Cheng et al (2003)
utilized the first-order temporal statistics of time-integrated speckle to obtain a 2D distribution of blood flow. With their mLSI method, the mean velocity of the scattering particles of the flow is inversely proportional to the parameter Nt
are the mean and mean-square values, respectively, of time-integrated speckle intensities during the time interval t
for a specific pixel.
is the ‘temporal’ contrast.
For the Lorentzian spectrum approximation, where I
are defined as in equation (1)
is the integration time and τ
is the correlation time. The second term in equation (3)
is, in fact, the parameter 1/Nt
defined in equation (1)
From equation (5)
, it is clear that the physical meaning of the parameter 1/Nt
is the number of coherence intervals captured during the exposure time T
. However, there are multiple combinations of velocity and T
that yield the same value of 1/Nt
. Also from equation (5)
, the physical meaning of the speckle flow index (SFI
) is the rate of coherence intervals captured over unit time:
is similar to equation (2)
, with the important difference that it accounts for image exposure time so that the target range of velocity sensitivity can be varied.
Incorporation of the exposure time to the mLSI method is particularly useful when the blood flow speeds in the field of view are expected to span a wide range of values. A large dynamic range would be necessary to study blood flow dynamics in vessels of different type, as well as in response to flow-modulating stimuli (i.e. photocoagulation, vasoactive drugs, etc). Since LSI is typically used to estimate relative changes in blood flow, it is important to operate in the linear response range of LSI. The flow speeds contained within this range depend on the image exposure time (Choi et al 2006
). We propose that judicious use of multiple exposure times can be used to expand the linear response range of LSI. With the conventional mLSI method (equation (2)
), this expansion cannot be performed; however, with the use of equation (6)
, multiple exposure times can be used in an automated fashion, as we will now demonstrate.
We now must address the following practical question: How does an end user know that multiple image exposure times may be required during data analysis to operate continuously in the linear response range of each exposure time? Yuan et al (2005)
defined the sensitivity of LSI to relative changes in flow rate as the ratio of the relative speckle contrast change to the relative flow speed change:
is the speckle contrast given by
is the number of coherent intervals captured per unit time (i.e. 1/Nt
). From , we can see that Sr
reaches an asymptotic value of 0.5 for values of r
greater than ~50. Hence, for r
> 50, the relative speckle contrast response is proportional to the actual relative change in flow speed (Yuan et al 2005
). Our experimental data () support this statement, as we observe that a linear response range is achieved for r
Sensitivity as a function of the number of coherence intervals captured over unit of time (i.e. 1/Nt).
Figure 2 (a) Both SFI and 1/Nt values maintain a linear relationship to the actual flow rate for an actual flow rate greater than 5 mm s−1 and an image exposure time of 1 ms. For an actual flow rate less than 5 mm s−1, it is necessary to employ (more ...)
Hence, to determine the optimal image exposure time to use in analysis of relative flow rate changes assessed with LSI, the end user should calculate relative flow rate changes only if the data sets satisfy the r ≥ 50 criterion. This rule-of-thumb applies to both mLSI and spatial LSI data. Our experimental data (see section 4 below) support this rule-of-thumb.
For an image in which multiple flow speeds are encountered (i.e. microvasculature in a cranial or dorsal window chamber preparation), ideally one would collect sequences of images at multiple exposure times and, with analysis of the ensuing 1/Nt maps identify the optimal exposure-time images to use to analyze relative blood flow changes for each pixel. In many experimental scenarios for which high temporal resolution is not required (i.e. cortical spreading depression following focal cerebral ischemia), this approach is viable.