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FDA to decide by June on future of COVID vaccines
Publish date: April 7, 2022
The next generation of COVID-19 vaccines should be able to fight off a new strain and be given each year, a panel of experts that advises the Food and Drug Administration said April 6.
But members of the panel also acknowledged that it will be an uphill battle to reach that goal, especially given how quickly the virus continues to change.
The members of the Vaccines and Related Biological Products Advisory Committee said they want to find the balance that makes sure Americans are protected against severe illness and death but doesn't wear them out with constant recommendations for boosters.
"We don't feel comfortable with multiple boosters every 8 weeks," said committee chairman Arnold Monto, MD, professor emeritus of public health at the University of Michigan, Ann Arbor. "We'd love to see an annual vaccination similar to influenza but realize that the evolution of the virus will dictate how we respond in terms of additional vaccine doses."
The virus itself will dictate vaccination plans, he said.
The government must also keep its focus on convincing Americans who haven't been vaccinated to join the club, said committee member Henry H. Bernstein, DO, given that "it seems quite obvious that those who are vaccinated do better than those who aren't vaccinated."
The government should clearly communicate to the public the goals of vaccination, he said.
"I would suggest that our overall aim is to prevent severe disease, hospitalization, and death more than just infection prevention," said Dr. Bernstein, professor of pediatrics at Hofstra University, Hempstead, N.Y.
The FDA called the meeting of its advisers to discuss overall booster and vaccine strategy, even though it already authorized a fourth dose of the Pfizer and Moderna vaccines for certain immune compromised adults and for everyone over age 50.
Early in the all-day meeting, temporary committee member James Hildreth, MD, the president of Meharry Medical College, Nashville, Tenn., asked why that authorization was given without the panel's input. Peter Marks, MD, the director of FDA's Center for Biologics Evaluation and Research, said the decision was based on data from the United Kingdom and Israel that suggested immunity from a third shot was already waning.
Dr. Marks later said the fourth dose was "authorized as a stopgap measure until we could get something else in place," because the aim was to protect older Americans who had died at a higher rate than younger individuals.
"I think we're very much on board that we simply can't be boosting people as frequently as we are," said Dr. Marks.
Not enough information to make broader plan
The meeting was meant to be a larger conversation about how to keep pace with the evolving virus and to set up a vaccine selection and development process to better and more quickly respond to changes, such as new variants.
But committee members said they felt stymied by a lack of information. They wanted more data from vaccine manufacturers' clinical trials. And they noted that so far, there's no objective, reliable lab-based measurement of COVID-19 vaccine effectiveness – known as a correlate of immunity. Instead, public health officials have looked at rates of hospitalizations and deaths to measure whether the vaccine is still offering protection.
"The question is, what is insufficient protection?" asked H. Cody Meissner, MD, director of pediatric infectious disease at Tufts Medical Center in Boston. "At what point will we say the vaccine isn't working well enough?"
Centers for Disease Control and Prevention officials presented data showing that a third shot has been more effective than a two-shot regimen in preventing serious disease and death, and that the three shots were significantly more protective than being unvaccinated.
In February, as the Omicron variant continued to rage, unvaccinated Americans aged 5 years and older had an almost three times higher risk of testing positive, and nine times higher risk of dying, compared with those who were considered fully vaccinated, said Heather Scobie, PhD, MPH, a member of the CDC's COVID-19 Emergency Response team.
But only 98 million Americans – about half of those aged 12 years or older – have received a third dose, Dr. Scobie said.
It's also still not clear how much more protection a fourth shot adds, or how long it will last. The committee heard data on a just-published study of a fourth dose of the Pfizer vaccine given to some 600,000 Israelis during the Omicron wave from January to March. The rate of severe COVID-19 was 3.5 times lower in the group that received a fourth dose, compared with those who had gotten only three shots, and protection lasted for at least 12 weeks.
Still, study authors said, any protection against infection itself was "short lived."
Psychotropic med use tied to 'striking' post-COVID dementia risk
Fingers take the fight to COVID-19
Skin reactions to first COVID-19 vaccine don't justify forgoing second dose
Ivermectin doesn't help treat COVID-19, large study finds
More evidence that COVID 'brain fog' is biologically based


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\section{Introduction}

\IEEEPARstart{Z}{ero} Echo Time pulse sequences, otherwise known as Zero TE or ZTE sequences, are designed to capture the weak and fleeting signal emitted by hard biological tissues and solid-state matter in Magnetic Resonance Imaging (MRI) scanners \cite{ZTE1,ZTE2}. ZTE sequences are particularly suitable for ultra-short $T_2$ or $T_2^*$ MRI \cite{Weiger2011}, and have been successfully used for a wide variety of applications \cite{Weiger2019}, including imaging of tendons and bones \cite{Weiger2015,DeMello2020}, teeth \cite{Weiger2012,Algar_n_2020,Gonzalez2021}, myelin \cite{Seifert2017} or lungs \cite{Bae2020}. Two other families of sequences used for MR imaging of short $T_2$ samples are Ultra-short Echo Time (UTE, \cite{UTE1}) and SWeep Imaging with Fourier Transformation (SWIFT, \cite{Idiyatullin2006}). Despite their success, one limitation shared by all three families is that, in their basic forms, they are necessarily 3-dimensional, i.e. it is not possible to produce a 2D image of a pre-selected sample slice.

The capability to selectively excite a given slice in the sample and obtain a 2D image is an essential part of the general MRI toolbox. With slice selection, the overall acquisition time for a single slice can be shortened, and 3D aliasing and ringing artifacts from slice to slice are avoided \cite{BkMcRobbie}. Besides, it can be critical for quantitative MRI, where furthermore slice profile assessment is a concern \cite{Keenan2019}.

Slice selection typically employs a soft radio-frequency (RF) pulse in the presence of a magnetic gradient perpendicular to the desired plane \cite{HOULT197969}. This long excitation stage is incompatible with the short-lived signals from hard tissues. Consequently, sequences for MR imaging of short $T_2$ tissues are inherently volumetric and the only slice selection procedure observed is unintentional and deleterious due to insufficient RF bandwidth to excite the complete Field of View (FoV). Slice selection can be realized with UTE by dividing the RF pulse into two halves, which are imaged sequentially and then merged into a unique signal \cite{Macovski2003}. Unfortunately, this doubles the scan time and the RF half pulses are sensitive to Eddy currents from the fast switching of the slice selecting gradient, making it challenging even with recent advances \cite{FABICH2014116, Stumpf2DUTE}. For ZTE and SWIFT sequences, we are not aware of any prior work illustrating the possibility of slice selection.

In this paper, we demonstrate a technique for slice-selective ZTE of ultra-short $T_2$ species, based on quantum spin-locking techniques in the presence of a linear magnetic gradient field \cite{Wind_1978}. We show that spin-locking is a versatile, robust and well suited complement to ZTE (and potentially other) pulse sequences. During spin-locking, a single-tone RF excitation of amplitude $B_\text{1SL}$ is resonant only with spins in the selected slice, due to the presence of the gradient. This ``locks'' the selected magnetization to the transverse direction, and slows down the signal loss characteristic time from $T_2$ to $T_{1\rho}$ \cite{callaghan}, which can be an order of magnitude longer than $T_2$ for hard tissues (where $T_1\gg T_2$). In the following sections, we show control over the position, shape and thickness of the selected slice, and present 2D and 3D ZTE images of ultra-short $T_2$ samples and hard tissues including cow-bone or teeth. We call the simpler sequence DiSLoP (\textit{Direct Spin-Locked PETRA}), where imaging can take place right after slice selection for moderately short $T_2$ times. Optionally, we can include a preservation pulse \cite{ROMMEL1990264} after spin-locking to safely store the magnetization while the slice and encoding gradients are switched off/on, respectively, allowing for ultra-short $T_2^*$ 2D-MRI. We call this variant PreSLoP (\textit{Preserved Spin-Locked PETRA}), which we find to be clean, immune to Eddy currents, and delivers a higher signal-to-noise ratio (SNR) per unit time than both DiSLoP and PETRA. PETRA stands for Pointwise Encoding Time-reduction with Radial Acquisition and is a well-known ZTE sequence where the unavoidable gap at the center of $k$-space, typical of these acquisitions, is filled in a pointwise fashion \cite{Grodzki2012,Algar_n_2020}.

\begin{figure*}
	\centering
	\includegraphics[width= 2\columnwidth]{pulseseqdiagram}
	\caption{Scheme of proposed protocols for 2D imaging of short $T_{2}$ samples. Left) DiSLoP. Right) PreSLoP. Inset) Rotating frame field vectors. The empty circles in the ADC (analog-to-digital converter) line indicate the dead time before the start of the acquisition, which in turn leads to the gap at the center of $k$-space.}
	\label{fig:pulseseqdiagram}
\end{figure*}

\section{Theory}

\subsection{Spin-locking}
\label{sec:spinlocking}

Spin-locking (SL) was reported in the 1950s by A.\,G.\,Redfield while investigating Nuclear Magnetic Resonance saturation (NMR) in solids \cite{Redfield1955}, applied in the late 1970s as an alternative means of slice selection by R.\,A.\,Wind \emph{et al.} \cite{Wind_1978}, it is now a mainstay in the field of solid-state NMR \cite{BkSchmidt-Rohr}, and is broadly used in MRI for $T_{1\rho}$-weighted imaging \cite{Borthakur}. In the context of this work, its main advantage compared to the usual soft pulse approach for slice selection is that in-slice magnetization is kept aligned (locked) with the resonant RF field. Consequently, the transverse magnetization is lost at a rate defined by $T_{1\rho}$, rather than $T_2$. In general, $T_{1\rho}$ is significantly longer than $T_{2}$ and its dependence on $B_\text{1SL}$ is weak. This enables the detection of short-lived tissues and samples whose signal would have faded away after slice selection by common procedures, where spectrally selective RF pulses are typically $>1$\,ms.

Slice selection through spin-locking works by first applying a gradient $g_\text{SL}$ in the slice direction ($z$ in the inset of  Fig.\,\ref{fig:pulseseqdiagram}), and then a hard $90^{\circ}$ pulse which flips all sample magnetization into the plane transversal to $B_{0}$. Immediately after this, the RF locking field is pulsed on for a time $t_\text{SL}$. This has strength $B_\text{1SL}$, it is phase-shifted by $90^{\circ}$ with respect to the first excitation pulse so that it is aligned with the precessing magnetization direction ($-y$ in Fig.\,\ref{fig:pulseseqdiagram}), and it is resonant with $\gamma \left( B_{0} + g_\text{SL} z_{0} \right)$, with $z_{0}$ the position of the slice to be selected. In the inset of Fig.\,\ref{fig:pulseseqdiagram} we show the situation for $z_0=0$: spins which are close to this plane see only a locking field along $-y$, while off-slice spins mostly see a field $g_\text{SL}\cdot z$ along $z$, with a rather abrupt transition between both regimes. Therefore, off-slice magnetization is both homospoiled by the inhomogeneity created by $g_\text{SL}$ and also dephased by its intrinsic short $T_{2\rho}$ (transverse decay in the rotating frame), while {\it in-slice} magnetization is locked by $B_\text{1SL}$ and decays with the much longer $T_{1\rho}$. The selected slice has an approximate width (see Appendix)
\begin{equation}\label{eq:thickness}
 \Delta z \approx 2B_\text{1SL}/g_\text{SL}.
\end{equation}
The spin-locking time required for the slice to be selected, which we arbitrarily define as having suppressed off-slice magnetization contributions by around 90\,\% in an homogeneous sample, can be roughly estimated as
\begin{equation}\label{eq:time}
	t_\text{SL} \gtrsim \frac{7\pi}{2\Omega_\text{1SL}}\,\text{, where } \Omega_\text{1SL} = \gamma B_\text{1SL} = \gamma g_\text{SL} \Delta z/2,
\end{equation}
with $\gamma$ the gyromagnetic factor ($\approx 2\pi\cdot 42$\,MHz/T for protons). Slice selection can be faster for short $T_{2\rho}$ samples. The detailed equations governing magnetization are derived in the Appendix. All in all, the experimental knobs for slice selection are $g_\text{SL}$, $B_\text{1SL}$ and $t_\text{SL}$. In the rotating frame, the longitudinal relaxation time becomes $T_{1\rho}$, which is given by the spectral density of heat-bath fluctuations at the frequency $\gamma \sqrt{B_\text{1SL}^2+(g_\text{SL} \cdot z)^2}$. Thus the fundamental condition for SL to work is that
\begin{equation}
	T_2^*\ll t_\text{SL}\ll T_{1\rho},
\end{equation}
where $T_2^*$ in this case can be extremely short because it is due to $g_\text{SL}$.

\subsection{Advanced spin-locking}
As in standard slice selection, the shape of the slice achieved with SL is determined by the Fourier Transform of the time envelope of the resonant RF pulse. The diagrams in Fig.\,\ref{fig:pulseseqdiagram} show square pulses, which result in spatial profiles following a sinc funtion. It is sometimes convenient to produce sharp rectangular profiles, e.g. for quantitative MRI, so that off-slice contributions do not contaminate the resulting reconstructions \cite{Josan2009}. Slice selection based on SL also allows for this, using a single-tone field with a sinc modulation envelope. Although we demonstrate the viability of this approach in Fig.\,\ref{fig:SquareSL}, we encounter two disadvantages with respect to square SL pulses: i) a sharp square profile necessitates several sinc lobes, thus lengthening the spin-locking duration, and ii) the modulation of $B_\text{1SL}(t)$ means $T_{1\rho}$ is given by a sampling of the heat-bath spectral function at locking fields lower than $B_\text{1SL}^\text{max}$, thus leading to a shorter `effective' $T_{1\rho}$, which is the crux of the matter. For this reason, we have used unmodulated locking fields in the remaining studies.

A further interesting possibility is multi-slice selection, which can speed up imaging significantly through the simultaneous excitation and readout of multiple slices, either through RF phase encoding, gradient phase encoding or by parallel imaging coil arrays (see \cite{BreuerSMS} for a review). This advantage can be translated to slice selection based on spin-locking by means of a multi-tone excitation resonant with spins at multiple locations. Although we have not explored this experimentally in this work due to hardware limitations, we refer to the Appendix for a more detailed discussion.

\section{Methods}
In the following we present and motivate DiSLoP and PreSLoP (Fig.\,\ref{fig:pulseseqdiagram}), the slice-selective Zero Echo Time pulse sequences we have devised for 2D imaging of short $T_{2}$ samples. All experiments have been performed in a 260\,mT custom-built DentMRI- Gen I system described elsewhere \cite{Algar_n_2020}. Images are reconstructed with Algebraic Reconstruction Techniques (ART)\cite{kaczmarz,Gordon1970}, which do not require density compensation and allow for highly undersampled $k$-space data \cite{Algar_n_2020}. $T_1$ characteristic times have been measured by inversion recovery \cite{Bydder1998} and $T_2$ times by spin-echo \cite{Carr1958,Meiboom1958}, both by fitting single or double exponential functions (see Tab.\,\ref{tab:SampleRelaxationParameters}). Magnetic field inhomogeneities can be shimmed down to the 10\,ppm level with small gradient corrections in the 260\,mT system. This corresponds to $T'_2\sim 10$\,ms, so $T_2$ and $T_2^*$ values are very similar for all samples used  in this work, with the sole exception of ham, since magnetic susceptibilities do not play a significant role. Where given, SNR values are estimated by averaging in three different image regions with and without sample (see Appendix and Fig.\,\ref{fig:ROIs}).

\subsection{DiSLoP: Direct Spin-Locked PETRA}
This sequence is designed for 2D imaging of samples whose $T_2$ are not extremely short, in the order of units of milliseconds. DiSLoP starts with an \textit{excitation block}, where we ramp up the slice selection gradient $g_\text{SL}$ and later transfer the whole sample magnetization to $-y$ with a hard $90^{\circ}_x$ RF pulse, i.e. a pulse that rotates the magnetization by $90^{\circ}$ around the $x$ axis in the frame of reference that revolves at the spin precession frequency. Importantly, this pulses needs to be short and intense enough to span the bandwidth given by $g_\text{SL}$ in the sample volume. Then comes the \textit{spin-locking block}, where we switch on $B_\text{1SL}$ along $-y$ for a time $t_\text{SL}$ long enough to dephase off-slice spins. This time can be estimated from Eq.\,(\ref{eq:time}) or found empirically if the sample consists mostly of short $T_{2\rho}$ components. For a given slice width, slice selection is faster with higher $g_\text{SL}$ values, which in turn requires also higher $B_\text{1SL}$ strength, as seen from Eqs.\,(\ref{eq:thickness}) and (\ref{eq:time}). This is an important criterion if one seeks to retain in-slice signal coherence, which decays as $T_{1\rho}$ during SL. Third comes the \textit{rephasing block}, where we ramp down $g_\text{SL}$ as fast as possible to constrain the $T^{*}_{2}$ decay of in-slice spins. An extra gradient blip - previously calibrated to prevent distortions due to Eddy currents - compensates the in-slice dephasing caused by ramping down $g_\text{SL}$. Finally, in the \textit{acquisition block} we acquire data along radial spokes in $k$-space following the ZTE procedure, i.e. we ramp up a magnetic gradient $g_\text{RO}$ along the readout direction, and we start the acquisition after its onset. Alternatively, one could start acquiring data while ramping up the gradient, as in UTE, but this would have precluded the performance comparisons we present in Sec.\,\ref{sec:Results}.

\subsection{PreSLoP: Preserved Spin-Locked PETRA}
The PreSLoP protocol is similar to DiSLoP, but it is designed to prevent $T_{2}^*$ decay by replacing the rephasing block with a \textit{preservation \& spoiling block} prior to acquisition. This is achieved by a preservation pulse (hard $90^\circ_{-x}$ RF pulse) directly after spin-locking, which places the in-slice magnetization along $z$. In this way we preserve the coherence while we switch off/on the slice/encoding gradients, which is crucial for 2D imaging of tissues with extremely short $T_2$. During this switching, an additional spoiling gradient pulse can be included to remove remaining off-slice coherences, even if we have found this unnecessary in our system. In the acquisition block of PreSLoP, the magnetization can be excited to an arbitrary flip angle $\theta$ and the acquisition starts after the onset of $g_\text{RO}$, as in a standard PETRA sequence. This is an advantage compared to DiSLoP, since the long scan times inherent to PETRA can be partly compensated by using Ernst angle excitations and shortening the repetition time TR \cite{Weiger2011}. For simplicity, however, we have used $\theta=90^\circ$ throughout the paper.

PreSLoP is subject to distortions in the slice profile due to Eddy currents for short repetition times (TR). Inverting the polarity of $g_\text{SL}$ for each radial acquisition mitigates this effect, because the contributions average out to a large extent. All the PreSLoP images in this paper are therefore taken in this way (see Appendix and Fig.\,\ref{fig:polarity}).

\subsection{DiSLoP vs PreSLoP}
DiSLoP is a simpler sequence than PreSLoP and potentially faster because it can be made immune to the finite dead time ($t_{\text{dead}}$) required to switch the electronics from transmission (Tx) to reception (Rx) mode, thus avoiding the Cartesian single-point encoding scheme to fill the $k$-space gap in PETRA. Instead, in DiSLoP one can simply ramp up and down the encoding gradient $g_\text{RO}$ during the rephasing block, so that acquisitions start at $k=0$ and pointwise encoding is unnecessary. Unfortunately, this possibility requires accurate control and calibration of Eddy currents for different values of $g_\text{RO}$ in each repetition, so in the results below we have used the simpler DiSLoP sequence shown in Fig.\,\ref{fig:pulseseqdiagram}, which includes a pointwise-encoding stage.

The main advantage sought with PreSLoP is its (partial) immunity to $T_{2}^*$ decay after the spin-locking block, allowing for much higher SNR images than DiSLoP for hard biological tissues, solid-state matter, and samples with short-lived MR signals in general. To quantify this gain, in the following sections we show images of the same sample with both sequences under conditions as similar as possible.

\subsection{1D and 3D imaging}
DiSLoP and PreSLoP are conceived as 2D imaging sequences where the through-slice spin contribution is integrated in the recorded signals. Nevertheless, we show also images taken with sequence variants where the slice selection gradient is used for encoding as well. In this way, a 3D image of the slice-selected sample is obtained, which can be useful to benchmark the efficiency of the slice selection block. We call these 3D-DiSLoP and 3D-PreSLoP for clarity. We also find it useful to run the 1D versions of our sequences for fast characterization of slice profiles of simple, homogeneous samples (see Figs.\,\ref{fig:SLcontrol}-\ref{fig:ChainPulses} in Sec.\,\ref{sec:Results}).

\section{Results \& analysis}
\label{sec:Results}

\subsection{Control over spin-locking and preservation blocks}\label{sec:control}

\begin{table}[h]
	\caption{Relaxation parameters of employed samples and figures where they have been used.}
	\centering
	\begin{tabular}{c c c c}
		\hline
		Parameter & $T_1$ (ms) & $T_2$ (ms) & Figures \\
		\hline
		York ham  & \SI{289}{ms}  & \SI{18}{ms} & \ref{fig:t1rhosamples} \\
		1\% CuSO$_{4}$ doped water & \SI{16}{ms}  & \SI{7.5}{ms} & \ref{fig:t1rhosamples}  \\
		3\% CuSO$_{4}$ doped water & \SI{3}{ms}  & \SI{2.5}{ms} & \ref{fig:SLcontrol},\ref{fig:SquareSL},\ref{fig:ChainPulses},\ref{fig:t1rhosamples},\ref{fig:3DDiSLoPcontrol}  \\
		Honey & \SI{14.4}{ms}  & \SI{1.5}{ms} & \ref{fig:t1rhosamples},\ref{fig:honeysample}  \\
		Eraser  & \SI{27}{ms}  & \SI{800}{\micro s} & \ref{fig:t1rhosamples}  \\
		Photopolymer resin  & \SI{23.1}{ms}  & \SI{650}{\micro s}  & \ref{fig:t1rhosamples} \\
		Clay  & \SI{36}{ms}  & \SI{550}{\micro s} & \ref{fig:t1rhosamples},\ref{fig:clayphantom}  \\
		Bone  & \SI{7}/\SI{30}{ms}  & 315 / \SI{630}{\micro s} & \ref{fig:t1rhosamples},\ref{fig:bone}  \\
		Teeth  & \SI{3}/\SI{29}{ms}  & \SI{275}{\micro s} / \SI{6}{ms} & \ref{fig:t1rhosamples},\ref{fig:horsetooth}  \\
		\hline
	\end{tabular}
	\label{tab:SampleRelaxationParameters}
\end{table}

\begin{figure*}[t]
	\includegraphics[width= 2\columnwidth]{SpinlockingControl}
	\caption{Control over the spin-locking block with 1D-DiSLoP and a PLA (polylactic acid) cuboid container filled with 3\,\% CuSO$_{4}$ doped water. a) Slice profile as a function of $t_\text{SL}$ ($B_\text{1SL} \approx \SI{90}{\micro T}$, $g_\text{SL} \approx 60$\,mT/m). b) Slice thickness as a function of $B_\text{1SL}$ ($t_\text{SL}= \SI{900}{\micro s}$, $g_\text{SL} \approx 60$\,mT/m). c) Slice position as a function of Larmor detuning ($B_\text{1SL} \approx \SI{90}{\micro T}$, $g_\text{SL} \approx 60$\,mT/m, $t_\text{SL}= \SI{900}{\micro s}$).}
	\label{fig:SLcontrol}
\end{figure*}

In this section we first demonstrate experimental control over the slice selection process with 1D-DiSLoP and a cuboid container filled with 3\,\% CuSO$_{4}$ doped water ($T_1$ and $T_2$ in Tab.\,\ref{tab:SampleRelaxationParameters}). The hard $90^\circ$ RF pulses are typically \SI{10}{\micro s} long with an amplitude $\approx \SI{550}{\micro T}$. We focus initially on the \emph{spin-locking time} required for slice selection. Here, after the slice selection block, we use a rephasing block and then lift an encoding gradient in the direction of slice selection. In Fig.\,\ref{fig:SLcontrol}a we show the resulting 1D profiles after different SL times, and observe that slice selection is practically achieved for $t_\text{SL} \gtrsim \SI{500}{\micro s}$ with $B_\text{1SL}\approx\SI{90}{\micro T}$ and $g_\text{SL}\approx 60$\,mT/m, for $\Delta z \approx 3$\,mm. From Eq.\,(\ref{eq:time}) we would expect the SL procedure to need $\approx \SI{460}{\micro s}$. We have observed that the estimation in Eq.\,(\ref{eq:time}) suffices in the general case, even if for \textit{ex vivo} hard biological tissues we have used shorter times because their short $T_{2\rho}$ values speed up slice selection. In this sense we found it useful to reproduce Fig.\,\ref{fig:SLcontrol}a for each type of sample, to find the shortest $t_\text{SL}$ in each case, but always checking the image obtained by 3D-PreSLoP for correct slice selection.

To demonstrate control over the \emph{slice thickness} with 1D-DiSLoP, we fix $t_\text{SL}= \SI{900}{\micro s}$ and $g_\text{SL} \approx 60$\,mT/m and use multiple spin-locking field amplitudes ($B_\text{1SL} \approx 30,\, 60,\, 90,\, \SI{120}{\micro T}$, corresponding to slice thicknesses $\Delta z \approx 1,\,2,\,3,\,4$\,mm, see Fig.\,\ref{fig:SLcontrol}b). Since the slice-selected magnetization follows a Lorentzian profile (see Appendix), the off-slice contribution is more notable for higher $\Delta z$. Therefore, square SL pulses are more convenient for thinner slices, and thicker slices may require sinc-modulated pulses. The profile asymmetries observed are compatible with a decaying drift of $B_0$ caused by Eddy currents. We have observed these in many other scenarios and for the images presented in this paper we suppress their effect substantially with interleaved data acquisition, where each radial spoke uses a different $g_\text{SL}$ polarity.

Finally, to show control over the \emph{slice position}, we set $B_\text{1SL} \approx  \SI{90}{\micro T}$, $g_\text{SL} \approx 60$\,mT/m and $t_\text{SL}= \SI{900}{\micro s}$ ($\Delta z \approx 3$\,mm), and we detune the SL frequency by $\Delta f=-25.5$, 0 and 25.5\,kHz from the Larmor frequency at the gradient isocenter, shifting the selected slice to $z_0 \approx -10$, 0 and 10\,mm respectively.

\begin{figure}
	\centering
	\includegraphics[width=1\columnwidth]{SquareSpinLocking}
	\caption{Comparison between square (green) and sinc-modulated spin-locking (red) and sinc-modulated standard slice selection (black) for the same 3\,\% CuSO$_{4}$ doped water sample as in Fig.\,\ref{fig:SLcontrol}. We have normalized all curves to the same height for ease of comparison (see text).}
	\label{fig:SquareSL}
\end{figure}

Next we investigate the performance of square and sinc-modulated SL pulses and the slice profiles they produce (Fig.\,\ref{fig:SquareSL}). For this we use the same sample and experimental parameters as in Fig.\,\ref{fig:SLcontrol}c. Because its $T_2$ is not extremely short (see Tab.\,\ref{tab:SampleRelaxationParameters}), we could slice-select also by means of a standard sinc-modulated excitation using gradient echo encoding (i.e. without spin-locking), with the shortest echo time possible in our setup. Both sinc functions have five lobes in total. We observe similar profile transitions for both sinc-modulated experiments, and a peaked profile for spin-locking without modulation, with longer tails, as expected. We have normalized the profiles in Fig.\,\ref{fig:SquareSL} to the same peak values for visual aid. However, the standard gradient echo acquisition has a lower signal than the constant SL curve by a factor of 1.5, since the magnetization is lost at a rate given by $T_2^*$ instead of $T_{1\rho}$. The signal is even lower with sinc-modulated SL (factor of 3.2), due to the longer SL pulse duration and the shorter effective $T_{1\rho}$.

\begin{figure}
	\centering
	\includegraphics[width=1\columnwidth]{ChainPulses}
	\caption{Profile of the transverse magnetization after each stage in PreSLoP for the same 3\,\% CuSO$_{4}$ doped water sample as in Figs.\,\ref{fig:SLcontrol} and \ref{fig:SquareSL}, with $\Delta z \approx2$\,mm: after initial $90^\circ_x$ excitation (black), after spin-locking (red), after $90^\circ_{-x}$ storage pulse (green), and after final $90^\circ_x$ excitation (dashed blue). In the last case, there is a delay $\tau=\SI{200}{\micro s}$ where gradients are ramped between the $90^\circ_{-x}$ and $90^\circ_{x}$ pulses. We have used $B_\text{1SL} \approx \SI{60}{\micro T}$, $g_\text{SL} \approx 60$\,mT/m, $t_\text{SL}=1$\,ms. The full (black) curve is not flatter due to capillarity effects and bubble formation in the small PLA container.}
	\label{fig:ChainPulses}
\end{figure}

Having characterized our control with DiSLoP, we now move to PreSLoP. Figure\,\ref{fig:ChainPulses} shows the evolution of the 1D sample profile (3\,\% CuSO$_{4}$ solution) along the sequence: after the initial $90^\circ$ excitation, after spin-locking, after the preservation pulse (-$90^\circ$) and after the final excitation pulse (prior to image encoding). For each of these stages we 1D-encode the transverse magnetization after the chosen set of steps. We have used $B_\text{1SL} \approx \SI{60}{\micro T}$, $g_\text{SL} \approx 60$\,mT/m, $t_\text{SL}=1$\,ms and $\Delta z\approx 2$\,mm. After the preservation pulse, only off-slice magnetization is observed, since in-slice magnetization has been stored along $z$ and its transverse component is negligible. The profiles after preservation and in the final stage are asymmetric presumably due to drifting Eddy currents, as in Fig.\,\ref{fig:SLcontrol}b.

Finally, we have measured the dependence of $T_{1\rho}$ on the SL amplitude $(B_\text{1SL})$ for the samples used throughout this work (Fig.\,\ref{fig:t1rhosamples}). The main value of these measurements is that it is hard to predict $T_{1\rho}$ based on any hard/soft material distinction, and the $B_\text{1SL}$ strength that saturates $T_{1\rho}$. Thus, we found it useful to carry out these measurements before imaging a new sample to optimize the DiSLoP and PreSLoP sequence parameters. Every data point in Fig.\,\ref{fig:t1rhosamples} is determined from sequences consisting only of the excitation and spin-locking blocks, where we sweep the duration $t_\text{SL}$ of the latter. For every value of $t_\text{SL}$, we use a single data point\footnote{In fact, we read in a complete free induction decay curve after each SL pulse and we select a data point around 1\,ms after the beginning of the acquisition. In this way we ensure that ringing in the RF Tx line due to the prolonged SL pulses has faded away.}, and we fit an exponential model to determine $T_{1\rho}$ from the data set for a given $B_\text{1SL}$. This procedure is repeated for all the $B_\text{1SL}$ values in the plot, where the lines are included merely to guide the eye. As expected, for low $B_\text{1SL}$ the decay in the SL rotating frame $T_{1\rho}$ tends to $T_2^*$. For higher $B_\text{1SL}$ it can increase to a significant fraction of $T_1$, which is one of the key advantages of the proposed slice selection method. We observe $T_{1\rho}< T_1$ in all samples except for bone, consistent with expectations ($T_{1\rho}$ cannot get much longer than $T_1$ for soft tissues, see \cite{Kelly1992}). Also, note that there are two $T_1$ and $T_2$ values for bone and dental samples in Tab.\,\ref{tab:SampleRelaxationParameters}, because they consist of two types of tissues, but we only show the average $T_{1\rho}(B_\text{1SL})$ curve in Fig.\,\ref{fig:t1rhosamples} to lighten the plot. Nevertheless, for the bone and dental images in Figs.\,\ref{fig:bone} and \ref{fig:horsetooth}, we give both $T_{1\rho}$ values for each sample at the corresponding $B_\text{1SL}$.

\begin{figure}
	\centering
	\includegraphics[width=1\columnwidth]{t1rho}
	\caption{$T_{1\rho}$ as a function of the applied locking RF field $B_\text{1SL}$ for the samples employed throughout this work. $T_{1\rho}$ values associated to $B_\text{1SL}=0$ correspond to $T^{*}_{2}$, virtually the same as the $T_2$ values reported in Tab.\,\ref{tab:SampleRelaxationParameters} except for ham. The lines simply connect the data points and are there only for readability.}
	\label{fig:t1rhosamples}
\end{figure}

\subsection{DiSLoP and PreSLoP for structured phantoms}
\label{sec:phantoms}

\begin{figure*}
	\centering
	\includegraphics[width=1.8\columnwidth]{3DDiSLoPcontrol}
	\caption{Control over slice selection for two PLA structured phantoms filled with 3\% CuSO$_{4}$ doped water. Leftmost images correspond to PETRA, while the rest are obtained with 3D-DiSLoP, with a) slice positions $z=-8$, -4.5, 0, 4.5 and 8 mm, and b) slice thicknesses $\Delta z=$1, 2, 3, 4 mm.}
	\label{fig:3DDiSLoPcontrol}
\end{figure*}

In this section we test the imaging capabilities of DiSLoP and PreSLoP with short and ultra-short $T_{2}$ samples in structured (rather than homogeneous) phantoms. To demonstrate control over the \emph{slice position}, the phantom in Fig.\,\ref{fig:3DDiSLoPcontrol}a was filled with 3\,\% CuSO$_{4}$ doped water ($T_2\approx 2.5$\,ms). The top row includes the $y=0$ slice from a 3D-PETRA acquisition (top left), followed by 3D-DiSLoP reconstructions where slice selection is along the $z$ direction, namely at $z=-8$, -4.5, 0, 4.5 and 8\,mm (corresponding to detunings of -20.4, -11.5, 0, 11.5, 20.4\,kHz with respect to the bare Larmor frequency). Here we use $B_\text{1SL} \approx \SI{90}{\micro T}$, $g_\text{SL}\approx 60$\,mT/m, $t_\text{SL} = \SI{800}{\micro s}$ and $\Delta z \approx 3$\,mm. To show control over the \emph{slice thickness} (Fig.\,\ref{fig:3DDiSLoPcontrol}b) we use a different phantom, but also filled with 3\,\% CuSO$_{4}$ doped water. The sequence parameters in this case are: $g_\text{SL}\approx 60$\,mT/m and $t_\text{SL} = \SI{1}{ms}$, with $B_\text{1SL}$ values ranging from 1\,mm (\SI{30}{\micro T}) to 4\,mm (\SI{120}{\micro T}) in steps of 1\,mm. As expected, the Lorentzian spatial profile (consequence of square SL pulses) becomes more evident for thicker slices. From this perspective, thinner slices are preferable as long as the SNR suffices. For this reason, we have tried to balance slice thickness and scan durations, so all the images presented in Secs.\,\ref{sec:phantoms} and \ref{sec:biologicaltissues} have a fixed slice thickness of $\approx 3$\,mm.

\begin{figure}
	\centering
	\includegraphics[width=1\columnwidth]{honeysample}
	\caption{Performance of DiSLoP and PreSLoP for a short $T_2$ sample (honey). a) CAD image of the PLA holder for the honey. b) 3D reconstructions with PETRA (left) and 3D-PreSLoP (right), where the slice selection effect becomes evident. c) 2D images with PETRA (left) with slice resolution $\approx3$\,mm, and PreSLoP (middle) and DiSLoP (right) with $\Delta z\approx3$\,mm.}
	\label{fig:honeysample}
\end{figure}

\begin{figure}
	\centering
	\includegraphics[width=1\columnwidth]{clayphantom}
	\caption{Performance of DiSLoP and PreSLoP for an ultra-short $T_2$ sample (clay). a) Image of the sample. b) 3D reconstructions with PETRA (left) and 3D-PreSLoP (right), where the slice selection effect becomes evident. c) 2D images with PETRA (left) with slice resolution $\approx3$\,mm, and PreSLoP (middle) and DiSLoP (right) with $\Delta z\approx3$\,mm.}
	\label{fig:clayphantom}
\end{figure}

Next we test the performance of DiSLoP and PreSLoP as compared to standard PETRA for short and ultra-short $T_{2}^*$ 2D MRI. From this point on, we plot PETRA vs 3D-PreSLoP in the upper row, and 2D images in the lower row, with PETRA on the left, 2D-PreSLoP in the middle and 2D-DiSLoP on the right.

In Figs.\,\ref{fig:honeysample} and \ref{fig:clayphantom} we have used, respectively, a PLA 3D-printed phantom filled with honey ($T_2\approx1.5$\,ms), and a phantom made of modeling clay ($T_2 \approx \SI{550}{\micro s}$). We have gathered all sequence parameters in Tab.\,\ref{tab:imageParameters} for quick reference. Figure\,\ref{fig:honeysample}(b) shows 3D reconstruction of the honey sample from a standard PETRA sequence (left, where the full sample is excited), and 3D DiSLoP (right, where the central slice has been selected with SL). In Fig.\,\ref{fig:honeysample}c) we compare 2D images of the central slice ($z=0$, $\Delta z\approx 3$\,mm): left) 3D PETRA sequence, middle) 2D-PreSLoP and right) 2D-DiSLoP (with gradient ramps of \SI{100}{\micro s}, so data acquisition starts \SI{400}{\micro s} after phase locking). Both DiSLoP and PreSLoP are capable of obtaining enough SNR to distinguish the internal phantom structures. The PreSLoP image is slightly contaminated due to imperfections in the storage and reexcitation pulses. Also, DiSLoP reveals slight shape distorsions probably due to Eddy currents created by the fast gradient transitions in the rephasing block. To avoid this, the DiSLoP acquisition could start much later, but this would lead to an increased $T_2^*$ decay. The SNR in the DiSLoP image is much lower than that of PreSLoP, since DiSLoP is subject to $T_2^*$ decay during gradient switching. On the other hand, the PETRA image has twice as much SNR as PreSLoP, due to the increased scan time $t_\text{scan}$ (i.e. averaging). To double the SNR with PreSLoP we would require $t_{\text{scan}}\approx 20$\,min ($\times 1.5$ faster than PETRA). In Sec.\,\ref{sec:discussion} we discuss in detail the expected performance of PETRA, DiSLoP and PreSLoP in terms of $t_\text{scan}$ and SNR.

\begin{table*}[t]
	\centering
	\caption{Image acquisition parameters. ``NA'' and ``NR'' stand for ``not applicable'' and ``not relevant'' respectively.}
	\label{tab:imageParameters}
	\resizebox{\textwidth}{!}{
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Image        & Sequence & \begin{tabular}[c]{@{}c@{}}spin-locking\\ parameters \\ \{$B_\text{1SL}$, $g_\text{SL}$, $t_\text{SL}$\} \\ \{$\mu$T, mT/m, $\mu$s\} \end{tabular} & \begin{tabular}[c]{@{}c@{}}Nyquist \\ undersampling\end{tabular} & \begin{tabular}[c]{@{}c@{}}FOV\\ (mm$^3$)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Pixel \\ size\\ (mm$^3$)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Dead\\ time (us) /\\ Acquisition\\ time (us)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Bandwidth\\ (kHz)\end{tabular} & \begin{tabular}[c]{@{}c@{}}TR\\ (ms)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Radial\\ spokes \end{tabular} & \begin{tabular}[c]{@{}c@{}}Single\\ points\end{tabular} & Averages & \begin{tabular}[c]{@{}c@{}}Scan\\ time\\ (min)\end{tabular} & \begin{tabular}[c]{@{}c@{}}SNR \end{tabular} \\ \hline

Fig.\ref{fig:honeysample}(b)Left    & PETRA    & NA                                                      & 2                                                         & 28$\times$36$\times$28                             & 0.5$\times$0.5$\times$1                            & 85 / 1000               &36                                                              &  75                                                & 3276                                                   & 56                                                     & 10    & 41.65   & NR
                                                       \\ \hline
Fig.\ref{fig:honeysample}(b)Right   & 3D-DiSLoP    & \{60, 40, 750 \}                                                       & 2                                                         & 28$\times$36$\times$28                             & 0.5$\times$0.5$\times$1                            & NA / 1000               &36                                                              &  75                                                & 3276                                                   & 16                                                     & 10    & 41.15    & NR
                                                        \\ \hline
Fig.\ref{fig:honeysample}(c)Left  & PETRA    & NA                                                       & 2                                                         & 28$\times$36$\times$30                             & 0.5$\times$0.5$\times$3                            & 85 / 1000               &36                                                              &  75                                                & 1222                                                   & 0                                                    & 20   & 30.55    & 18.7
                                                       \\ \hline
Fig.\ref{fig:honeysample}(c)Middle   & 2D-PreSLoP    & \{60, 40, 750 \}                                                       & 2                                                        & 28$\times$36                             & 0.5$\times$0.5$\times$3                            & 85 / 1000               &36                                                              &  75                                                & 160                                                   & 36                                                    & 20   & 4.90     & 9.3
                                                       \\ \hline
Fig.\ref{fig:honeysample}(c)Right    & 2D-DiSLoP    & \{60, 40, 750 \}                                                       & 2                                                        & 28$\times$36                             & 0.5$\times$0.5$\times$3                            & NA / 1000               &36                                                              &  75                                                & 160                                                   & 12                                                    & 20   & 4.30      & 4.2                                                        \\ \noalign{\hrule height 2pt}

Fig.\ref{fig:clayphantom}(b)Left    & PETRA    & NA                                                      & 8                                                         & 40$\times$30$\times$30                             & 0.5$\times$0.5$\times$0.5                            & 80 / 750               &53.3                                                              &  50                                                & 1926                                                   & 312                                                     & 25    & 46.61     & NR                                                        \\ \hline

Fig.\ref{fig:clayphantom}(b)Right    & 3D-PreSLoP    & \{90, 60, 600 \}                                                       & 8                                                         & 40$\times$30$\times$30                             & 0.5$\times$0.5$\times$0.5                            & 80 / 750               &53.3                                                              &  50                                                & 1926                                                   & 312                                                     & 25    & 46.61    & NR                                                         \\ \hline

Fig.\ref{fig:clayphantom}(c)Left    & PETRA    & NA                                                      & 2                                                         & 40$\times$30$\times$30                             & 0.5$\times$0.5$\times$3                            & 90 / 600               &66.6                                                              &  120                                                & 1358                                                   & 128                                                     & 20    & 59.40    & 6.3                                                      \\ \hline

Fig.\ref{fig:clayphantom}(c)Middle    & 2D-PreSLoP    & \{90, 60, 600 \}                                                      & 2                                                         & 40$\times$30                             & 0.5$\times$0.5$\times$3                            & 90 / 600               &66.6                                                              &  120                                                & 178                                                   & 112                                                     & 20    & 11.60    & 3.3                                                          \\ \hline

Fig.\ref{fig:clayphantom}(c)Right    & 2D-DiSLoP    & \{90, 60, 600 \}                                                       & 2                                                         & 40$\times$30                             & 0.5$\times$0.5$\times$3                            & NA / 600               &66.6                                                              &  120                                                & 178                                                   & 36                                                     & 20    & 8.50      & 1.8
                                                    \\ \noalign{\hrule height 2pt}

Fig.\ref{fig:bone}(b)Left    & PETRA    & NA                                                      & 8                                                         & 46$\times$34$\times$30                             & 1$\times$1$\times$1                            & 80 / 600               &38.3                                                              &  75                                                & 572                                                   & 96                                                     & 25    & 20.88     & NR                                                        \\ \hline

Fig.\ref{fig:bone}(b)Right    & 3D-PreSLoP    & \{150, 100, 100 \}                                                       & 8                                                         & 46$\times$34$\times$30                             & 1$\times$1$\times$1                            & 80 / 600               &38.3                                                              &  75                                                & 572                                                   & 96                                                     & 25    & 20.88     & NR                                                        \\ \hline

Fig.\ref{fig:bone}(c)Left    & PETRA    & NA                                                       & 2                                                         & 46$\times$34$\times$30                             & 0.5$\times$0.5$\times$3                            & 90 / 600               &76.6                                                              &  75                                                & 1556                                                   & 152                                                     & 15    & 32.03      & 3.8                                                         \\ \hline

Fig.\ref{fig:bone}(c)Middle    & 2D-PreSLoP    & \{150, 100, 100 \}                                                       & 2                                                         & 46$\times$34                             & 0.5$\times$0.5$\times$3                            & 90 / 600               &76.6                                                              &  75                                                & 204                                                   & 136                                                     & 15    & 6.34      & 3.6                                                         \\ \hline

Fig.\ref{fig:bone}(c)Right    & 2D-DiSLoP    & \{150, 100, 100 \}                                                       & 2                                                         & 46$\times$34                             & 0.5$\times$0.5$\times$3                            & NA / 600               &76.6                                                              &  75                                                & 204                                                   & 44                                                     & 15    & 4.65      & 1.0                                                         \\ \noalign{\hrule height 2pt}

Fig.\ref{fig:horsetooth}(b)Left    & PETRA    & NA                                                      & 8                                                         & 38$\times$90$\times$21                             & 1$\times$1$\times$1                            & 110 / 600               &75                                                              &  25                                                & 764                                                   & 288                                                     & 375    & 164.37      & NR                                                       \\ \hline

Fig.\ref{fig:horsetooth}(b)Right    & 3D-PreSLoP    & \{90, 60, 190 \}                                                       & 8                                                         & 38$\times$90$\times$21                             & 1$\times$1$\times$1                            & 110 / 600               &75                                                              &  25                                                & 764                                                   & 288                                                     & 375    & 164.37     & NR                                                        \\ \hline

Fig.\ref{fig:horsetooth}(c)Left    & PETRA    & NA                                                       & 2                                                         & 38$\times$90$\times$21                             & 1$\times$1$\times$3                            & 110 / 600               &75                                                              &  25                                                & 1010                                                   & 112                                                     & 150    & 70.12     & 6.2                                                          \\ \hline

Fig.\ref{fig:horsetooth}(c)Middle    & 2D-PreSLoP    & \{90, 60, 190 \}                                                       & 2                                                         & 38$\times$90                             & 1$\times$1$\times$3                            & 110 / 600               &75                                                              &  25                                                & 200                                                   & 112                                                     & 150    & 19.37     & 4.7                                                          \\ \hline

Fig.\ref{fig:horsetooth}(c)Right    & 2D-DiSLoP    & \{90, 60, 190 \}                                                       & 2                                                         & 38$\times$90                             & 1$\times$1$\times$3                            & NA / 600               &75                                                              &  25                                                & 200                                                   & 24                                                     & 150    & 14.00      & 1.2                                                         \\ \noalign{\hrule height 2pt}
\end{tabular}}
\end{table*}

We have followed the exact same procedure to analyze the clay phantom reconstructions. The clay used exhibits an ultra-short $T_2 \approx \SI{550}{\micro s}$. In Fig.\,\ref{fig:clayphantom} we now observe a significantly lower SNR in DiSLoP than in PreSLoP, even for similar $t_{\text{scan}}$ (see Tab.\,\ref{tab:imageParameters}). Note that DiSLoP would need $\times 2.5$ averages (i.e. $\approx 21$\,min) to reach the SNR in the PreSLoP reconstruction. Similarly, to obtain an SNR$=6.33$ (that of PETRA) for PreSLoP we would need $t_{\text{scan}}\approx 44$\,min ($\times 1.36$ faster than PETRA).

\subsection{Hard biological tissues}
\label{sec:biologicaltissues}

\begin{figure}[h!]
	\centering
	\includegraphics[width=1\columnwidth]{bone}
	\caption{Performance of DiSLoP and PreSLoP for an ultra-short $T_2$ biological tissue (cortical bone). a) Photograph of bovine femur sample. b) 3D PETRA (left) and 3D-PreSLoP (right). c) 2D images for PETRA (left) with slice resolution $\approx 3$\,mm, PreSLoP (middle) and DiSLoP (right) with $\Delta z\approx 3$\,mm. We provide $T_{1\rho}$ for both tissues, and the average $T_1$ and $T_2$ values (see Tab.\,\ref{tab:SampleRelaxationParameters}).}
	\label{fig:bone}
\end{figure}

\begin{figure}[h!]
	\centering
	\includegraphics[width=0.85\columnwidth]{horse}
	\caption{Performance of DiSLoP and PreSLoP for an ultra-short $T_2$ biological tissue (horse tooth). a) Photograph of the sample. b) 3D PETRA (left) and 3D-PreSLoP (right). c) 2D images for PETRA (left) with slice resolution $\approx 3$\,mm, PreSLoP (middle) and DiSLoP (right) with $\Delta z \approx 3$\,mm. We provide $T_{1\rho}$ for both tissues, and the average $T_1$ and $T_2$ values (see Tab.\,\ref{tab:SampleRelaxationParameters}).}
	\label{fig:horsetooth}
\end{figure}

Finally, following the same procedure as in previous figures, we present images of \textit{ex vivo} hard biological tissues obtained with DiSLoP and PreSLoP and compare them with PETRA in terms of SNR and scan time for the same slice and in-plane resolution.

The images in Fig.\,\ref{fig:bone} are from a piece of cortical bone from a bovine femur ($T_2 \approx \SI{440}{\micro s}$), obtained from a local butcher and stripped off of the surrounding soft tissues. Figure\,\ref{fig:bone}b shows 3D reconstructions using both a standard PETRA sequence, where the full sample is excited and imaged, and 3D-PreSLoP. Details on the sequence parameters are provided in Tab.\,\ref{tab:imageParameters}. Given the ultra-short $T_{2}$ values in the sample, PreSLoP performs significantly better than DiSLoP, where the resulting image is dominated by noise despite a very short rephasing block of only \SI{400}{\micro s}. Regarding SNR, PreSLoP and PETRA yield very similar results, but the acquisition with the former is $\times 5$ faster.

Next, we show results for the shortest $T_2$ sample used in this work: an \textit{ex vivo} horse tooth stripped off of soft tissues and dehydrated to remove water residues in internal cavities. The average $T_2$ for this sample is only around \SI{260}{\micro s}. Again, DiSLoP fails to form an image showing the hardest tissues. Only the lower part of the tooth, which is significantly softer ($T_2 \approx 6$\,ms), is visible. For a similar scan time PreSLoP shows a much better image. In order to reach the SNR of the PETRA acquisition, PreSLoP would need $\approx 35$\,min, i.e. a factor $\times 2$ faster than PETRA.

\section{Discussion}
\label{sec:discussion}
From the images in Figs.\,\ref{fig:honeysample}-\ref{fig:horsetooth} we conclude that PreSLoP allows for slice-selective ZTE of ultra-short $T_2$ samples, which was the main goal of this work. Admittedly, there is some contamination in the PreSLoP reconstruction of the honey sample (Fig.\,\ref{fig:honeysample}), but this should be solvable with improved RF hardware (see Sec.\,\ref{sec:control}). DiSLoP performs reasonably well with samples where the measured $T_2$ is $\gtrsim 1$\,ms, but otherwise fails. This highlights the critical importance of the preservation block for hard biological tissues and solid-state matter.

The devised sequences can be modified in at least two ways: i) for 2D-DiSLoP the encoding gradient can be ramped up during the rephasing block (with an inverted triangle as shown for the slice selection gradient) so that acquisitions start at $k=0$, thus eliminating the dead time (i.e. the $k$-space gap) for this sequence, given that Eddy currents can be calibrated for each amplitude of the encoding gradient; and ii) the final spin excitation (flip angle $\theta$) in 2D-PreSLoP could be pulsed before/during the encoding gradient ramp-up, as in UTE, even if this would involve a $T_2^*$ signal loss which could be intolerable for some applications.

All in all, the fact that the efficiency of each sequence depends on detailed experimental parameters (see below) and on the sample properties ($T_{1\rho}$ and $T_2$) leaves much room for sequence optimization for specific application, and shall be further explored as required.

\subsection{Efficiency comparison}

\begin{figure}[h!]
	\centering
	\includegraphics[width=1\columnwidth]{kSpacesvert}
	\caption{Zoom into the central region of $k$-space of the cow bone images presented in Fig.\,\ref{fig:bone}. a) PETRA. b) PreSLoP.}
	\label{fig:kSpaces}
\end{figure}

Here we discuss the advantage of PreSLoP with respect to DiSLoP and PETRA in terms of SNR efficiency and scan time. The underlying reasons are rather subtle and parameter-dependent, but some insight can be gained by comparing the three sampling schemes in $k$-space. Two important concepts in this regard are: i) scan time in these sequences is dominated by the number of pointwise acquisitions (radial spoke acquisitions cover many $k$-space points in a single TR); and ii) the largest contribution to the reconstruction SNR comes from the central region of $k$-space.

For illustration purposes, in Fig.\,\ref{fig:kSpaces} we plot $k$-space positions (not values) for the PETRA and 2D-PreSLoP sequences used to image the bovine femur (Fig.\,\ref{fig:bone}), highlighting the pointwise encoding regions (larger black/blue points). A priori, one may expect that the number of pointwise acquisitions in PETRA must be much larger than in 2D-PreSLoP, since the gap in the former is spherical and only a 2D surface in the latter. However, for the chosen slice direction, dead time and resolution, our PETRA implementation (for an even number of slices) requires pointwise sampling only at $k_z=\pm \delta k_z/2$. Consequently, the amount of pointwise acquisitions is similar for PETRA and 2D-PreSLoP (152 vs 136, see Tab.\,\ref{tab:imageParameters}). A slightly different configuration may have required three pointwise planes for PETRA, and 2D-PreSLoP would have scaled even more favorably.

Compared to 2D-PreSLoP, 2D-DiSLoP requires significantly fewer points for a similar scan time (136 vs 40). This is because the $k$-space gap in DiSLoP is smaller, since the readout gradient starts to ramp when the magnetization is already transversal, whereas it is already at its full strength during the final excitation pulse in PreSLoP.

In terms of SNR, 2D-DiSLoP always suffers $T_2^*$ decay, and it is to be expected that it performs worse than 2D-PreSLoP for the same scan time. The comparison with PETRA is less straight-forward. For instance, the SNRs of the bovine images are very similar, but PETRA takes $\times 5$ longer than 2D-PreSLoP. As mentioned above, the SNR has a heavy bias towards the number of central points in $k$-space, and the pointwise acquisitions are comparable (152 for PETRA vs 136 for 2D-PreSLoP). Hence, a PETRA sequence will need to fill a 3D $k$-space with many radial spokes, while a 2D-PreSLoP sequence will only fill a 2D $k$-space (1556 vs 204 spokes). This explains why 15 averages of PETRA and 2D-PreSLoP yield similar SNR values, but PETRA takes much longer.

To sum up, it is difficult to predict the efficiency of the different sequences for specific cases, but two rule-of-thumb guidelines could be: i) for samples with longer $T_2$ one might prefer DiSLoP to PreSLoP because the former requires a smaller pointwise region (which can be even completely avoided if Eddy currents are under control), and the contrary applies for ultra-short $T_2$ samples; and ii) 2D-PreSLoP should yield a higher SNR than PETRA per unit scan time, because PreSLoP has a 2D scaling for the pointwise region, and because PETRA's 3D filling of non-central $k$-space contributes much less to the SNR.

\subsection{Outlook}

In addition to the discussed advantages as compared to standard PETRA, the proposed 2D imaging protocols feature also several benefits with respect to the double half-pulse RF excitation for slice selection with UTE \cite{FABICH2014116}. First, our protocols are robust against Eddy currents because one can wait for gradients to stabilize and then fire the RF pulses. Second, they are faster by construction, since they do not require two acquisitions for every $k$-space line. Third, signal decay during slice selection with DiSLoP and PreSLoP is subject to $T_{1\rho}\gg T_2^*$, and thus easier to deal with than with 2D-UTE in terms of timing and hardware. For instance, well-defined rectangular slice profiles are easier to attain with SL than with a standard sinc-modulated pulse, where most SNR can get loss in the process. Finally, slice selection by SL, both with and without preservation pulse, is compatible with UTE approaches.

\begin{figure}[h]
	\centering
	\includegraphics[width=1\columnwidth]{chase}
	\caption{Possible embodiment of PreSLoP where the preservation block includes a CHASE pulse train of length 5, allowing for zero dead time before data acquisition.}
	\label{fig:CHASE}
\end{figure}

We have devised also a possible alternative to the preservation block shown in Fig.\,\ref{fig:pulseseqdiagram}, based on a CHASE-5 sequence \cite{Waeber2019}. This is shown in Fig.\,\ref{fig:CHASE} and is basically a modification of the well-known WAHUHA sequence\cite{WAHUHA} with a 180$^{\circ}$ rephasing pulse in the middle. This sequence is able to undo dephasing caused by both homogeneous (spin-spin interactions) and inhomogeneous (gradient) sources. In our case, it can be used to avoid $T_2^*$ decay during the preservation block, while the dephasing caused by ramping gradients is compensated with the waveforms shown in the figure. Note that the latter compensation does not need opposite polarity because CHASE-5's central 180$^{\circ}$ changes the effective sign of spin evolution. Because this sequence compensates gradient evolution too, the acquisition could start at $k=0$, thus eliminating the dead time central gap in $k$-space and therefore the need of pointwise encoding. This would lead to a reduced scan time at the expense of more complicated RF pulse trains and potentially increased SAR (specific absorption rate) \cite{IEC2010}.

\section{Conclusion}
\label{sec:concl}
We have presented two protocols that combine slice selection through spin-locking with Zero Time Echo 2D imaging. DiSLoP is especially suited to moderately short $T_2$ tissues (in the order of few milliseconds), and has the advantage that it can avoid TxRx switching dead time. However, for sub-millisecond $T_2$ tissues, we have presented PreSLoP, which adds a preservation pulse and is capable of 2D imaging the hardest tissues in the body: bone and teeth. PreSLoP suffers from dead time, and thus leaves a central $k$-space gap that has to be filled by Cartesian pointwise encoding, as in standard PETRA, but has a favorable SNR and 2D scaling, which can lead to significant scan time reduction. All in all, we have shown sequences that can combine superior slice selection (which suffers from $T_{1\rho}\gg T_2$ decay) with the most efficient imaging sequence available for ultra-short $T_2$ samples (ZTE) and which have enabled 2D imaging of {\it ex vivo} bone and teeth.

\section{Contributions}

Experiments were performed by JB, with analysis of experimental data by JB, JMA, FG and JA. Theoretical analysis performed by FG and JA. The paper was written by JB, FG and JA, with input from all authors. Experiments conceived by FG, JA and JMB.

\appendices

\section*{Acknowledgment}

We thank present and former members of the MRILab team for their support and participation in the design and assembly of the experimental setup, and Aloma Mayordomo Febrer, from the Clinical Veterinary Hospital of Cardenal Herrera University, for the horse tooth. This work was supported by the Ministerio de Ciencia e Innovaci\'on of Spain through research grant PID2019-111436RB-C21. Action co-financed by the European Union through the Programa Operativo del Fondo Europeo de Desarrollo Regional (FEDER) of the Comunitat Valenciana (IDIFEDER/2018/022 and IDIFEDER/2021/004). JB acknowledges support from the Innodocto program of the Agencia Valenciana de la Innovaci\'on (INNTA3/2021/17).

\section*{Ethical statement}
All animal parts were obtained from a local butcher and research was conducted following the 3R principles.

\section*{Conflict of interest}
The authors have a patent (WO2021245024A1) protecting the techniques presented in this paper and licensed to Tesoro Imaging S.L. JB is a research scientist at Tesoro Imaging S.L. JMB is a co-founder of Tesoro Imaging S.L.

redpajama_set_name: RedPajamaArXiv


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Please note that North West Tractor Pulling Club does not transfer data outside of the EEA for marketing purposes. In the event there is a requirement to transfer data outside of the EEA from time to time, we will take all necessary steps to ensure the data is afforded the same safeguards and controls as those applied within the EEA.
North West Tractor Pulling Club will retain your data for as long as is reasonably necessary for the required services to be provided to you and will not be retained indefinitely or for reasons incompatible with relevant data protection legislation, including the General Data Protection Regulation.
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text:
The Porpoise: A Novel (Hardcover)
By Mark Haddon
From the Whitbread and Los Angeles Times Prize-winning author of The Curious Incident of the Dog in the Night-Time, a stunningly ambitious, fantastical novel about the theft of female agency by rapacious men and the ways in which archetypal stories can warp history and the present
Mark Haddon's breathtaking novel begins with a harrowing plane crash: Maja, the pregnant wife of the unimaginably wealthy Philippe, is killed, but their daughter Angelica survives. Philippe's obsession with the girl's safety morphs into something sinister and grotesque as she grows into a beautiful teen. A young man named Darius, visiting Philippe with a business proposition, encounters Angelica and intuits their secret -- he decides to rescue her, but the attempt goes awry and he flees England by sea.
This contemporary story mirrors the ancient legend of Antiochus, whose love for the daughter of his dead wife was discovered by the adventurer Appolinus of Tyre. The tale appeared in many forms through the ages; Apollinus becoming the swashbuckling Pericles in Shakespeare's eponymous play. In The Porpoise, as Angelique comes to terms with a life imprisoned on her father's estate, Darius morphs into Pericles, voyaging through a mythic world. In a bravura feat of storytelling, Haddon recounts his many exploits in thrilling fashion, mining the meaning of the old legends while creating parallels with the monstrous modern world Angelica inhabits. The language is rich and gorgeous; the conjured worlds are perfectly imagined; the plot moves forward at a ferocious pace.
But as much as Haddon plays with myth and meaning, his themes speak deeply to the current moment. As profound as it is entertaining, The Porpoise is a major literary achievement by an author whose myriad talents are on full, vivid display.
Mark Haddon is the author of the bestselling novels The Red House and A Spot of Bother. His novel The Curious Incident of the Dog in the Night-Time won the Whitbread Book of the Year Award and the Los Angeles Times Book Prize for First Fiction and is the basis for the Tony Award–winning play. He is the author of a collection of poetry, The Talking Horse and the Sad Girl and the Village Under the Sea, has written and illustrated numerous children's books, and has won awards for both his radio dramas and his television screenplays. He teaches creative writing for the Arvon Foundation and lives in Oxford, England.
"Staggeringly ambitious, innovative, beautifully written. . .The Porpoise has the pace of a really good thriller, combined with a subtlety and depth that few thrillers possess."
--Pat Barker, author of The Silence of the Girls and the Booker Prize-winning The Ghost Road
"A full-throttle blast of storytelling mastery. Ancient and modern overlap in exhilarating ways, it's like romping through a literary Netflix: an episode of something historical and bloody, then something slick and contemporary, then something really weird and unnerving. . .The Porpoise is a joy to read.
--Max Porter, author of the International Dylan Thomas Prize-winning Grief is the Thing With Feathers
"Mark Haddon cuts down to the grittiness of humanity every time he writes. The Porpoise is a beautiful, unputdownable, ancient tangle with its own sweeping tides and dangerous depths."
--Daisy Johnson, author of the Booker Prize finalist Everything Under
"An artfully crafted story of layered lives. . .Haddon's ambitious tale captures the ethos of tragic Shakespearean vibrations and the tangle of lives that magically intersect. The prose is exquisite and elevates this story that blends reality and mythology to great effect."
--Publishers Weekly
Publisher: Doubleday
Fiction / Historical
Fiction / Magical Realism
Kobo eBook (June 18th, 2019): $13.99

redpajama_set_name: RedPajamaCommonCrawl


"God helps those who helps themselves" is not from the Bible.
Yet we know, we need to do our part.
We can't just sit around all day humming and wait for answers to fall from the sky. That's the rub. That's the tension. It's hard to know when we need to "do" something and when we simply need to wait on God.
Maybe the answer is to wait before we do.
None of us are good at waiting these days–these days of cell phones, drive-thrus, microwaves, and text messages. We don't have to wait very long for anything. Impatient is our culture's middle name–or first.
Waiting upon God is vital in order to see Him and receive a vision from Him. And the amount of time spent before Him is also critical, for our hearts are like a photographer's film–the longer exposed, the deeper the impression. For God's vision to be impressed on our hearts, we must sit in stillness at His feet for quite a long time. Remember, the troubled surface of a lake will not reflect an image.
I know all too well what it's like to try to fix things on my own. Usually my heart beats out of my chest; my head pounds trying to figure out the solution. And a knot makes itself home in my stomach.
Isaiah 30:15 is very clear.
Digging under our translation clarifies the meaning.
The word "salvation" is the Hebrew word Yasa and it means to "save, rescue, deliver, help, preserve, give victory; to get help." It is not referring to eternal salvation in this verse, but physical help.
That is so cool. In repentance and rest will come physical help. What do you need help with in your life? According to this verse, repentance must come first to open the way for God's hand to work. Repentance means turning back to God. Changing our thought patterns to His thoughts (Scripture). Replacing that sticking thinking believing God is punishing you to God's goodness, kindness, and mercy.
What have you been trying to fix on your own? What problems keep surmounting? Ask God to reveal any places of unforgiveness or control issues in your heart.
Permission to take a nap.
The hardest thing for some of us. We feel guilty if we're not doing something. But there is a difference between lazy and obedient waiting on God. We need to tune our ears to His voice.
Which brings us to the next word.
That's a powerful word. Do we have confidence that God's got it; He will work it out?
Strength lies in confidence in God's goodness again! When we have confidence that He's got good plans worked out, we can rest.
Confess our lack of trust and trying to do it on our own.
Give up. Do nothing. Rest.
When we do this, our "waters" are stilled. And we reflect His image.
What do you need to stop doing and wait for God to do?
So good Andy. I need the reminder to stay with God a long time in order for him to make an impression. The disturbed lake surface is the perfect visual. Love, love, love this post. Thank you.
Thank you Cathy! Thanks for stopping by and sharing how this blessed you. Boy, this blogging journey can be awfully silent and lonely sometimes. Blessings to you and your time spent waiting on the Lord!
"The troubled surface of a lake will not reflect an image." Love it, Andy. Thanks for reminding us.
Hey Terry! Thanks for reading and commenting. That is a beautiful line isn't it? Wish i thought of it!
Andy..WAIT…has always been so very hard for me! I am a "doer"! Not a "waiter"!
Janice, I think it is hard for all of us to wait.
Enjoyed your "Word Wednesday" this morning. My husband loves studying the languages as he prepares his Sunday School lessons. He uses the NASB with both English and Greek translations, but he studies Hebrew online. He's my teacher so we study a lot together. I love studying the Greek words, but find the Hebrew much harder. Have a blessed day!
That's awesome Anne! What a blessing!
YAY!!! Word Wednesday posts are back!!
Yay! Thanks Samantha! I've missed them too!


Matthew Schweitzer is a Dean's Scholar at the University of Chicago, where he helps lead a multi-institutional project to examine the decline of Iraq's university system and intelligentsia since 1980. Harith Hasan al-Qarawee is a political scientist whose research focuses on the state-society relations, political transitions, and identity politics in Iraq and the Middle East. He is the former Robert G. James Scholar at Risk Fellow at Harvard University's Radcliffe Institute (2014-2015) and an incoming Fellow at Brandeis University's Crown Center for Middle East Studies.


The Camlad 34 is a modern clarsach with a strong, bright, yet expressive tone; fitted with medium-tension nylon strings. It has a soundboard of aircraft-grade laminated Finnish birch, making it less vulnerable to changes of temperature and humidity than harps with a solid spruce soundboard; and a round-backed sound-box. It is available in a variety of beautiful British and American hardwoods. The student model is the same as the other models in every respect, except that it is built in native ash with a plain birch sound-box.
Weight (approximate, depending on timber) 13.5 kgs.


text:
Massachusetts General Hospital Psychiatry Academy
Massachusetts General Hospital Visiting
Women's Mental Health
Mind Body Medicine
Yeung, Albert, MD, ScD
Director of Primary Care Study, The Depression Clinical and Research Program, Massachusetts General Hospital
Associate Professor of Psychiatry, Harvard Medical School
Dr. Albert Yeung is Director of Primary Care Research at the Depression Clinical and Research Program at Massachusetts General Hospital (MGH) and Associate Professor of Psychiatry at Harvard Medical School. He is the principal investigator of the study on "Evaluating changes in resting state networks before and after a Tai Chi training Intervention for Chinese Americans with depression".
Dr. Yeung obtained his medical degree from National Taiwan University. He also obtained a Doctor of Science degree with a major in epidemiology from Harvard School of Public Health. He completed residency training in psychiatry at MGH.
Dr. Yeung's major research interests include integrating primary care and mental health services to improve treatment of depression, mental health issues of under-served populations, and the use of complementary and alternative methods in treating mood and anxiety disorders. He has authored or co-authored over 80 original articles, numerous book chapters, and a book on self-management of depression.
For more than 30 years, Massachusetts General Hospital has been a leader in educating mental health professionals, and the Psychiatry Department has been ranked #1 in US News & World Report's Survey of America's Best Hospitals 18 times.
APA CE Sponsor Information
MGH Psychiatry Academy
1 Bowdoin Sq, Ste 900
Email: mghcme@mgh.harvard.edu
Mon-Fri 9:30 a.m. - 4:30 p.m.
© 2020 Massachusetts General Hospital. All Rights Reserved.


On June 8-10, Saint Petersburg hosted a conference commemorating the 60th anniversary of Vertex Standard. BE2B company participated in organizing of this event. After an eventful business programme, about 100 participants from Russia, Austria, Belarus, United Kingdom, Hungary, Kazakhstan, Romania and Czech Republic enjoyed a dinner on a steamboat and a fascinating trip along the Neva River.


text:
A very rich historical and cultural heritage
Known as La Ville Rose ('The Pink City') due to its unique architecture of ubiquitous terra-cotta brick buildings, Toulouse has a very rich historical and cultural heritage.(with 3 historical monuments classified as UNESCO World Heritage sites). A global aviation and European aerospace capital, Toulouse is serviced by an international airport connected to 90 world destinations.
Toulouse is also a reference in biotechnology, microbiology and life sciences and technologies. The city has also developed a competitiveness cluster: Cancer Bio Santé (Cancer-Bio-Health). France's second-largest research hub, Toulouse today counts more than 400 laboratories and 110,000 researchers, forming a centre for research and higher education.
The Capital of the Occitanie region, Toulouse occupies an ideal geographical location with numerous strengths for business tourism.
- France's 4th largest city
- The 3rd university city
- 90 destinations and 120 direct flights departing daily from the Toulouse Blagnac airport
- 12,000 hotel rooms
- A global aviation and European aerospace capital
- 50 historical monuments including 3 UNESCO World Heritage sites
Discover MEETT - Toulouse Exhibition and Convention Centre
Discover Pierre Baudis Convention Centre
Discover The Espaces Vanel
Share this destination


text:
from dataclasses import dataclass

from _py2tmp.compiler.testing import main, assert_compilation_succeeds, assert_conversion_fails

@assert_compilation_succeeds()
def test_custom_class_simple_success():
    from dataclasses import dataclass
    @dataclass
    class MyType:
        x: bool
        y: int
    assert MyType(True, 15).x

@assert_compilation_succeeds()
def test_custom_class_constructor_using_keyword_args_success():
    @dataclass
    class MyType:
        x: bool
        y: int
    assert MyType(x=True, y=15).x

@assert_compilation_succeeds()
def test_custom_class_constructor_using_keyword_args_fields_in_different_order_success():
    @dataclass
    class MyType:
        x: bool
        y: int
    assert MyType(y=15, x=True).x

@assert_conversion_fails
def test_custom_class_constructor_using_mix_of_keyword_and_non_keyword_args_error():
    @dataclass
    class MyType:
        x: bool
        y: int
    assert MyType(True, y=15).x  # error: Function calls with a mix of keyword and non-keyword arguments are not supported. Please choose either style.

@assert_compilation_succeeds()
def test_custom_class_used_as_function_success():
    @dataclass
    class MyType:
        x: bool
        y: int
    def f(b: bool):
        return MyType
    def g(b: bool):
        return f(b)(True, 15).x
    assert g(False)

@assert_compilation_succeeds()
def test_custom_class_variable_success():
    @dataclass
    class MyType:
        x: bool
        y: int
    def f(b: bool):
        v = MyType(True, 15)
        return v.x
    assert f(True)

@assert_compilation_succeeds()
def test_custom_class_as_function_param_success():
    @dataclass
    class MyType:
        x: bool
        y: int
    def f(u: MyType):
        return u.x
    assert f(MyType(True, 15))

@assert_compilation_succeeds()
def test_custom_class_as_function_return_value_success():
    @dataclass
    class MyType:
        x: bool
        y: int
    def f(b: bool):
        return MyType(b, 15)
    assert f(True).x

@assert_conversion_fails
def test_custom_class_with_same_name_as_previous_function_error():
    def X(b: bool):  # note: The previous declaration was here.
        return b
    @dataclass
    class X:  # error: X was already defined in this scope.
        x: bool

@assert_conversion_fails
def test_constructor_with_same_name_as_previous_custom_class_error():
    @dataclass
    class X:  # note: The previous declaration was here.
        x: bool
    def X(b: bool):  # error: X was already defined in this scope.
        return b

@assert_conversion_fails
def test_variable_with_same_name_as_previous_custom_class_error():
    @dataclass
    class X:  # note: The previous declaration was here.
        x: bool
    def f(b: bool):
        X = b  # error: X was already defined in this scope.
        return b

@assert_conversion_fails
def test_custom_type_match_error():
    from tmppy import match
    @dataclass
    class X:
        x: bool
    def f(b: bool):
        return match(X(True))(  # error: All arguments passed to match must have type Type, but an argument with type X was specified.
            lambda x: {
                x: x,
            })

@assert_conversion_fails
def test_custom_type_declared_as_return_type_before_definition_error():
    '''
    def f(b: bool) -> X:  # error: Unsupported \\(or undefined\\) type: X
        return True
    @dataclass
    class X:
        x: bool
    '''

@assert_conversion_fails
def test_constructor_call_wrong_number_of_arguments():
    @dataclass
    class X:  # note: The definition of X was here
        x: bool
    def g(x: bool):
        return X(x, x)  # error: Argument number mismatch in function call to X: got 2 arguments, expected 1

@assert_conversion_fails
def test_constructor_call_wrong_argument_type():
    from tmppy import Type
    @dataclass
    class X:  # note: The definition of X was here
        x: bool
    def g(
            x: Type):  # note: The definition of x was here
        return X(x)  # error: Type mismatch for argument 0: expected type bool but was: Type

@assert_conversion_fails
def test_constructor_call_wrong_argument_type_expression():
    from tmppy import Type
    @dataclass
    class X:  # note: The definition of X was here
        x: bool
    def g(x: Type):
        return X([x])  # error: Type mismatch for argument 0: expected type bool but was: List\[Type\]

@assert_conversion_fails
def test_constructor_call_additional_and_missing_keyword_arguments():
    @dataclass
    class X:  # note: The definition of X was here
        foo: bool
        bar: bool
    def g(x: bool):
        return X(fooz=x, barz=x)  # error: Incorrect arguments in call to X. Missing arguments: \{bar, foo\}. Specified arguments that don't exist: \{barz, fooz\}

@assert_conversion_fails
def test_constructor_call_additional_keyword_arguments():
    @dataclass
    class X:  # note: The definition of X was here
        foo: bool
    def g(x: bool):
        return X(foo=x, bar=x, baz=x)  # error: Incorrect arguments in call to X. Specified arguments that don't exist: \{bar, baz\}

@assert_conversion_fails
def test_constructor_call_missing_keyword_arguments():
    @dataclass
    class X:  # note: The definition of X was here
        foo: bool
        bar: bool
        baz: bool
    def g(x: bool):
        return X(bar=x)  # error: Incorrect arguments in call to X. Missing arguments: \{baz, foo\}

@assert_conversion_fails
def test_constructor_call_wrong_keyword_argument_type():
    from tmppy import Type
    @dataclass
    class X:  # note: The definition of X was here
        x: bool
    def g(
            x: Type):  # note: The definition of x was here
        return X(x=x)  # error: Type mismatch for argument x: expected type bool but was: Type

@assert_conversion_fails
def test_constructor_call_wrong_keyword_argument_type_expression():
    from tmppy import Type
    @dataclass
    class X:  # note: The definition of X was here
        x: bool
    def g(x: Type):
        return X(x=[x])  # error: Type mismatch for argument x: expected type bool but was: List\[Type\]

@assert_compilation_succeeds()
def test_constructor_call_keyword_argument_success():
    from tmppy import Type
    from typing import List
    @dataclass
    class X:
        foo: bool
        bar: Type
        baz: List[bool]
    def g(x: bool):
        return X(bar=Type('int'), foo=True, baz=[x])
    assert g(True).foo == True

@assert_conversion_fails
def test_constructor_call_keyword_and_non_keyword_arguments_error():
    from tmppy import Type
    from typing import List
    @dataclass
    class X:
        foo: bool
        bar: Type
        baz: List[bool]
    def g(x: bool):
        return X(True, bar=Type('int'), baz=[x])  # error: Function calls with a mix of keyword and non-keyword arguments are not supported. Please choose either style.

@assert_conversion_fails
def test_custom_class_access_to_undefined_field_error():
    @dataclass
    class MyType:  # note: MyType was defined here.
        x: bool
        y: int
    assert MyType(True, 15).z  # error: Values of type "MyType" don't have the attribute "z". The available attributes for this type are: \{"x", "y"\}.

@assert_conversion_fails
def test_custom_class_with_base_class_error():
    @dataclass
    class MyType(
        int):  # error: "Exception" is the only supported base class.
        x: bool
        y: int

@assert_conversion_fails
def test_custom_class_with_keyword_class_arguments_error():
    @dataclass
    class MyType(x=1):  # error: Keyword class arguments are not supported.
        x: bool

@assert_conversion_fails
def test_custom_class_with_decorator_error():
    @staticmethod  # error: "@dataclass" is the only supported class decorator.
    class MyType:
        x: bool
        y: int

@assert_conversion_fails
def test_custom_class_with_no_dataclass_annotation_error():
    class MyType:  # error: Custom classes must either inherit from Exception or be decorated with @dataclass.
        pass

@assert_conversion_fails
def test_custom_class_with_method_error():
    @dataclass
    class MyType:
        def f(self):  # error: Dataclasses can contain only typed field assignments \(and no other statements\).
            return True

@assert_conversion_fails
def test_custom_type_multiple_parameters_with_same_name_error():
    '''
    @dataclass
    class MyType:
        x: bool  # note: A previous field with name "x" was declared here.
        x: bool  # error: Found multiple dataclass fields with name "x".
    '''

@assert_conversion_fails
def test_field_with_no_type_annotation_error():
    @dataclass
    class MyType:
        x = 0  # error: Dataclasses can contain only typed field assignments \(and no other statements\).

@assert_conversion_fails
def test_custom_type_with_no_fields_error():
    @dataclass
    class MyType:
        pass  # error: Dataclasses can contain only typed field assignments \(and no other statements\).

@assert_conversion_fails
def test_custom_type_default_argument_error():
    @dataclass
    class MyType:
        x: bool = True  # error: Dataclass field defaults are not supported.

if __name__== '__main__':
    main()

redpajama_set_name: RedPajamaGithub


I've been looking for velvet pants...I'm totally hitting up Target this weekend!
Man, I LOVE Target. I can't wait till next year when it opens up in Canada. I enjoy the Velvet pants and love the addition of the ducks. Also, I stumbled upon your blog mainly for it's witty title. Would you like to follow each other?
Love these target finds! You look great!
Cute velvet pants! I would have never thought to check Target!


A picture is worth a thousand words and we want your image to speak volumes about your brand.
Poor brand designs can cost you business opportunities, YAGU helps you transform your brand in a memorable piece that will increase its value.
We provide an expert team of graphic designers ready to turn your ideas into amazing visuals that perfectly convey your brand image and identity.
We help you update your logo (or design a new one) to make an impact and become a memorable brand.
At YAGU we work closely with our client to understand their needs and what they want to communicate with their new image.
The services we offer includes the effective application of type, space, image and color to provide multi-sensory solutions for your business.


This deluxe hard-cover book provides 130 scores of every song on the Pearl Jam albums Ten through Lightning Bolt. Over 800 pages of music contain lyrics and streamlined transcriptions of every instrument that was recorded for an amazing written documentation of this influential band. Guitar and bass parts are written in both standard notation and tablature.
Songs include: Alive • Animal • Better Man • Black • Breakerfall • Corduroy • Daughter • Dissident • Do the Evolution • Elderly Woman Behind the Counter in a Small Town • Even Flow • Given to Fly • Go • Grievance • Indifference • Jeremy • My Father's Son • Not for You • Nothing As It Seems • Once • Porch • Rearviewmirror • Wishlist • and more. Book is packaged in its own protective box. A must-own for any serious Pearl Jam fan or collector! 7-2/8″ x 10-7/8″.


text:
Sex Is a Spiritual Need
By Juli Slattery
Part of the Understanding Your Husband's Sexual Needs Series
Understanding Your Husband's Sexual Needs
Understanding His Sexuality
Sex Is a Physical Need
Sex Is an Emotional Need
Sex Is a Relational Need
So, What's the Holdup?
Your Husband's Sex Drive Is God's Gift to You
Milenko Bokan/iStock/Thinkstock
Read what the apostle Paul wrote to the Corinthian church:
It is good for a man not to marry. But since there is so much immorality, each man should have his own wife, and each woman her own husband. The husband should fulfill his marital duty to his wife, and likewise the wife to her husband. … I wish that all men were as I am. But each man has his own gift from God; one has this gift, another has that.
Now to the unmarried and the widows I say: It is good for them to stay unmarried, as I am. But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion. (1 Corinthians 7:1B–3, 7–9)
Paul commanded husbands and wives to be sexually available to each other to avoid temptation. He then encouraged Christians to remain unmarried, unless they have a strong sexual desire. According to Paul, battling sexual temptation is a significant reason for Christians to marry! So, what happens to the man who marries because he "burns" only to find that his wife doesn't "burn"?
Dr. Archibald Hart writes, "Most men face a lifelong struggle to control their sexuality. The struggle is between their hormones and their higher aspirations. It is a battle between their seemingly uncontrollable urges and the fear of succumbing to these urges. Ultimately, it is a struggle over integrity, right and wrong, uprightness and wholeness."Hart, The Sexual Man, 70.
Hart's statement explains why sex is a spiritual need for a married man. He likely battles daily to stay pure. His walk with the Lord and his integrity are largely determined by how he handles sexual temptations and impulses. When he gives in to lust, pornography, or inappropriate sexual relationships, he carries a tremendous burden of guilt. He may doubt his salvation and feel disqualified from the body of Christ. Because he feels so ashamed about his struggle or failure, he may feel that he can't share his burden with anyone else.
Initially, Sheila and Mark really enjoyed their sexual relationship. The first couple of years of their marriage was the honeymoon stage that most couples hope for. As time wore on, though, their sexual desires changed. Sheila was busy and exhausted taking care of their young children, and she lost interest in sex. While Sheila seemed content to put their sexual relationship on hold for the time being, Mark responded by initiating more frequently. If he was a deer panting for water, she was a camel who seemed capable of walking through the desert for months at a time without a water break.
When Mark got the message that his advances were likely to be thwarted, he stopped asking for intimacy. He had no idea how to express his frustration and despair to Sheila. Her loud sighs and condescending expression at the mention of sex communicated that she could never understand how critical their sexual relationship was to him.
Over time, Mark began to direct his sexual needs through masturbation and light pornography. A few nights a week, he would stay up late, surfing channels, hoping to catch a glimpse of something sexual. The guilt and shame he felt only intensified the rift of intimacy in their marriage. Although he rationalized his actions, Mark knew that Sheila would be devastated to discover what he was doing. More than anything else, he longed to be pure, to share his sexuality only with Sheila. But life was too busy, his desire too strong, his will too weak, and the gulf between them too great.
Like Mark, your husband depends on you to be his partner in his battle against sexual temptation. Although you aren't responsible for his actions, you are a key component in his victory. You're the only woman in the world whom your husband can look at sexually without compromising his integrity!
Again, please understand: You aren't responsible for your husband's sexual behavior. Don't be motivated out of fear that he will act out if you don't meet his needs; rather be motivated out of love and a desire to share his spiritual journey with him.
Visit Juli Slattery's website Authentic Intimacy to learn more about God's design for sexuality.
From No More Headaches, published by Tyndale House Publishers, Inc. © 2009 Julianna Slattery. Used by permission.
Next in this Series: Sex Is a Relational Need


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