The Principle of Measurements of Circulating Blood Volume: Phenomenological Model
Three basic methods have been used to determine blood volume in humans using indicators (tags) (132, 133). The first measures plasma volume using a plasma protein tag, the second measures the red cell volume by the injection of tagged RBCs, and the third method depends on separate determinations of both plasma and RBC volume (true total volume determination). All the three methods are based on the dilution principle: agents are injected into blood flow, dye dilution is monitored using spectrophotometry, PT spectrometer, or other means (stated in the Introduction), and the dilution curve is recorded (Fig. 3). From this curve of the relative decrease in the dye concentration, CBV (VCBV) is calculated from the ratio of dye concentrations of the initial solution and the diluted solution of dye in the blood according to the following simple equation (30, 37, 56, 134):
Here, A is the signal amplitude, V0 and c0 are initial volume and concentration of the dye solution, and cx is the equilibrium dye concentration in the blood after the dilution curve is developed, measured at equilibrium or calculated from multiple timed samples by extrapolation to zero time (Fig. 3). The volume of the agent injected can be neglected compared with the total volume of the blood (132). The precision of this approach is determined by the fact that mixing time is not significantly altered by hypotension, shock, hypertension, or congestive heart failure (135).
Figure 3. The actual dilution curve of ICG in PT CBV measurements at 808 nm (after the subtraction of blood background). A is PT signal amplitude. The dilution plateau results from a combination of immediate dilution in the circulation followed by later hepatic clearance. CBV is estimated from the plateau.
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Total blood volume is calculated from the plasma or RBC volumes and simultaneously determined Ht. For correct CBV assessment, three basic assumptions have to be met (132): (i) the indicator is tightly bound to the plasma protein or to the RBC used at least for the period of measurements; (ii) plasma protein or tagged red cell is uniformly mixed with the entire “plasma or volume” to be determined, i.e., no important pools are sequestered away from the main intravascular space; and (iii) there is no loss of the indicator during the period of measurement or any loss occurs at a regular rate in order to allow back-calculation to time zero (132). These assumptions are better fulfilled by RBC tags than by plasma protein tags: there is virtually no loss of RBCs to the extravascular space in the short time needed for equilibration (132, 133).
Calculation of total blood volume from either method assumes that Ht determined from peripheral blood samples is equal to the total body hematocrit; this was shown not to be the case (135, 136). This difference, in part, is the result of the fact that the total blood volume calculated from red cell volume consistently underestimates (by 9–10%), but calculated from plasma volume consistently overestimates the true blood volume (by 5–10%) (49). To some extent, this can be accounted for by the use of correction factors based on the peripheral Ht. This precision is not always enough for correct clinical decisions. The method depending on the determination of plasma and RBC volume is independent of Ht and therefore, provides a more accurate measure for total blood volume, although it takes much time as it requires three independent tests, for Ht, for RBC-based measurements and for plasma-based measurements.
We propose to use two-dye mixtures for intravenous administration followed by dynamic PA/PT monitoring of their components in circulating blood. Thus, we propose to increase the number of dyes and the wavelengths for each dye and to use a more sensitive detection technique.
The use of a single wavelength is flawed as many spectral, spectrochemical, and other factors affect the dilution curves. Thus, a single dye requires at least two wavelengths to improve precision (137, 138). In blood, the introduction of wavelengths corresponding to Hb will allow the correction for blood absorption, which is used in PDD (35, 78, 79), however, several wavelengths for Hb makes it possible to measure Hb species with increased precision.
Moreover in blood, we cannot use any wavelength of the dye; the selection depends on the interference with blood spectrum. Thus, the wavelength of a dye giving the maximum sensitivity could lie at a disadvantageous part of the spectrum (at steep growth/tailing parts, experiencing the interference from scattering, etc.) which would result in seriously degraded precision, which was discussed elsewhere (35, 55, 78, 139). Thus, the use of a second dye, fully independent from the first with its own working wavelength pair considerably increases the precision of CBV assessment. Moreover, (i) if the maximum reproducibility is required, both dyes may be of the same type (RBC-bound or plasma-bound) or (ii) if we need the maximum accuracy (true CBV value), both dyes can be of different types. Thus, we can estimate the true value of CBV in a single run. In fact, the dye cocktail could be comprised of three or more dyes, thus combining these two cases (i) and (ii).
Dye-cocktail techniques are extensively used in chemical analysis and in vitro tests, but this approach was not used in CBV measurements. This is not due to technical difficulties but because of the fact that simultaneous accurate determination of two (or more) dyes requires their significant concentrations, which is risky in vivo. The use of PA/PT techniques provide the increased precision over absorption measurements (140) at a concentration level at least 100-fold (usually more) lower.
As a whole, we approach the CBV assessment problem with (i) higher instrumental sensitivity; (ii) higher instrumental precision; (iii) lower toxicity of the measurements; and (iv) simultaneous implementation of all CBV approaches and, thus, better assessment of true CBV.
Thus, the key idea is to intravenously inject two dyes with minimal overlap in absorption spectra with each other and with the absorption spectrum of the RBCs. Required concentrations are very low (submicromolar) and, hence nontoxic. Real-time PA monitoring of dye dilution and clearance at multiple wavelengths allows measurement of CBV because the dye concentration is inversely proportional to the ratio of CBV and injected dye volume. CBV (VCBV) is measured as the average of two PA/PT signals for each dye to decrease the interference of both dyes and thus, to improve the accuracy. For two simultaneously injected dyes, these calculations took into account the constraints c0a ≈ c0b and c0a/c0b = const, which are valid for preprepared dual mixtures of “a” and “b” dyes.
Direct assessment of cx in Eq. (1) from PA/PT signals is needed in order to account for the effect of RBC absorption. Before these calculations, the signals are corrected using [Hb] determined from PA measurement at two wavelengths (e.g., 532 nm and 1,064 nm) and background Hb absorption at selected wavelengths for the dyes. The determination of [Hb] is based on previously developed approach (141). In particular, we can measure the PT signals at 532 nm (or 610 nm, 635 nm, 660 nm, and 690 nm, depending on the selected dye) and 1,064 nm and calculate the total [Hb] at 532 nm and the fraction of HbO2 at 1,064 nm. An overdetermined Vierordt's equation system (i) at two wavelengths (142–146) is used for dyes and hemoglobin species at a nanomolar level (147):
and (ii) an overdetermined Vierordt's system at four wavelengths is used to further decrease the overall error (137, 138):
Here A is absorbance acquired from PA measurements in vivo or calculated from PT measurements. As the wavelengths for Vierordt's method, the maxima of functions and are used. For the overdetermined system, Eq. (3), λ1 and λ3 are at the maxima, and λ2 and λ4 at the minima of the absorption spectra of “a” and “b” dyes.
In vivo time-resolved PAFC setup was described elsewhere (8–13). Briefly, it was built on the platform of an Olympus BX51 microscope (Olympus America Inc.) and two pulsed lasers: (i) wavelength, 671 nm; pulse width, 25 ns; pulse rate, up to 100 kHz; pulse energy, 35 μJ (at 10 kHz rate); model, QL671-500, CrystaLaser, Reno, NV; and (ii) wavelength, 820 nm; pulse width, 8 ns; pulse rate, up to 30 kHz; pulse energy, 70 μJ (at 10 kHz rate); model, LUCE 820, Bright Solutions. Laser radiation was delivered to the sample through microscope condenser.
PA signals from the transducer/amplifier (models XMS-310/5662; Panametrics) were recorded with a Tektronix TDS 3032B oscilloscope (Hayward, CA), or collected with a high-speed 200-MHz 12-bit ADC board (National Instruments, Austin, TX), LabVIEW software (National Instruments), and a Dell Precision 690 workstation.
To verify some in vivo PA data, in vitro PT measurements were performed with the setup described elsewhere (148). It is known that the basic physical effects are similar in PA and PT methods, while the absorption sensitivity of PT spectrometry is better in vitro (149). Briefly, continuous-wave (cw) mode PT thermal-lens schematic (Fig. 1B) is based on recording of laser-induced (lasers IDLS5, Polyus, Moscow; 532, 610, 635, 660, 690, 808, and 1064 nm; waist diameter, 80 ± 1 μm in sample; power range, 20–50 mW) change of refractive index (thermal-lens effect) causing defocusing of a collinear diode laser probe beam [wavelength, 980 nm; waist diameter, 25.0 ± 0.2 μm; (attenuated) power, 0.4 mW]. Hence, a reduction in the probe beam intensity at its center (referred to as PT signal) is detected by a far-field (sample-to-detector distance 180 cm) photodiode with preamplifier (PDA36A, 40 dB amplification, ThorLabs Inc. with a 2-mm-diameter pinhole) as the response from a whole cell (Fig. 1B). The synchronization of the measurements is implemented by in-house developed software. The PT spectrometer (148, 150) has linear dynamic range of four orders of magnitude (the corresponding range of absorption coefficients for 10 mm optical pathway is 1 × 10−6 to 2 × 10−2 cm−1) and response time of 0.005 to 2 s (depending on the selected measurement parameters, namely, data throughput rate and time, number of points to be averaged, etc.). The spectrometer implements a secondary channel for gathering scattered signal, if present. The probe beam is reflected by the dichroic mirror; the residual excitation beam is removed with a stained-glass bandpass filter and after a 2-mm pinhole at the primary PT detector. If the photometric or PT channel is not needed, the corresponding detector is switched off. The scattering at the excitation wavelengths is collected with the secondary photodiode and used to correct the absorbance value, Eq. (6).
In this PT schematics, the advantages are (i) the possibility of detection under batch and flow conditions with no change in the optical-scheme design of the instrument; (ii) the possibility to switch between transient and steady-state thermal-lens measurements within a single set of experiments; and (iii) wide linear dynamic range (see above).
Thermal-lens signal (148–150), θ, was acquired as a relative change in the probe-beam intensity at a far-field detector as traditionally used in PT spectroscopy (149)
where Pe is the excitation laser power, E is the enhancement factor of PT lensing for unit excitation laser power [depends on geometry parameters of the optical scheme and thermal properties of the solution (149)], ε is the molar absorptivity, c is molar concentration of the dye in the sample, and A is sample absorbance. For comparison, A from direct optical (photometric) measurements was compared with A recalculated from Eq. (4). The experimental values of the PT signal, θ, were corrected to take into account the decrease in the excitation power due to light-scattering losses, As, in solutions:
where A is sample absorbance. Whenever possible, the experimental values of sample absorbance, Aexp, were corrected for scattering effect:
Reagents and Solutions
The following dyes were used throughout: ICG, MB, Brilliant Green (BG), Crystal Violet (CV), Indigo Carmine (CAS no. 860-22-0), Bromsulphalein (CAS no. 71-67-0), and EB (Fig. 2) from Sigma-Aldrich (St. Louis, MO). All the aqueous model solutions were prepared in 0.10% wt PBS (20 mM, pH 7.4). Water from a TW-600RU water purification system (Nomura MicroScience; Okada, Atsugi-City, Kanagawa, Japan) was used: pH 6.8; specific resistance 18.2 MΩ·cm, Fe, 2 ppt; dissolved SiO2, 3 ppb; total ion amount, <0.2 ppb; TOC, <10 ppb. Solutions were made using a Branson 1510 ultrasonic bath, power 1 W (exposure times 10–15 min). The blood of rats and mice stabilized with heparin was used at the stages of blood flow tests.