurement for the displacement metric of the anatomy-of-interest
between the consecutive frames was not accurate as shown in Table 3. The
approaches deriving from the motion values by taking the deformation fields
defined by the elastic image registration show a clear advantage, from which
the highest accuracy was the one using the weighted deformation fields (see in
Table 3). The approach with deformation fields is clearly more robust to
slight inaccuracies of localization results. The Gaussian weighting further
improves the performance of the system, as it allows to focus on the target-
of-interest, and eliminates the area which is not of interest, such as the
blood flow in the atrium contained in the RCA ROI.
The metric for assessing the motion values from the weighted deformation
fields was reasonably chosen as 50 percentile by the accuracy analysis. The
absolute threshold value is selected based on AUC-ROC analysis, evaluated on
the testing datasets from the different 1.5T, 3T scanners and CINE sequences
and no specific data selection, thus shows versatility in the results (Figure
7). The classification of the RP by the absolute threshold value is possible
due to the quantitative outputs of the deformation field-based approach which
enables the detection of the phases with minimal motion, which can be either
end-systolic or mid-diastolic or end-systolic and mid-diastolic RPs. In Figure
7, the quantified motion values of the clinically acquired dataset with
different CINE sequences and the corresponding predicted RPs were well matched
with the expert’s annotation. As shown in Table 4, Table 5, the proposed
framework performed robust in different field strengths as well.
Interestingly, in the dataset visualized in the center, there was no RP found
by a medical expert, and the proposed system was also able to classify the
non-RP case demonstrating the advantage of the system. In such cases, the
system gives the user the possibility to take the quantified curve as a
reference and select the phase with minimum motion based on the motion curve.
Based on the Bland-Altmann plots (Figure 8), the systolic RP did not perform
as well as the diastolic RP, especially the classification of the start
systolic RP was challenging. The predicted systolic RP window was usually
slightly longer than the experts’ annotations. However, the mean range
difference was 15ms, which is negligible since the temporal resolution of CINE
series is 30ms. In a recent study, the proposed system was evaluated in a
clinical validation, in which the interobserver variability was extensively
validated and revealed that the automatically detected RPs were consistent
with those of the experts (Ogawa et al., 2022). As shown in Figure 10, the RCA
was sharply visualized without severe residual motion artifacts that was
acquired during the automatically detected RPs.

The study presents some limitations. First, the proposed method depends on two
factors: the performance of the RCA localization network and the registration
algorithm that may lead to inaccurate results in the presence of severe
artifacts in reconstructed CINE series, even though the network performed well
on difficult cases as shown in Figure 3 and Figure 4. Second, the absolute
thresholding used for classification, can be further investigated, whether
other algorithms can be used for binary classification. Third, in this study,
the focus was highly on method evaluation on patient dataset, however the
clinical feasibility and interobserver variability study using this method was
performed in (Ogawa et al., 2022). In the following research, a further
clinical study can be of interest to compare the image quality between once
acquired with the automatic approach and the other with manually determined
resting phases.

Previous methods have shown the feasibility to detect the imaging acquisition
window automatically using the shim box volume positioning and cross-
correlation calculation (Jahnke et al., 2005; Ustun et al., 2007). However,
these semi-automated methods still require the careful positioning of the shim
volume coverage. Further, the RP detection is targeted to the whole heart
instead of a specific anatomy of interest. These methods were validated on
healthy in vivo subjects on a single field strength. Moreover, approaches
based on the standard deviation of pixel intensity (Huang et al., 2014) or
difference of gradient magnitudes (Piccini et al., 2017) were introduced,
allowing the RP detection in real time. This method however performs the RP
detection globally based on the entire field-of-view, and the detected RPs are
always two RPs as the search is done by two local minima. Several approaches
have been proposed for the automated determination of targeted RP on regions
such as RCA (Sato et al., 2009; Asou et al., 2018). A template matching was
performed for finding the area with the outer edge of the cross-section of the
coronary artery, however the template was defined based on randomly selected
five datasets (Sato et al., 2009). In a more recent study, the regions were
extracted from the high-speed component within CINE series by the frequency
domain analysis, however by doing so, the cardiac anatomy structures can be
disregarded. The authors stated that this method was validated on healthy
volunteers, and uncertain the performance on large dataset especially with
high heart rates. In Adam et al. (2020), the deep learning-based RP detection
network is built by combining the CNN and Long short-term memory models taking
the CINE series as input, and outputs the binary output which is either a RP
or not a RP. Therefore, this method is not quantitative and unclear which
cardiac structure is weighted, or whether the network tries to detect global
RP.

##  5 Conclusions

To our knowledge, this proposed study is the first to present the fully
automated localized RP detection framework from a CINE series that was
validated with a large dataset with multiple 1.5T and 3T scanners acquired
with different CINE protocols, such as with free-breathing or breath-held
techniques. We investigated the robustness and feasibility of the proposed
system for fully automated systolic and diastolic RP detection. The proposed
system can improve the workflow efficiency, automation, and standardization of
the static cardiac imaging that broaden the applicability towards any static
cardiac imaging. The RP detection system can be applied in various
applications, such as 2-D and 3-D LGE, mapping, 3-D coronary imaging, or any
other applications in which the information of RP of heart can be useful.
Future work will focus on clinical validations, improving the accuracy of RP
classification and integration of automatic detection of other regions, such
as the atria and ventricles.

Acknowledgments

This work was supported by Siemens Healthineers GmbH.

Ethical Standards

The local ethics committee approved the study, and a written informed consent
was provided by all subjects. The declaration of consent to participate in the
study was signed by all subjects.

Conflicts of Interest

The authors declare no conflict of interest and no financial disclosure in
relation to this study. A. Maier is Associate Editor of the Journal of Machine
Learning for Biomedical Imaging (MELBA). Seung Su Yoon, Elisabeth Preuhs,
Michaela Schmidt, Christoph Forman, Teodora Chitiboi, Puneet Sharma, Juliano
L. Fernandes, and Jens Wetzl are employees of Siemens Healthcare GmbH.

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#  Sub-barrier fusion excitation for the system 7Li+28Si

Mandira Sinha,1,2 H. Majumdar,1,∗ P. Basu,1 Subinit Roy,1 R. Bhattacharya,2 M.
Biswas,1 M. K. Pradhan,1 S. Kailas3 E.mail<EMAIL_ADDRESS>1
Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata-700064, India
2 Gurudas College, Narikeldanga, Kolkata-700054, India  3 Nuclear Physics
Division, Bhabha Atomic Research Centre, Mumbai-400085, India
<EMAIL_ADDRESS>
###### Abstract

The sub-barrier fusion excitation functions are measured for the first time
for the system 7Li +28Si by the characteristic $\gamma$-ray method in the
energy range $E_{\textit{lab}}$= 7-11.5 MeV. The results show an enhancement,
below the barrier, by about a factor of two when compared with the one-
dimensional barrier penetration (1D BPM) model. Introduction of coupling with
the rotational 2+ state (1.779MeV) of the target improves the fit somewhat,
but still an enhancement of about 25-40$\%$ remains.

###### pacs:

25.60.Pj;25.70.$-$z;25.70.Gh

††preprint: APS/123-QED

Exploring the structure and reaction mechanism with loosely bound stable
projectiles or with radioactive ion beams (e.g. halo/skin nuclei), at sub- and
near-barrier energies, appears to be an interesting and challenging problem at
the present time. Recent theoretical studies Dass96 ; Huss93 ; Taki93 ; Hagi00
; NZag ; Huss06  have yielded new insights into the fusion reaction dynamics
leading to enhancement/suppression of fusion, weakening of usual threshold
anomaly found with tightly bound projectiles and appearance of new type of
break-up threshold anomaly around the barrier energy. The interplay among
fusion, loose structure, breakup to the continuum, and transfer channels are
considered to be responsible for the above phenomena.

Precise measurements exist for the fusion of loosely bound stable projectiles
with heavy targets like 165Ho, 206,208Pb, 209Bi Mdas99 ; YW ; Sign97 ; VT ;
YuE . Most of these experiments found appreciable enhancement of complete
fusion (CF) compared to the one-dimensional barrier penetration model (1D BPM)
calculation at the sub-barrier energy region. However role of the breakup and
other nonelastic channels are not explicitly and unambiguously discerned. In
the medium mass range there have been some recent experimental investigations
SMores ; Padro02 ; Anjos ; cbeck ; mromo ; Gomes  where only the total fusion
could be measured owing to limitations of the techniques used. Most of these
studies were done at energies above the Coulomb barrier and observed that TF
is not affected by breakup. However Beck $et$ $al$. cbeck  reported some small
enhancement of 6Li induced fusion with 59Co at energies very close to the
barrier.

The experimental attempts for the sub- or near-barrier fusion studies in the
light mass region (A$\sim$20-50) are rare. Most of the recent investigations
Fig06 ; Anjos1 ; Padro02 ; GMar05  are pursued at well above the barrier
energies. The fusion cross sections were found not to be hindered by breakup
and agree well with 1D BPM predictions. Reference Padro02  showed that fusion
excitations induced by stable weakly bound projectiles like 6,7Li and 9Be, at
energies above the barrier, are almost similar to those produced by strongly
bound nuclei 11B and 16O. But this observation is in contradiction to the
findings of Figuiera $et$ $al$. Fig06 , where it has been shown that a
hindrance to fusion cross section is systematically larger for reactions
induced by weakly bound projectiles (e.g., 9Be) than for those with strongly
bound nuclei (e.g., 11B and 12C). Of all the existing studies, only one
experiment GMar05  measured the total fusion cross section by the time of
flight technique, at energies very close to but above the nominal barrier.
Here also total fusion was seen not to be affected by the break-up process.
However, the deduced reaction cross section, even nearest to barrier energy,
was found to be larger than the fusion cross section.

Most of the above works showed neither enhancement nor suppression of
excitation function in the near-barrier energies. Moreover, none of these
experiments explored the fusion behaviour below the Coulomb barrier. In this
perspective we present, for the first time, an experimental measurement of
fusion cross section for the system 7Li +28Si, at sub-barrier energies, and
extend it to just above the barrier. This study is complementary to our
earlier work mand  for the same system, measuring excitation function at
energies well above the barrier, where some sort of suppression was observed
beyond twice the barrier energy.

To measure the total fusion (TF) cross-sections for 7Li +28Si, an experiment
was done at 3 MV Pelletron accelerator of Institute of Physics (Bhubaneswar)
with 7Li (2+, 3+) beam (8-30 pnA) at energies, $E_{\textit{lab}}$= 7, 8, 8.5,
10, and 11.5 MeV. A self-supported thin target of 28Si (175$\mu$g/cm2) was
used. A specially designed small thin walled target chamber made of stainless
steel (in the 0o beam line) was used to measure the fusion cross section using
the characteristic $\gamma$-ray method. The $\gamma$-rays emitted from the
evaporation residues were detected using a HPGe detector placed at 125o with
respect to the beam direction. A long insulated metallic cylinder with proper
electron suppressor was used as Faraday cup and standard current integrator
was employed to measure the incident beam current. Efficiency runs were taken
both at the beginning and at the end of the main experiment with a number of
standard sources (152Eu, 133Ba, 207Bi) spanning the energy range 81-1770 keV.

Some of the important residues in the fusion of 7Li +28Si detected are 30Si,
32S, 33S and 30P. Their characteristic $\gamma$-ray cross sections are shown
in Fig. 1. The solid lines show CASCADE six  predictions. The agreement
between experiment and the compound nuclear evaporation estimation is apparent
for data at energies above the Coulomb barrier, but at Coulomb barrier and
below, the $\gamma$-ray augmentation is noticeable. These cross sections
(${\sigma}_{\gamma}$) were extracted after analyzing the $\gamma$-ray spectra
and using relevant efficiencies, beam and target specifications as described
in Ref. mand . To subtract/correct for $\gamma$-rays arising out of beam
impingement on the slit, beam line or the Faraday cup, one additional spectra
was taken with a beam using a Ta-frame having a hole in place of the target
position.

The main contributions to fusion come from channels like $p$$n$+33S,
$d$$n$+32S, $\alpha$$p$+30Si for E $\leq$ 9 MeV and $p$$n$+33S,
$\alpha$$p$+30Si, $\alpha$$n$+30P, $d$$n$+32S for E$\geq$9 MeV. Some of the
prominent identified $\gamma$-rays are 1.263 MeV(30Si), 2.230 + 2.235 MeV
(32S+30Si), 1.967 MeV (33S), 0.677 MeV(30P). The contributions of the observed
channels are almost about 85-80$\%$ of the total fusion cross section for
7Li+28Si system, in the energy region 7-11.5 MeV, respectively. The total
fusion cross section was extracted as the ratio of the total experimentally
measured $\gamma$-ray cross-sections and the corresponding branching factor
$F_{\gamma}$. As there were overlapping $\gamma$-rays and weak transitions
$F_{\gamma}$ was estimated theoretically, following a procedure used in Refs.
Day ; Mukh  as the ratio of the total theoretical $\gamma$-ray cross sections
and the corresponding theoretical fusion cross section, both obtained from a
statistical model calculation using the code CASCADE .The uncertainty in the
measurement of the fusion cross-section was estimated to be about 16$\%$ for
all energies, except for the lowest energy, where it was nearly 20$\%$, owing
to a very poor yield.

Figure 1:  ${\sigma}_{\gamma}$ vs $E_{c.m.}$ for 7Li+28Si . Theoretical
CASCADE predictions are shown by solid lines. Figure 2:  Experimental fusion
excitation function and theoretical predictions.

The estimated projectile energy loss in the half thickness target is about 134
keV at 7 MeV and 125 to 102 keV in the high energy regime 8-11.5 MeV. The
intrinsic energy resolution and uncertainty in beam energy calibration yields
an error of about 30 keV. These factors were taken into account and fusion
cross sections were plotted as a function of effective projectile energy in
Fig. 2. The effective projectile energy was also used in the other figures.
The overall resulting uncertainty in projectile energy is also shown. The one-
dimensional barrier penetration model (1D BPM) estimates were found out using
the coupled channel code CCFULL Ccfull  in the no coupling mode, and are shown
in Fig. 2 for comparison. The input optical model parameters ($V_{0}$ = 130
MeV, $r_{0}$ = 0.97 fm and $a_{0}$ = 0.63 fm) were extracted as described in
ref. mand . It is seen that below the nominal barrier ($V_{b}$ = 6.79 MeV) the
theoretical prediction underestimates the experimental excitation function and
the difference is more near the barrier, pointing to the effective role of
coupling in this region. Sub-barrier enhancement with respect to 1D BPM is
apparent and it is more prominent just below the barrier. The experimental
results are also compared with Wong’s phenomenological prediction wong  using
the input parameters like, barrier and barrier radius from the prescription of
Vaz $et$ $al$. vaz  and curvature from Wong parametrization. These values are
respectively 6.74 MeV ($V_{b}$), 8.18 fm ($R_{b}$) and 3.24 ($\hbar$$w$).

As expected, the Wong formulation overestimates the fusion excitation well
below the barrier owing to assumption of parabolic nature of the potential,
whereas the shape of real nucleus-nucleus potential may be asymmetric and
broad at lower energies. Our experimental observations are somewhat similar to
the recent findings of Penionzhkevick $et$ $al$. YuE  for 6He + 208Pb having
large enhancement and of Beck $et$ $al$. cbeck  for 6Li + 59Co yielding small
enhancement. We have explored the effects of rotational coupling employing the
exact coupled channels calculation with CCFULL where the rotational state
$2^{+}$ (1.779 MeV) of 28Si (with g.s. deformation $\beta_{2}$= -0.407) was
coupled to the g.s. The results are also shown in Fig. 2. Though it yields a
reasonable fit to the experimental data there is still a 25-40$\%$ under
prediction in the sub-barrier energy range $E_{c.m}$= 5.6-6.4 MeV. Effect of
projectile deformation is seen to be small and is not shown. It is possible
that other types of coupling, e.g., transfer and/or breakup are responsible
for the remaining discrepancy.

A recent observation Jing  at sub-barrier energies showed that the product of
the fusion cross section ($\sigma$) and the c.m. energy ($E$) for 60Ni+89Y
falls much faster than the usually accepted exponential falloff. They analyzed
this steep falloff in terms of the logarithmic derivative ($L$) of the product
$\sigma$$E$ defind by $L(E)$=
$dln$($\sigma$$E$)/$dE$=(1/$\sigma$$E$)[d($\sigma$$E$)/$dE$]. Their results
showed a continuous increase with decreasing bombarding energy in
contradiction to theoretical prediction with Wong’s prescription wong . This
discrepancy was attributed by Hagino $et$ $al$. hag  to a deviation of the
parabolic shape of potential assumed by Wong wong , from the asymmetric shape
of the Coulomb barrier and was explained by using a large diffuseness of the
ion-ion potential. To investigate the nature of the fall of $\sigma$$E$ for
our system we have plotted in Fig. 3 the experimental values of $L$ obtained
from consecutive fusion data points together with the Wong prediction. Here
also we find increasing $L$ with decreasing $E$ below the barrier while the
theoretical prediction saturates to a constant value below the barrier.
However the increase is not that steep as is observed by Jiang $et$ $al$. Jing
.

Figure 3:  Experimental slope function L(E), extracted from measured fusion
cross-section alongwith the theoretical prediction from Wong model (solid
line).

To summarize, we have experimentally found the excitation function for 7Li +
28Si at near- and mostly sub-barrier energies, for the first time, employing
the usual characteristic $\gamma$-ray method. Below the barrier our results
show some sort of enhancement when compared with the 1D BPM prediction.
Introduction of coupling to target rotational motion improves the fit with
experiment to some extent. Recently Shrivastava $et$ $al$. Asriv  have
advocated in their work on 7Li +65Co that neutron transfer is more probable
than all other possible direct reactions and hence an $n$-transfer followed by
fusion may be a possibility. Sub-barrier enhancement owing to $n$-transfer
(with positive $Q$-value) has been shown by Zagrebaev NZag  for the fusion of
6He with 206Pb. However Pakou $et$ $al$. Pako  pointed out in their work on
the direct and compound contribution in the reaction 7Li+28Si that
$d$-transfer is the dominant mechanism at near-barrier energies. These imply
that the picture is not yet clear. So it is necessary to do a detailed
theoretical analysis (utilizing a more realistic coupled reaction channels
model) introducing these possible couplings for a better and complete
understanding of the phenomenon.

We would like to acknowledge the Department of Atomic Energy (DAE) and Board
of Research in Nuclear Science (BRNS) for the financial support under the
project (grant no. 2002/37/38/BRNS). We also would like to thank B. Mallick of
Institute of Physics (Bhubaneswar), A. K. Mitra and S. Chatterjee of Saha
Institute of Nuclear Physics for their technical support during the experiment
and J. Panja of the same Institute for the preparation of Si Target.

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