While blood flow techniques have been greatly improved upon, pushing past some of the previous limitations, the acquisition of centerline velocity via dual sensor technique, and assuming the Baker Wayland ratio of 1.6 (Baker & Wayland, 1974) for blood flow calculations remains to be the most utilized method for calculating in vivo blood flows in skeletal muscle microvascular networks (Duling et al., 1982; Segal & Duling, 1987; Hester & Duling, 1988; VanTeeffelen & Segal, 2006; Jackson et al., 2010).
The wide use of the Baker Wayland ratio of 1.6 is a direct consequence of limited data characterizing in vivo skeletal muscle velocity RBC profile shapes, as use of this ratio has been criticized for introducing errors in velocity, and therefore blood flow calculations (Pittman & Ellsworth, 1986; Tangelder et al., 1986). These limitations arise as a result of both utilizing skeletal muscle preparations which provide access to a narrow range of vessel diameters, and the lack of a blood flow measurement technique which can be used to acquire in vivo velocity profile shapes for a large range of diameters.
Following the development and refinement of the GM preparation, we employed use of fluorescently-labeled red blood cells to act as tracers within the microvascular network in the GM muscle. As these labeled red blood cells maintained their intrinsic characteristics (e.g., biconcavity, and deformability), and the fraction of injected labeled red blood cells (1% of total blood volume) did not affect total hematocrit within the system, these fluorescent red blood cells acted as flow tracers which were representative of the native red blood cell flow patterns found within the microvasculature. Limiting the in vivo labeled fraction of red blood cells to 1% allowed for high contrast imaging between the labeled and unlabeled red blood cells. We then took advantage of our dual bright-
field/epi-fluorescent microscopy system by optimizing camera exposure time during data acquisition. This allowed for these labeled red blood cells to form “streaks” of light along the vessel, displaying distance traveled in the time that the camera shutter was opened and closed, thus providing a way to measure in vivo red blood cell velocities. With the increase in network visibility provided by the GM preparation, we were able to measure these velocities across the vascular lumen, for an entire arteriolar tree spanning multiple branch orders. These data are the first of their kind for providing much needed
information on velocity profile shapes in skeletal muscle microvasculature that can be immediately implemented in blood flow calculations.
For true parabolic velocity profiles, the fixed velocity ratio (VMax/VMean) would be 2, as the centerline velocity would be twice that of the mean velocity through the vessel. Baker and Wayland (Baker & Wayland, 1974) discovered that the average velocity profile through glass tubes had a blunted velocity profile shape where the centerline velocity was 1.6 times greater than the mean velocity averaged over the lumen. While Baker and Wayland assumed a parabolic velocity profile, the resulting velocity ratio factor of 1.6 comes as a consequence of spatial averaging that is inherent to the dual sensor red blood cell velocity measurement technique. Certainly, in vivo findings collected from the rabbit mesentery preparation have contradicted a constant velocity ratio for all diameters, as these velocity ratios were determined to be diameter-dependent (Tangelder et al., 1986).
The consequences of assuming a fixed velocity ratio are striking, as subsequent blood flow calculations would thereby over- or under-estimate blood flow values compared to using a diameter-dependent velocity ratio value. Specifically, our data show that using a velocity ratio of 1.6 for calculating blood flow in arterioles with diameters less than or greater than ~65 μm would result in under- and over-estimation of blood flow by up to 20%, respectively. Similar to Tangelder et al, in the thesis herein, we also developed a diameter-dependent velocity ratio equation; however, the equation we provide, to our knowledge, is the first to describe diameter-dependent velocity ratios for skeletal muscle arterioles for a wide range of arteriolar diameters encompassing feed to pre-terminal arterioles (compared to a range of 17-32 µm in the rabbit mesentery (Tangelder et al., 1986)). As well, the velocity ratio equation provided in this thesis (Chapter 2)
encompasses a large range of diameters, allowing it to be accessible for use in other microvascular preparations. As previously mentioned, data acquisition via use of the dual sensor technique is widely accepted, with many fundamental advancements in the field of microcirculatory hemodynamics made through its use. Certainly, we do not suggest that the dual sensor technique (or other red blood cell velocity measurement techniques) be replaced by use of our fluorescently-labeled red blood cell velocity measurement technique. We do recommend that our diameter-dependent velocity ratio equation be used, in conjunction with these measurement techniques, to determine an appropriate velocity ratio for use in blood flow calculations, as opposed to utilizing a constant velocity ratio such as the Baker Wayland ratio of 1.6. It should be noted that we
recommend that the experimentally-derived velocity ratio equation be constrained for use in arteriolar diameters within the appropriate diameter range (21-115 µm).
Indeed, there are other groups who have identified a velocity ratio equation that varies with hemodynamic parameters. For instance, in the seminal work carried out by Pittman and Ellsworth (1986) in the arterioles and venules of the hamster retractor muscle, a velocity profile bluntness parameter (“B”) was estimated as a function of both diameter and the centerline dual sensor velocity. This parameter has been beneficial in determining velocity ratios for use in mathematical modelling of the rat mesentery (Pries et al., 1989); however, as highlighted in their conclusions (Pittman & Ellsworth, 1986) their study was not based on absolute in vivo velocity calibrations such that any estimates made using their bluntness factor are subject to confounding variables that are inherent in the use of the dual sensor technique. Despite the fact that their bluntness parameter was not based on in vivo velocity calibrations, use of this parameter in calculation of velocity ratios is
far more advantageous than assuming a fixed velocity ratio. Our velocity ratio equation, described in the thesis herein, was derived from in vivo red blood cell velocity
calibrations and only requires diameter as an input variable which can easily be collected from intravital experiments.
Moreover, the diameter-blood flow relationships acquired using our “streak length” velocity measurement technique was in accordance with diameter-blood flow relationships for both the rat cremaster muscle (Mayrovitz & Roy, 1983; House & Lipowsky, 1987), and the theoretical “cubic law” first described by Murray (Murray, 1926). Therefore, we prescribe use of our velocity ratio equation over others as it is derived from in vivo red blood cell velocity measurements, and the diameter-blood flow relationship derived in our study is in agreement with that found by other groups.