# Requirements and Hardware Limitations of High-Frame-Rate 3-D Ultrasound Imaging Systems
## 2 Materials and Methods
### Requirement Examples for 2-D and 3-D Imaging  
In this Section, the dependence of digital RX requirements on the adopted TX/RX strategy is investigated. Specifically, for both 2-D and 3-D imaging, the following cases have been considered: line-by-line (LL) focused scan and plane-wave (PW) scan.  
The 2-D imaging examples are based on a small (128-element) linear array. The first example (2-D LL 128) reconstructs the image through a LL scan sequence, while the second one (2-D PW 128) implements an HFR imaging sequence consisting of the TX of a plane wave followed by parallel beamforming in RX (with nMLA = 6).  
In the first of the following 3-D examples, each image is reconstructed through a line-by-line (3-D LL 256) scan sequence based on a 256-element 2-D-probe. The same probe is considered in the second example (3-D PW 256), which assumes that 6 lines are parallel beamformed (i.e., nMLA = 6) after the transmission of each plane wave. In the last example (3-D PW 1024), the same sequence is assumed to be transmitted from a 2-D-probe having 1024 elements.  
In all cases, the pulse repetition frequency (PRF) was set to 1000 Hz, the number of channels was considered coincident with the number of transducer elements, and the ADC resolution was N\({}_{\text{bit}}\) = 12. Furthermore, it was assumed that BF\({}_{\text{bits}}\) = IQ\({}_{\text{bits}}\) = 32 and, N\({}_{\text{depths}}\) = N\({}_{\text{G}}\) = 1280, which involves that B\({}_{\text{BF}}\) = B\({}_{\text{IQ}}\).  
For the 2-D imaging cases, a beamformed frame of N\({}_{\text{L}}\) = 96 lines by N\({}_{\text{G}}\) = 1280 depths, corresponding to roughly 123k points, was considered. The transition to 3-D imaging heavily weighs on the system metrics: even considering a relatively small volume (N\({}_{\text{L}}\) = 32 \(\times\) 32 lines, each with N\({}_{\text{G}}\) = 1280), the number of beamformed points roughly increases by a factor of 10 (1.3M).  
The digital device requirements corresponding to each test case are on the right side of Table 1. The comparison between the 2-D imaging cases highlights that:  
1. in 2-D LL 128, a significantly higher amount of raw data (22.5 MB vs. 0.23 MB) per frame is involved although the frame rate turns out to be very limited (R \(\approx\) 10 Hz);
2. the bandwidth B\({}_{\text{wr}}\) is the same for both 2-D LL 128 and 2-D PW 128 while B\({}_{\text{BF}}\), MAC/s, and B\({}_{\text{IQ}}\) are much higher for 2-D PW 128.  
In all 3-D cases, the number of points needed to reconstruct one volume significantly increases. The 3-D LL 256 case confirms that the reconstruction of a single volume requires a huge amount of data (RD = 480 MB), although the achievable volume rate (R \(\approx\) 1 Hz) does not enable a sufficient time resolution.  
When HFR (R = 1 kHz) 3-D PW imaging methods are used, RD drops down (0.47-1.88 MB) while B\({}_{\text{wr}}\) linearly increases with the number of channels (468.8-1875 MB/s). At the same time, B\({}_{\text{BF}}\), B\({}_{\text{IQ}}\), and, overall, MAC/s dramatically raise making the real-time implementation extremely challenging.