Venous excess ultrasound: A mini-review and practical guide for its application in critically ill patients

Table 1 The essential ultrasonography formulae relevant to venous excess ultrasound

Formula	Relevance
λ = c/f. λ is the wavelength, c stands for the sound velocity in the tissue, and f is the frequency[8,11,12]	The equation illustrates the inverse relationship between frequency and wavelength. The lower frequency corresponds to longer wavelengths, which allow them to penetrate deeper into the tissues as longer wavelengths reduce scattering and absorption. However, longer wavelengths lead to reduced spatial resolution, thereby diminishing the ability to distinguish between two objects. Thus, lower-frequency probes have better penetration but lower resolution images, while higher-frequency probes have the opposite characteristics
Doppler shift = (2 × f) × (V/c) × cos θ. f is ultrasound frequency, V stands for blood flow velocity, c for speed of sound in the tissue, and θ for insonation angle	The Doppler shift is directly proportional to blood flow velocity, and aliasing tends to happen when the Doppler shift surpasses the Nyquist limit[12,13]. Besides, this formula illustrates the importance of the insonation angle in the PW study. Adjusting PW's insonation angle to zero, or at least less than 60 degrees, is ideal as it maximizes the Doppler shift at zero degrees (cos 0 = 1), whereas at 90 degrees (cos 90 = 0), there is essentially no Doppler shift
Nyquist limit = PRF/2. PRF stands for pulse repetition frequency	PRF is the rate at which the ultrasound system emits pulses of sound waves and receives their echoes. It is also known as the sampling rate, measured in hertz (Hz), and typically ranges from 1000 to 5000 Hz in clinical settings
PRF = 1/pulse duration. PRF stands for pulse repetition frequency. Pulse duration is the period between pulses	According to the inverse proportional relationship, the lower the PRF, the longer the pulse duration. Prolonging the pulse duration allowed for deeper transmission and improved sensitivity to low-velocity flow. But the trade-off features of lower PRF will include lowering the Nyquist limit and increasing the chances of aliasing, where the Doppler signal falsely creates an appearance of the flow reversing or oscillating in the opposite direction[12,13]

PRF: Pulse repetition frequency.