A Mathematical Basis for the Application of the Modified Geometric Method to Maximum Frequency Estimation

Application of the Magnitude-Squared Coherence Function Between Uterine and Umbilical Flow Velocity Waveforms for Predicting Placental Dysfunction: A Preliminary Study

“…The blood flow velocity waveform was reconstructed from the audio signals using the modified geometric method for maximum frequency estimation (Fernando et al 2004a). The pulsatility index was defined as the maximum velocity minus the end diastolic velocity divided by the time averaged velocity.…”

Mixture Models for Estimating Maximum Blood Flow Velocity

“…Moreover, the very notion of maximum flow velocity is ambiguous because theoretically flow velocity has no upper bound. Many envelope estimation algorithms have been proposed 10 – 15 ; one that is frequently 16 used is the modified geometric method (MGM) 10 . That method essentially searches for a “kink” in the cumulative histogram of flow velocity and defines the maximum flow velocity as the flow velocity at which the kink occurs.…”

“…Many envelope estimation algorithms have been proposed [10][11][12][13][14][15] ; one that is frequently 16 used is the modified geometric method (MGM). 10 That method essentially searches for a "kink" in the cumulative histogram of flow velocity and defines the maximum flow velocity as the flow velocity at which the kink occurs. It provides reliable envelope estimates but lacks the important feature of allowing one to quantify the uncertainty in maximum flow velocity.…”

A Double‐Gaussian, Percentile‐Based Method for Estimating Maximum Blood Flow Velocity

“…Therefore, to obtain a useful estimate of maximum flow velocity, one must introduce some criterion that defines what is meant by maximum. Many such criteria (standards for transcranial Doppler measurements [11][12][13][14][15] ) are based on the cumulative histogram of flow velocity. Figure 2 shows an example of the relative frequency histogram of flow velocity (top) and the corresponding cumulative histogram (bottom) at a specific time for a specific patient (hereafter, patient X); the latter is obtained by integrating the former from left to right.…”

“…One may define the maximum flow velocity as the value at which the cumulative histogram "levels off," but there exist different criteria corresponding to different objective measures of that point. [11][12][13][14][15] The vertical bar in Figure 2 marks the flow velocity at which it is maximum according to the modified geometric method. 11,12 The top panel in Figure 3 shows the spectrogram and the modified geometric method envelope (in black) for patient X.…”