## 2 Methods
### Parallelized Scan Sequence  
In order to find the best scan sequence for a given FOV, the cross-talk energy level of several MLT setups can be quantified by computer simulation. In particular, a 2D square phased array transducer (10 \(\times\) 10 mm\({}^{2}\), 32 \(\times\) 32 elements, 312.5 \(\upmu\)m pitch) transmitting a Gaussian pulse with a central frequency of 2.5 MHz and 50% bandwidth was simulated using a graphical computer unit (GPU) based implementation of the spatial impulse response method (Simpulse) [20]. The transmit beams were focused at a depth of 60 mm while dynamic focusing was used during receive. Tukey apodization (\(\alpha\) = 0.5) was applied in both transmit and receive to suppress cross-talk artifacts. Furthermore, the MLT beams were spread circumferentially around the conically shaped FOV in an equiangular manner, and were staggered in the radial direction between neighboring beams to increase the inter-beam spacing and therefore to reduce cross-talk. Such staggering was chosen to be half the thickness of the hollow cone at the focal depth. The cross-talk energy level of the MLT systems can be determined using the process described in [17]. As such, simulations of the two-way beam profiles were performed on a plane parallel to the transducer surface (i.e., C-plane) at a depth of 65 mm (i.e., around halfway the common imaging depth for cardiac applications). This depth was chosen based on our previous in silico findings [17] while using the exact same system configuration. It was shown that the best performing system at this depth was also the system of choice at other depths and steering angles. In this study, we therefore focused on evaluating the systems' performance at this depth only.  
To quantify how the energy of a beam spreads in the volume and potentially interferes with other MLT beams, the same procedure as in [17] was followed. In short, a beam was transmitted into one of the MLT directions (\(\theta_{i}\)) and subsequently received along each of the MLT beam directions (including the same transmit direction: \(\theta_{1...i...j}\)). Next, the sum of the energy while transmitting and receiving in the same MLT direction was considered as single-line-transmission (SLT) energy (i.e., the ideal situation), whereas cross-talk was computed as the sum of the energy that deviates from the transmit beam towards the other remaining MLT directions, i.e., when transmitting in a given MLT direction but receiving in one of the other remaining MLT directions. This procedure was repeated for every MLT beam in the setup. The final cross-talk energy level (\(E_{xtalk}\)) was quantified in decibels. Mathematically, this can be expressed as:  
\[E_{xtalk}=10\cdot log10\left(\frac{\sum_{i=1}^{\#mlt}\sum_{j=1,j\
eq i}^{\#mlt} E^{\theta_{ij}}}{\sum_{i=1}^{\#mlt}E^{\theta_{ii}}}\right) \tag{1}\]  
where: \(i\) is a given MLT direction being assessed; \(j\) is a MLT direction different from the direction being tested (\(i\)); \(\#mlt\) is the total number of MLT beams in the system; \(E^{\theta_{ij}}\) is the energy in the C-plane when transmitting in a given MLT direction \(i\) and receiving in one of the other directions (\(j\)) (i.e., cross-talk); and, \(E^{\theta_{ii}}\) is the energy in the C-plane when transmitting in a given MLT direction \(i\) while receiving in the same direction \(i\) (i.e., SLT energy).  
Please note that in the present study, the FOV definition and its associated parallel scanning sequence have been proposed considering apical view acquisitions only.