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The refractive index of human hemoglobin in the visible range
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IOP PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 56 (2011) 4013–4021
doi:10.1088/0031-9155/56/13/017
The refractive index of human hemoglobin in the visible range O Zhernovaya1 , O Sydoruk2 , V Tuchin1 and A Douplik3,4,5 1 International Research–Educational Center of Optical Technologies for Industry and Medicine ‘Photonics’, Saratov State University, 83 Astrakhanskaya str., 410012 Saratov, Russia 2 Optical and Semiconductor Devices Group, Department of Electrical and Electronic Engineering, South Kensington Campus, Imperial College London, London SW7 2AZ, UK 3 Medical Photonics Engineering Group, Chair of Photonic Technologies, Friedrich-Alexander University Erlangen-Nuremberg, Paul-Gordan-Strasse 3, 91052 Erlangen, Germany 4 Clinical Photonics Lab, SAOT Erlangen Graduate School in Advanced Optical Technologies, Friedrich-Alexander University Erlangen-Nuremberg, Paul-Gordan-Strasse 6, 91052 Erlangen, Germany
E-mail:
[email protected]
Received 18 January 2011, in final form 11 May 2011 Published 15 June 2011 Online at stacks.iop.org/PMB/56/4013 Abstract Because the refractive index of hemoglobin in the visible range is sensitive to the hemoglobin concentration, optical investigations of hemoglobin are important for medical diagnostics and treatment. Direct measurements of the refractive index are, however, challenging; few such measurements have previously been reported, especially in a wide wavelength range. We directly measured the refractive index of human deoxygenated and oxygenated hemoglobin for nine wavelengths between 400 and 700 nm for the hemoglobin concentrations up to 140 g l−1 . This paper analyzes the results and suggests a set of model functions to calculate the refractive index depending on the concentration. At all wavelengths, the measured values of the refractive index depended on the concentration linearly. Analyzing the slope of the lines, we determined the specific refraction increments, derived a set of model functions for the refractive index depending on the concentration, and compared our results with those available in the literature. Based on the model functions, we further calculated the refractive index at the physiological concentration within the erythrocytes of 320 g l−1 . The results can be used to calculate the refractive index in the visible range for arbitrary concentrations provided that the refractive indices depend on the concentration linearly. (Some figures in this article are in colour only in the electronic version)
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1. Introduction A part of a standard complete blood count is to determine the total hemoglobin concentration, the hematocrit, and the mean corpuscular hemoglobin. Independent optical methods of evaluating these blood parameters help develop quality control of blood analysis. Among these methods, measurements of the refractive index and the absorption of blood are routinely used for exact determination and monitoring of hemoglobin concentration (van Kampen and Zijlstra 1965, Fabry and Old 2009). One of the important applications is monitoring of hemolysis when hemoglobin leaks out from erythrocytes and, consequently, the local concentration of hemoglobin rapidly changes. Blood optics is also important for biophotonic and clinical applications, both in therapy and diagnostics. Light absorbing and scattering properties of blood depend on the refractive index of erythrocytes, which is mainly determined by the concentration of hemoglobin in erythrocytes. The major source of scattering in blood is the refractive-index mismatch between erythrocytes and blood plasma. High-accuracy measurements of the refractive and the spectral properties of hemoglobin facilitate monitoring and modification of the optical properties of blood and blood-containing tissues and improve optical immersion methods exploited in existing optical diagnostic and therapeutical techniques, such as optical coherence tomography, reflectance spectroscopy, photodynamic therapy, and laser surgery. The refractive index of hemoglobin is a complex value. Its imaginary part was described by absorption measurements and thoroughly tabulated for wavelengths between 250 and 1000 nm (Prahl 1999). On the other hand, measuring the real part of the refractive index is challenging, especially in a wide wavelength range. In 1957, Barer (1957) determined the real part of the refractive index of hemoglobin at a single wavelength of 589 nm, and his result has been actively used ever since, see e.g. Friebel and Meinke (2005, 2006), Rappaz et al (2008). Barer’s expression assumes that the real part of the refractive index, n, is proportional to the hemoglobin concentration, C n = nH2 O + αC,
(1)
where nH2 O is the refractive index of distillate water and α is the specific refraction increment. Recently, the refractive index within the visible and near-infrared range has been found by applying Kramers–Kronig relations (Faber et al 2004) and by simultaneous measurements of both specular reflection and light absorption spectra (Friebel and Meinke 2005, 2006). Both methods are indirect and rely on the imaginary part of the refractive index for calculating the real part. The reported values of the refractive index vary across publications. Moreover, most of the previous measurements of the refractive index have been carried out for the oxygenated form of hemoglobin. In blood, however, hemoglobin is present both in the oxygenated and in the deoxygenated forms, and, therefore, both forms must be studied. Using a refractometer based on the total internal reflection, we directly measured the real part of the refractive index of deoxygenated and oxygenated hemoglobin at nine wavelengths between 400 and 700 nm. Changing the concentration of the hemoglobin, we could determine specific refraction increments at these wavelengths assuming that the refractive index depends on the concentration linearly. Section 2 describes the preparation of the materials and the measurements. Section 3 presents the results of the measurements and the model functions we propose to describe the specific refraction increments. It also compares our results with those given in earlier publications. Section 4 draws conclusions.
The refractive index of human hemoglobin Table 1. 37 ◦ C.
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The refractive index of water and methemoglobin at temperatures of 20
◦C
and
Wavelength (nm) 401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5 n(water), 20 ◦ C n(water), 37 ◦ C n(metHb), 20 ◦ C n(metHb), 37 ◦ C
1.343 1.341 1.345 1.343
1.340 1.338 1.342 1.341
1.337 1.335 1.339 1.338
1.334 1.332 1.337 1.335
1.333 1.331 1.335 1.333
1.333 1.331 1.335 1.333
1.332 1.330 1.334 1.332
1.332 1.329 1.333 1.332
1.330 1.328 1.332 1.330
2. Materials and methods The digital multiwavelength refractometer DSR-λ (Schmidt&HaenschTM , Germany) used in our experiments measures refractive indices at nine wavelengths: 401.5, 435.8, 486.1, 546.1, 587.6, 589.3, 632.8, 656.3 and 706.5 nm, covering the entire visible range. The refractometer is designed to measure the refractive index of highly absorbing and non-translucent substances, particularly suitable for high-concentration hemoglobin solutions. The refractive index is determined from the measurements of the angle of total internal reflection. Human hemoglobin (lyophilized powder) obtained from Sigma-Aldrich was dissolved in phosphate buffered saline (PBS) to maintain pH at 7.4 and exclude changes of the refractive index due to changes of the pH value. The refractive index of PBS is about 0.002 higher than the refractive index of water at all wavelengths. Dry hemoglobin was in the form of methemoglobin. To obtain solutions of deoxygenated and oxygenated hemoglobin with the concentrations of 0–140 g l−1 , sodium dithionite and sodium bicarbonate, respectively, were added to all samples (Dalziel and O’Brien 1961). The optimal concentration of sodium dithionite for full conversion of methemoglobin to the deoxygenated hemoglobin was found to be 10 g l−1 . To convert methemoglobin to oxygenated hemoglobin, sodium bicarbonate with the concentration of 15 g l−1 was used. Addition of sodium dithionite and sodium bicarbonate increased the overall refractive index of hemoglobin solution. When the amount by which the refractive index increased was subtracted, the refractive index of both deoxygenated and oxygenated hemoglobin became almost equal to the refractive index of the methemoglobin initial solution. One can assume that the chemical interaction between hemoglobin and the solutions of sodium dithionite and sodium bicarbonate does not lead to a considerable change of the refractive index of hemoglobin, and therefore, the increase of the refractive index of the hemoglobin solution due to sodium dithionite and sodium bicarbonate can be neglected. The values of the refractive index of water measured at the nine wavelengths are given in table 1. They are in good agreement with data presented by other authors, see e.g. Thormahlen et al (1985). The measurement error was estimated experimentally for multiple preparations of samples. The absolute measurement error was calculated and its average value did not exceed 0.001. In addition, the sample-layer thickness did not influence noticeably the measured values of the refractive index. For most of our measurements, we stabilized the temperature of the samples inside the refractometer at 20 ◦ C to minimize evaporation of water in the sample chamber. We have, however, also estimated the temperature dependence of the refractive index of hemoglobin for the hemoglobin solution with a concentration of about 0.5 g l−1 . Dry hemoglobin (lyophilized powder) was in the form of methemoglobin. As the measurements showed, methemoglobin had the same refractive index as oxygenated and deoxygenated hemoglobin at the wavelengths beyond the regions of anomalous dispersion, in the range of 487–707 nm. The refractive index
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O Zhernovaya et al Table 2. The refractive index of deoxygenated hemoglobin (Hb), measured at different wavelengths and for different values of the concentration. The measurements at zero concentration correspond to the pure solvent (phosphate buffered saline).
Wavelength (nm) Concentration (g/l) 401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5 0 20 30 40 50 60 70 80 90 100 110 120 130 140
1.345 1.349 1.350 1.351 1.353 1.354 1.355 1.357 1.359 1.360 1.362 1.363 1.365 1.365
1.342 1.347 1.348 1.350 1.352 1.354 1.355 1.357 1.359 1.360 1.363 1.364 1.366 1.367
1.339 1.343 1.345 1.346 1.348 1.349 1.350 1.352 1.354 1.355 1.357 1.358 1.360 1.361
1.336 1.340 1.342 1.343 1.345 1.346 1.347 1.349 1.350 1.352 1.354 1.355 1.356 1.357
1.335 1.339 1.340 1.342 1.343 1.345 1.346 1.348 1.349 1.350 1.352 1.353 1.355 1.356
1.335 1.339 1.340 1.342 1.343 1.345 1.346 1.348 1.349 1.350 1.352 1.353 1.355 1.356
1.334 1.337 1.339 1.341 1.342 1.343 1.344 1.346 1.347 1.349 1.350 1.352 1.353 1.354
1.333 1.337 1.338 1.340 1.341 1.343 1.344 1.345 1.347 1.348 1.350 1.351 1.353 1.354
1.332 1.336 1.337 1.338 1.340 1.341 1.342 1.344 1.345 1.347 1.348 1.350 1.351 1.352
of the methemoglobin solution and water was measured for temperatures of 20 ◦ C and 37 ◦ C (table 1). The refractive index of hemoglobin at 37 ◦ C is about 0.001–0.002 lower than that at 20 ◦ C for all wavelengths. In addition, the refractive indices of water at these two temperatures differ by 0.002. It can, therefore, be assumed that the refractive index of hemoglobin solutions at various temperatures is influenced mainly by the refractive index of water in which it is dissolved. 3. Results Tables 2 and 3 show the values of the refractive index measured for the deoxygenated and oxygenated hemoglobin, respectively. When plotted against the concentration, the values of the refractive index at different wavelengths (circles in figure 1) fit into straight lines. We assumed that the lines are determined by an equation similar to (1): n = n0 + αC,
(2)
where α is, as above, the specific refraction increment and n0 is the ‘effective’ refractive index at zero concentration. At each wavelength, we then determined the values of α and n0 by the linear least-squares method using the Matlab function ‘polyfit’. These values are given in table 4 and the corresponding lines are plotted in figure 1. For the whole concentration range, the calculated lines agree with the measured values within the experimental error (0.001). For the deoxygenated hemoglobin, figure 1(a), the slope of the line at 402 nm is smaller than that of the line at 436 nm, indicating a region of anomalous dispersion matching the Soret band of deoxygenated hemoglobin (432–434 nm) (Prahl 1999). For the deoxygenated hemoglobin, however, we observed normal dispersion at all wavelengths, see figure 1(b). For a detailed comparison between the refractive indices of oxygenated and deoxygenated hemoglobin, we plot in figure 2(a) the values measured at the concentration of 100 g l−1 . There is almost no difference between refractive indices of deoxygenated and oxygenated
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Table 3. The refractive index of oxygenated hemoglobin (HbO2 ), measured at various wavelengths and different values of concentration. The measurements at zero concentration correspond to the pure solvent (phosphate buffered saline).
Wavelength (nm) Concentration (g/l) 401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5 0 20 30 40 50 60 70 80 90 100 110 120 130 140
1.345 1.349 1.350 1.352 1.354 1.355 1.357 1.359 1.360 1.362 1.364 1.366 1.367 1.369
1.342 1.347 1.348 1.350 1.351 1.353 1.354 1.356 1.358 1.359 1.361 1.362 1.364 1.366
1.339 1.343 1.345 1.346 1.348 1.349 1.350 1.352 1.353 1.355 1.356 1.358 1.359 1.361
1.336 1.340 1.342 1.343 1.345 1.346 1.347 1.349 1.350 1.352 1.353 1.355 1.356 1.357
1.335 1.339 1.340 1.342 1.343 1.345 1.346 1.348 1.349 1.350 1.352 1.353 1.354 1.357
1.335 1.339 1.340 1.342 1.343 1.344 1.346 1.348 1.349 1.350 1.352 1.353 1.354 1.357
1.334 1.338 1.339 1.340 1.342 1.343 1.344 1.346 1.347 1.349 1.350 1.352 1.353 1.355
1.333 1.337 1.338 1.340 1.341 1.342 1.344 1.345 1.347 1.348 1.350 1.351 1.352 1.354
1.332 1.336 1.337 1.339 1.340 1.341 1.342 1.344 1.345 1.347 1.348 1.350 1.351 1.352
Table 4. The effective refractive indices at zero concentration and the specific refraction increments for the deoxygenated (Hb) and oxygenated hemoglobin (HbO2 ) as determined from the slope of the curves in figure 1.
Wavelength (nm) 401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5 n0 1.345 1.343 1.340 1.337 1.336 1.336 1.334 1.334 1.330 0.146 0.177 0.154 0.148 0.147 0.147 0.144 0.146 0.140 α, Hb (ml g−1) α, HbO2 (ml g−1) 0.170 0.163 0.150 0.150 0.147 0.148 0.144 0.145 0.143
hemoglobin between 486 and 707 nm. There is a difference, however, at 402 and 436 nm, which can be explained by different positions of the Soret bands of deoxygenated and oxygenated hemoglobin. Compared with the Soret peak of deoxygenated hemoglobin, the Soret peak of oxygenated hemoglobin is shifted to the ultraviolet region. The anomalous dispersion in this region determines the behavior of the refractive index of deoxygenated hemoglobin. Our measurements, therefore, do not show any significant difference between deoxygenated and oxygenated hemoglobin in the visible range for the wavelengths away from the Soret absorption bands. The linear dependence between the refractive index and the concentration (2) is valid not only in the concentration range used in our experiments but also for higher concentrations (Friebel and Meinke 2006). We experimentally observed such a linear dependence for solutions of methemoglobin in water with the hemoglobin concentrations up to 280 g l−1 . Figure 2(b) shows the spectrum of refractive indices at 320 g l−1 , which corresponds to the physiological concentration of hemoglobin within the erythrocytes, calculated using (2) and the values from table 4. The region of anomalous dispersion due to the Soret band of the deoxygenated hemoglobin (orange circles and line in figure 2) can be clearly seen. On the other hand, the change of the refractive index due to the Q-band (with the maximum at 556 nm) is almost
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(a)
(b)
Figure 1. The measured values of the refractive index (dots) depend linearly on the concentration at all wavelengths both for (a) deoxygenated and (b) oxygenated hemoglobin. The black lines are calculated using the least-squares method. From the slope of the lines, we determined the specific refraction increments (see table 4) from (2).
indistinct. Instead, anomalous dispersion is seen for deoxygenated hemoglobin between 633 and 656 nm, but because the difference between the corresponding values of the refractive index is only 0.001, it can be attributed to experimental error. For oxygenated hemoglobin (black circles and lines in figure 2), the dispersion is normal for the whole wavelength range. The values of the refractive indices of oxygenated and deoxygenated hemoglobin differ considerably only at 402 and 436 nm, and they differ little from each other for the rest of the wavelength range, in agreement with the behavior at lower concentrations (compare with figure 2(a)). We will now compare our results with those available in the literature. At the wavelength of 589 nm and the concentration of 320 g l−1 , our calculated value of the refractive index is 1.383 for both hemoglobins, whereas the value given by Friebel and Meinke (2006) for oxygenated hemoglobin is 1.418 and that given by Barer (1957) is 1.394. Our value is lower than the other two, although the difference between our and Barer’s results, 0.011, is two times smaller than the difference between the results of Barer and Friebel and Meinke (0.024). Barer’s value for the specific refraction increment is 0.193 ml g−1 , whereas our value for the oxygenated hemoglobin is 0.147 ml g−1 . For the hemoglobin concentration of 64.5 g l−1 at 25 ◦ C, Jin et al (2006) reported the value of the refractive index of 1.335 at 632.8 nm, whereas our value is about 1.343 at the same wavelength. At 633 nm, Friebel and Meinke measured the refractive index of 1.360 for the hemoglobin solution with the concentration of 104 g l−1
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(a)
(b)
Figure 2. (a) Measured values of the refractive index of deoxygenated (Hb, orange), and oxygenated (HbO2 , black) hemoglobin for the concentration of 100 g l−1 . (b) Refractive index for the deoxygenated and oxygenated hemoglobin at a concentration of 320 g l−1 calculated using the model functions. The lines serve as a guide for the eyes.
(Friebel and Meinke 2006). This value is 0.011 higher than our results for the hemoglobin concentration of 100 g l−1 at 632.8 nm (see tables 2 and 3). Faber et al (2004) measured the refractive index of oxygenated and deoxygenated hemoglobin solutions at 800 nm as 1.392 for oxygenated hemoglobin and 1.388 for deoxygenated hemoglobin with the concentration of 93 g l−1 . Their difference of 0.004 between the refractive indices of oxygenated and deoxygenated hemoglobin is much larger than would be expected from our measurement. Moreover, the values obtained by Faber et al are much higher than our results: our refractive measurements give 1.347 for both oxygenated and deoxygenated hemoglobin at 706.5 nm for the concentration of 100 g l−1 . As can be seen, our results differ from those reported in the literature at various wavelength and concentrations. There is, however, no agreement also between the earlier results. The discrepancy between different experiments can be due to different methods of extracting hemoglobin from fresh blood samples. In contrast, we have used hemoglobin prepared from a commercially available chemical reagent. The advantage of this method is that it allows us to obtain reproducible results that could be compared between different research groups. Our results could be useful for estimating the refractive index of blood and hemoglobin in erythrocytes. The concentration of hemoglobin inside erythrocytes is 250–350 g l−1 (Meinke et al 2011). Hemoglobin in erythrocytes is dissolved in intracellular fluid supposed to have a higher refractive index than that of water (for example, the refractive index of cytoplasm is about 1.350–1.367 at the wavelengths of 400–700 nm (Duck 1990)). Our calculations for the hemoglobin concentration of 320 g l−1 (as it is in erythrocytes) give the value of the refractive
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index of about 1.380 for the wavelengths in the range of 600–700 nm. Inside erythrocytes, hemoglobin at this concentration is supposed to have the refractive index value slightly higher than 1.380 due to the contribution of the refractive index of the intracellular medium. Human whole blood consists of about 40–45% erythrocytes and 55–60% plasma. The refractive index of blood plasma varies from 1.358 at 400 nm to 1.344 at 700 nm (Cheng et al 2002, Meinke et al 2011). The membrane of erythrocyte has a slightly higher refractive index than plasma (Barer 1957), and the refractive index of erythrocyte is mainly determined by the hemoglobin concentration inside the erythrocyte. The refractive index of whole blood can be estimated using the Gladstone–Dale equation (Fikhman 1967) nblood = ne Ve + np Vp ,
(3)
where ne and np are the refractive indices of erythrocytes and plasma, respectively, and Ve and Vp are the corresponding volume fractions. Because experiments in the field of tissue optics are often being done in the near-infrared region, estimating the refractive index of hemoglobin in this range could be important for practical applications. Although our measurements were done in the visible range, the wavelength dependence of the refractive index can be extrapolated to the near-infrared region as there are no noticeable absorption peaks in this region and, consequently, anomalous dispersion do not influence significantly on index values (Friebel and Meinke 2005). 4. Conclusions The measured values of the refractive index cover the whole visible range. As our results indicate, there are no significant differences between the refractive index of deoxygenated and oxygenated hemoglobin in the visible range for the wavelengths beyond the regions of anomalous dispersion. Being directly measured, our results can be used for cross validation of results obtained by indirect methods. In particular, they can serve for resolving the controversy of using the Kramers–Kronig relations to obtain the real part of the refractive index of hemoglobin from its imaginary part or absorption spectra (Faber et al 2004, Friebel and Meinke 2005). The model functions derived can be used to determine the refractive index for arbitrary values of the concentration within the range where equations (1) and (2) are valid. This range includes the physiological concentration of hemoglobin both in blood (140 g l−1 ) and in erythrocytes (320 g l−1 ), which shows the potential of the model functions for clinical applications. Acknowledgments OZ and AD acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the framework of the Excellence initiative. VT and OZ were partly supported by grant PHOTONICS4LIFE-FP7ICT-2007-2 and the governmental contracts of the RF 02.740.11.0770 and 02.740.11.0879. References Barer R 1957 Refractometry and interferometry of living cells J. Opt. Soc. Am. 47 545–56 Cheng S, Shen H Y, Zhang G, Huang C H and Huang X J 2002 Measurement of the refractive index of biotissue at four laser wavelengths Proc. SPIE 4916 172–6 Dalziel K and O’Brien J R P 1961 The kinetics of deoxygenation of human haemoglobin Biochem. J. 78 236–45 Duck F A 1990 Physical Properties of Tissue: A Comprehensive Reference Book (London: Academic)
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Faber D J, Aalders M C G, Mik E G and Hooper B A 2004 Oxygen saturation-dependent absorption and scattering of blood Phys. Rev. Lett. 93 028102 Fabry M and Old J M 2009 Laboratory methods for diagnosis and evaluation of hemoglobin disorders Disorders of Hemoglobin ed M H Steinberg et al (Cambridge: Cambridge University Press) chapter 28, pp 656–86 Fikhman B A 1967 Microbiological Refractometry (Moscow: Medicine) Friebel M and Meinke M 2005 Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements J. Biomed. Opt. 10 064019 Friebel M and Meinke M 2006 Model function to calculate the refractive index of native hemoglobin in the wavelength range of 250–1100 nm dependent on concentration Appl. Opt. 45 2838–42 Jin Y L, Chen J Y, Xu L and Wang P N 2006 Refractive index measurement for biomaterial samples by total internal reflection Phys. Med. Biol. 51 371–9 Meinke M C, Friebel M and Helfmann J 2011 Optical properties of flowing blood cells Advanced Optical Flow Cytometry: Methods and Disease Diagnoses ed V V Tuchin (Weinheim: Wiley-VCH) chapter 5, pp 95–129 Prahl S A 1999 http://omlc.ogi.edu/spectra/hemoglobin/index.html Rappaz B, Barbul A, Emery Y, Korenstein R, Depeursinge C, Magistretti P J and Marquet P 2008 Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer Cytometry A 73 895–903 Thormahlen I, Straub J and Grigull U 1985 Refractive index of water and its dependence on wavelength, temperature and density J. Phys. Chem. Ref. Data 14 933–45 van Kampen E J and Zijlstra W G 1965 Determination of hemoglobin and its derivatives Adv. Clin. Chem. 8 141–87
