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A new technique was used to extract blood flow waveforms from these parametric images. The main principal of this technique is to measure blood flow velocities by tracking changes of concentration of contrast material along the blood vessel, rather than using predefined distances as in the bolus transport time method.

Fig. 6.3 presents the example of the distance-density curves obtained from a parametric image (fig. 6.2(a)) for two consecutive profiles. As is shown in fig. 6.3 the shape of the consecutive profiles appears to be very similar for short time intervals as the contrast material bolus travels along the vessel. The distance that the bolus moves along the vessel in two contiguous frames divided by the frame interval is equal to the flow velocity. This distance can be estimated by comparison of the two distance-density curves.

The following assumptions were made in the computation blood flow velocity information. We assume that: (1) in the time frame of each measurement of velocity (in our case 0.04 seconds) the degree of bolus dispersion is very small,

(2) blood flow is time dependent but independent of position down a non­ branching segment of blood vessel, (3) there must be overlap of portions of the bolus in adjacent frames. Our phantom work has shown that in practice, a frame to frame overlap of about 50% provides adequate data to match distance concentration functions.

Adjacent concentration-distance profiles in the parametric image of iodine concentration versus distance and time were shifted along the vessel axis until a match occurred. A match was defined as the point where the mean sum of the squares of the differences (MSSD) between the two profiles was a minimum. The distance of translation per frame interval is equal to the bolus velocity.

Matching (or re-registering) distance-density curves (or profiles of contrast concentration-distance) over time was performed in both directions (i.e. forward and reverse directions of blood flow along the vessel) and the disparity (or displacement) of matched curves was computed.

The matching criteria in the forward flow direction are satisfied when the function

,e ,,

is a minimum with respect to n (fig. 6.4). The integer n is the spatial shift (in pixels) along the vessel, A and B are consecutive profiles of contrast concentration along the blood vessel and corresponds to the maximum length of the vessel used for flow analysis.

The dependence of the MSSD on the spatial shifts is demonstrated in fig. 6.5. This data is generated from columns 25-28 (1-1.12 seconds) of the parametric image in fig. 6.2(a). The data demonstrate a sharp minimum at a certain value of the shift. The shift that yields the minimum MSSD is taken to be the distance traversed by the contrast material between the two frames. We also generated a cost function image where the image grey level represents the MSSD as a function of time (horizontal axis) and shifts (vertical axis) along a vessel segment (fig. 6.6). Fig. 6.6 was generated by the application of our velocity algorithm, matching profiles of contrast concentration-distance over time, to the parametric image in fig. 6.2(a). In this thesis these images were used for display purposes to check the behaviour of the search algorithm (MSSD). The use of these images to improve the generation of blood flow velocity waveforms in clinical studies especially in noisy images will be discussed in chapter 10, "future work".

The maximum velocity, which can be detected using our velocity algorithm

is given by:

(®-2)

where L is the vessel path length over which the measurement is made and R is the X-ray image frame rate (25 frames/sec). If the peak blood flow velocity along the vessel is greater than the length of the vessel segment analysed per frame

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Distance (mm)

Fig. 6.5. A example of the dependence of the mean sum of the square differences (MSSD) on the spatial shifts. The data demonstrate a sharp minimum at a certain value of the shift. This value is taken to be the distance transversed by the contrast material between the two frames. Graphic presentation of the MSSDs are from the parametric image shown in fig. 6.2 in four consecutive columns 25- 28 (1-1.12 seconds).

Time (seconds)

Fig. 6.6. A example of the cost function image, where the image grey level represents the mean sum of the square difference (MSSD) as a function of time (horizontal axis) and shift (vertical axis) along a vessel segment. The cost function image was generated by the application of our velocity algorithm to the parametric image in fig. 6.2(a).

interval, then the tracking algorithm will fail. In other words, in the comparison (using MSSD) of two distance-density curves, some of the same portions of the bolus must appear in the two profiles. This is entirely dependent on the frame rate acquisition and length of vessel imaged; the frame rate must be high enough so that a portion of the bolus imaged in one frame appears in the subsequent frame. The frame rate required can be estimated from the length of the vessel used in the flow analysis and the estimated peak velocity of the blood flow. For example with 25 frames per second and a 100 mm vessel length, the peak velocity should not exceed 2500 mm/second and this is adequate enough for most of the human vascular system (Caro et al 1974). Digital subtraction angiographic systems are sometimes capable of acquiring at a data rate of 50, 75 or even 100 frames per second.

6.3 METHOD

Here I describe the generation of parametric images using digital angiographic data and the extraction of blood velocity waveforms from these images.