Hemoglobin plus myoglobin concentrations and near infrared light pathlength in phantom and pig hearts determined by diffuse reflectance spectroscopy

Analytical Biochemistry 382 (2008) 107–115

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Hemoglobin plus myoglobin concentrations and near infrared light pathlength in phantom and pig hearts determined by diffuse reflectance spectroscopy Eugene Gussakovsky a,*, Olga Jilkina a,b, Yanmin Yang b, Valery Kupriyanov a,b a b

Institute for Biodiagnostics, National Research Council Canada, 435 Ellice ave, Winnipeg, Manitoba, Canada R3B 1Y6 Faculty of Medicine, University of Manitoba, Winnipeg, Manitoba, Canada R3E 3P5

a r t i c l e

i n f o

Article history: Received 12 June 2008 Available online 31 July 2008 Keywords: Hemoglobin and myoglobin NIR light diffuse reflectance First derivative Turbid media Cotton wool phantom Cardiac tissue

a b s t r a c t To noninvasively determine absolute concentrations of hemoglobin (Hb) plus myoglobin (Mb) in cardiac tissue by means of regular near infrared (NIR) light diffuse reflectance measurements, a first derivative approach was applied. The method was developed to separately calculate oxygenated and deoxygenated [Hb + Mb] as well as an effective pathlength, which NIR light passes through in the tissue between optodes. Applying a cotton wool-based phantom, which mimics muscle tissue, it was shown that the intensity of the pseudo-optical density first derivative depends linearly on both oxygenated and deoxygenated Hb concentration, thereby validating the Lambert–Beer law in the range of 0 to 0.25 mM tetrameric Hb. A high correlation (R = 0.995) was found between concentrations of Hb loaded onto the phantom and those determined spectrophotometrically, thereby verifying the first derivative method validity. The efficiency of the method was tested using in vivo pig hearts prior to and after ischemia initiated experimentally by left anterior descending artery branches occlusion. The results showed that the total [Hb + Mb] was 0.9–1.2 mM heme, the average tissue oxygen saturation was approximately 70% (which reduced to nearly 0% after occlusion), and the NIR (700–965 nm) light pathlength was 2.3 mm (differential pathlength factor [DPF] = 2.7–2.8) in a living heart tissue. Crown Copyright Ó 2008 Published by Elsevier Inc. All rights reserved.

Determination of the absolute concentration of hemoglobin (Hb)1 and myoglobin (Mb) in muscle tissues by means of transmittance spectrophotometric methods is difficult because of the high turbidity of the medium. To this end, various modifications of the Lambert–Beer law have been elaborated to extract pure optical density related to Hb and Mb [1]. Variants of the Lambert–Beer law have been applied to diffuse reflectance of light in the visible and near infrared (NIR) regions [2–5]. Besides the optical density problem, the Hb/Mb absolute concentration determination requires knowledge of the light pathlength (L). It has been proposed to determine L either by means of the diffuse reflectance measurements in the water or neodymium chelates absorption bands [6,7] or by frequency domain spectroscopy, allowing the determination of a direct time of the light traveling from the emitting optodes to the collecting optodes [3,4,8,9]. However, the L determination was a procedure separate from the Hb and/or Mb concentration measurement, which may * Corresponding author. Fax: +1 204 984 7036. E-mail address: [email protected] (E. Gussakovsky). 1 Abbreviations used: Hb, hemoglobin; Mb, myoglobin; NIR, near infrared; CW, cotton wool; LAD, left anterior descending artery; VIS, visible; DPF, differential pathlength factor; POD, pseudo-optical density; PBS–CW, 10.6% CW soaked in phosphate-buffered saline; HbO2–CW, 10.6% CW loaded with oxygenated Hb in PBS; deoHb–CW, 10.6% CW loaded with deoxygenated Hb in PBS; MetHb, methemoglobin; totHb, total Hb; OSP, oxygen saturation parameter.

be performed using various invasive biochemical approaches (e.g., see Refs. [10–13]). Accordingly, it has been difficult to use any spectrophotometric method for absolute Hb and Mb determination in muscles or other turbid media. A potential advantage of such methods is that they may be noninvasive and convenient for some tasks when a destructive approach (e.g., biopsy during surgery) is not desirable. In general, a spectrophotometric approach allows measuring the products of concentration and light pathlength, [Hb]  L. Deconvolution of this product should obviously provide an opportunity of simultaneous determination of absolute Hb/Mb concentrations and light pathlength, which may, in general, contain information on the tissue structure. Steady-state diffuse reflectance spectroscopy as a variant of a spectrophotometric approach for turbid media that takes into account both the direct spectra and their second derivatives has been developed (e.g., see Ref. [2]). Recently, we applied a first derivative of the diffuse reflectance spectra approach to determine the light pathlength in a phantom and white skeletal muscles in the absence of Hb [7]. In the current work, we developed a procedure based on the first derivative of the diffuse reflectance spectrum, allowing simultaneous determination of the absolute concentration of oxygenated and deoxygenated Hb + Mb, oxygen saturation of Hb + Mb, and NIR light pathlength in cardiac muscle tissue. The method

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was elaborated and verified using a muscle-mimicking phantom based on cotton wool (CW) [7] and then was tested on a living heart during surgery because, first, myocardial infarction is one of the leading causes of morbidity and mortality [14] and, second, instantaneous assessment of cardiac tissue perfusion and oxygenation immediately after coronary bypass surgery remains a major challenge. To this end, an NIR spectroscopic imaging technique was developed [15], allowing detection of areas of reduced perfusion and oxygenation in pig hearts in vivo following left anterior descending artery (LAD) occlusion. However, the absolute concentrations of Hb + Mb could not be determined by this method. Materials and methods Diffuse reflectance spectra Spectra were acquired in the dark background-corrected counts mode from 400 to 1100 nm with an increment of 1 nm and an integration time of 10 ms at either 25 °C (phantom) or 37 °C (heart) using a Control Developments model PDA-512 visible (VIS)/NIR spectrometer (South Bend, IN, USA). A total of 50 consecutive spectra in a set were averaged to increase the signal/noise ratio. Broadband VIS/NIR light from a fiber-optic illuminator Oriel model 77501 (Stratford, CT, USA) was transmitted to the sample through one arm of a bifurcated fiber-optic bundle. The common illumination/collection probe tip was placed in a contact with the sample perpendicular to its plane with zero distance between them, allowing the collection of predominantly diffuse reflected light through the other arm of the fiber bundle to the spectrometer. The light from the light source was delivered by a single fiber-optic filament of 650 lm diameter. The reflected light collection was provided by 36 fiber-optic filaments of 15 lm diameter randomly surrounding the illuminating filament. The numerical aperture for both emitted and collected optodes was measured to be 0.246. The mean effective distance between the illuminating and collecting filaments (d = interoptode distance) was determined to be 0.85 mm. The differential pathlength factor (DPF) was calculated as a light pathlength per interoptode distance, DPF = L/d. Pseudo-optical density (POD) spectra P(k) of phantom and heart were calculated according to the following equation:

PðkÞ ¼ log10

IðkÞ I0 ðkÞ

ð1Þ

in the wavelength range of 400 to 1100 nm, where I(k) and I0(k) are light intensities diffusely reflected from either a phantom or a heart and a reference, respectively. SpectralonÒ and CW served as the reference in the pig heart and phantom experiments, respectively. Practically, each I(k) spectrum needed a few seconds to be measured. The P(k) spectra were smoothed and then numerically differentiated, resulting in P0 (k) = dP/dk. No smoothing of the first derivative was applied. For calculations, a portion of the spectrum in a desired wavelength range was extracted from the total measured spectrum. The range of 650 to 965 nm was used for determination of absolute concentration of Hb in the phantom as well as light pathlength as described in Results and Discussion. For Hb + Mb and light pathlength in pig hearts, this wavelength range was 700 to 965 nm. The differential intensities at 970–1100 nm were too noisy to be used in the calculation. Smoothing, fitting, and calculations The raw diffuse reflectance spectra I(k) were smoothed, employing a Savitzky–Golay moving average approach [16] for 11 points. The P(k) spectra were calculated according to Eq. (1).

A v2 criterion of goodness-of-fit [17,18] was used to estimate statistical significance of the difference between the measured and calculated (fit) spectra. Following Meyer [17], the v2 parameter was calculated as

v2 ¼

n X ½yi  fi 2 i¼1

r2i

;

ð2Þ

where yi is a measured spectrum intensity at the ith wavelength, fi is its fit value, ri is a standard deviation for yi, and i refers to wavelength. In the phantom studies, i changed from 1 to n = 316, corresponding to the wavelength range from 650 to 965 nm with an increment of 1 nm. In the cardiac studies, n = 266 corresponded to the wavelength in the 700- to 965-nm range. A null hypothesis yi = fi is considered to be true if

1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2

v2 6 v2a ¼ ð 2n  3 þ z2a Þ2 :

ð3Þ

Here a critical v2a is given for n > 30 [18,19]. At a significance level of a = 0.05, we have z2a = 1.6 and v2a = 356, referring to the 650to 965-nm range (n = 316), or v2a = 304, belonging to the 700 965 nm range (n = 266). Absolute Hb concentration, light pathlength, and related calculations were performed with a program written using MatLab software (version 7.1, MathWorks, Natick, MA, USA). Phantom CW phantoms were constructed in a cylindrical well of 12.6 mm depth, 19.1 mm diameter, and 3.7 cm3 volume. Illumination and light collection were performed from the top of the phantom-packed well. At 12.6 mm depth, such turbid medium may be considered to be semi-infinite. The CW density was determined as its weight per the well volume (g/cm3). The Hb solution content was expressed as its volume per volume of well. The total volume of Hb solution-loaded CW was adjusted to the well volume by packing the wet CW. For each concentration of Hb, either oxygenated or deoxygenated, a new CW phantom was prepared. We used the following phantoms: 106 ± 1 mg/ml CW (10.6% CW) soaked in phosphate-buffered saline (PBS–CW), 10.6% CW loaded with oxygenated Hb in PBS (HbO2–CW), and 10.6% CW loaded with deoxygenated Hb in PBS (deoHb–CW). PBS contained 137 mM NaCl, 1.5 mM KH2PO4, 7.8 mM Na2HPO4, and 2.7 mM KCl (pH 7.4). Dry 10.6% CW was also used as a reference for the POD spectra determination. The deoHb–CW phantom was prepared in a few seconds before the I(k) spectrum measurement to avoid intensive reoxygenation (it is much faster in CW than in solution). Hb + Mb measurements in pig hearts in vivo Experimental myocardial ischemia was established in pig hearts. All pigs (24–26 kg, n = 5) received humane care in compliance with the guidelines of the Canadian Council on Animal Care [20]. Following acclimatization and fasting, preanesthesia was induced with midazolam, ketamine, and atropine (0.3, 20, and 0.02 mg/kg, respectively). After endotracheal intubation, the pig was ventilated mechanically with 60% oxygen and 40% air. The ventilator rate and tidal volume were adjusted to maintain the arterial pO2 of 350 mm Hg and pH at 7.4 to 7.5. Anesthesia was maintained with 1.5 to 2.0% isoflurane. A temperature probe was placed in the anus to monitor core temperature. A lateral thoracotomy was performed under sterile conditions, the pericardium was opened, and the LAD was isolated. A 1-mg/min/kg lidocaine infusion was administered to prevent the development of arrhythmias. The primary and secondary diagonal branches from

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Results and discussion HbO2 in a CW phantom The advantages of a CW-based phantom have been discussed elsewhere [7]. In the current work, we employed such a phantom for estimation of spectro–optical properties of Hb in a fibrous environment, which resembles muscle structure. Fig. 1A shows the POD spectrum of a 0.186-mM HbO2–CW phantom. For other concentrations of HbO2, the spectra were similar. HbO2 and water, as well as wavelength-dependent light scattering, should contribute to the spectrum. The POD intensity should depend linearly on the HbO2 concentration. However, its value at 680 nm (no water absorption) plotted versus HbO2 concentration (Fig. 1B) can hardly be estimated as a linear function with zero intercept (correlation coefficient R = 0.706, intercept 0.08 at POD values in the range of 0.08–0.30). A few reasons can explain the poor correlation. The Lambert– Beer law may be invalid in this case because of the high turbidity of the medium. Arakaki and coworkers [2] proposed that POD will depend linearly on the absorption coefficient, la(k), when la(k) > 1. As defined, la(k) is a product of a concentration and an extinction coefficient. In our case, HbO2 and deoHb molar extinction coefficient varies from 0.1 to 3 mM1 cm1 at 650 to 1050 nm [21,23], whereas total Hb (totHb) concentration was less than 0.25 mM, resulting in la(k) < 1, thereby explaining the nonlinear dependence of POD on [Hb]. However, the Lambert–Beer law may be valid in a modified form when POD contains a light-scattering component, s(k), and a constituent, ao, dependent on a sample and/or reference and independent of both HbO2 light absorption and wavelength. Dependence of ao on the sample/reference occurs because the sample and reference differ in both the chromophore content and the internal light-scattering (diffuse-reflecting) structure.

0.30

A

POD

0.25

0.20

0.15 650

750

850

950

1050

0.15

0.20

Wavelength, nm 0.3

B POD at 680 nm

the LAD were permanently occluded via surgical ligature, leading to an experimental ischemia. The diffuse reflectance spectra were measured from both intact and ischemic areas before ligation (four spectra) and just after ligation (two spectra from intact areas and two spectra from ischemic areas). The illumination/collection probe tip was placed against the areas devoid of large and medium-sized vessels. In most cases, six spectra from the intact areas and two spectra from the occluded areas were acquired for each heart. Molar extinction coefficient spectra of oxygenated and deoxygenated tetrameric Hb, as well as methemoglobin (MetHb) and water absorption coefficient spectrum, were taken from Matcher and coworkers [21,22] (650–1042 nm) and from Prahl and Zijlstra and coworkers [23,24] (250–1024 nm). The Hb spectra per heme were obtained by dividing intensities of these spectra by four (number of hemes in Hb). An HbO2 stock isotonic solution was prepared from heparinized pig blood according to Riggs’s method [25]. Absorption spectra of 8 to 12% HbO2 stock solutions in a 0.200-cm pathlength cuvette were measured in the wavelength range of 400 to 700 nm with a Beckman DU-650 spectrophotometer. The spectra demonstrated the presence of HbO2 without measurable contribution of MetHb (no band at 630 nm [24]) or deoHb (see Results and Discussion). The concentration of HbO2 solutions used in the CW phantom was calculated by employing molar extinction coefficients of 32.6 and 55.5 mM1 cm1 at 562 and 576 nm, respectively [22,23]. Deoxygenation of Hb was done by the addition of solid sodium dithionite to the HbO2 solution [26]. Residual oxygenated Hb in the sample was monitored in the light absorption spectrum.

0.2

0.1

0.0 0.00

0.05

0.10

[Hb] initial, mM Fig. 1. POD spectrum [POD = P(k)] of oxygenated Hb (0.186 mM) in a CW phantom. To calculate the POD spectrum, CW loaded with PBS was used as a reference (see Ref. [7] for details). The arrow shows that the spectrum has a minimum at 680 nm. (B) Plot of POD at 680 nm at various concentrations of Hb. The straight line represents the best linear fit with a correlation coefficient of 0.71.

In this case, the POD spectrum P(k) is

PðkÞ ¼ ½HbO2 eHbO2 ðkÞL þ lw ðkÞL þ sðkÞ þ ao ;

ð4Þ

where lw(k) is a water extinction coefficient and L is the light pathlength between the illuminating and light-collecting optodes of the diffuse reflection spectrometer. Although L in general is wavelength dependent, in a relatively short range of wavelengths it can be considered as wavelength independent in the NIR range. For gluteal and forelimb horse muscle, this was confirmed by the statistically insignificant difference of a differential pathlength factor at 744 to 860 nm [27]. The offset ao may reflect the sample-dependent structural inconsistency of the reference and the sample turbid media as well as, in part, the wavelength-independent contribution of the reference log10(Io). Although our CW phantom structures were similar for all samples with varied HbO2 concentrations, they were not identical. Therefore, POD here should depend on both HbO2 concentration and the structure of wet CW packed in the well (see Materials and Methods). Just this nonidentical packing determined the variation of ao. We assume that ao is wavelength independent and that dao/dk = 0. The first derivative of POD determined with dry CW as a reference may be expressed by

P’ ðkÞ ¼ ½HbO2 

deHbO2 dl ds Lþ wLþ : dk dk dk

ð5Þ

It does not contain an ao term and should not depend on CW packing variability; therefore, it should depend linearly on the HbO2 concentration if the Lambert–Beer law is valid. The P0 (k) spectra for 0.186 mM HbO2 (thin line 2 in Fig. 2A) or without HbO2 (bold line 1 in Fig. 2A) in PBS–CW with dry CW as a reference

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contain three aqueous bands (major band around 900–970 nm and two minor bands at 730 and 830 nm) [7] and a broad HbO2 band (thin line 2). If POD is determined relative to a PBS–CW phantom containing water, the water constituent is eliminated and Eq. (5) transforms to

P’ ðkÞ ¼ ½HbO2 

deHbO2 ds Lþ : dk dk

ð6Þ

Fig. 2B shows P0 (k) for 0.186 mM HbO2 in PBS–CW with PCS– CW as a reference. The deHbO2/dk spectrum of an HbO2 aqueous solution derived from the previously measured absorption spectrum of HbO2 [21] was adjusted to an HbO2 concentration of 0.186 mM and light pathlength L = 2.2 mm (see below):

0.0015

A

dP /d λ, nm-1

0.0010 1

0.0005 2

0.0000 -0.0005 -0.0010 -0.0015 650

750

850

950

1050

950

1050

wavelength, nm 0.0004

dP /d λ or d A/d λ, nm-1

B 0.0002

1 2

0.0000 -0.0002 -0.0004 -0.0006 650

750

850

over 750-800 nm

wavelength, nm

C 0.0004

l’s ðkÞ  sðkÞ  bk

0.0002

0 0.00

dA/dk = deHbO2/dk  [HbO2]  L  1.28. The factor 1.28 is described below. It allows equalizing dA/dk to the measured P0 (k) HbO2 spectrum at 750 to 800 nm. The adjusted HbO2 aqueous solution spectrum (bold curve 2 in Fig. 2B) has a shape similar to the measured P0 (k) spectrum. According to the v2 goodness-of-fit criterion, the difference between these two spectra is statistically insignificant because v2 = 163 is less than the critical v2a = 356. The minor differences were observed at 650–750 nm, at 830 nm, and at 930–960 nm. Obviously, a residual contribution of water absorption determines the bands at 730, 830, and 950 nm because of the CW effect on the diffuse reflectance. In addition, there is a small variation of the HbO2 absorption when aqueous solution is compared with the HbO2–CW phantom, which is similar to the difference of the absorption spectra of Hb in solution and tissue reported elsewhere [28]. The factor 1.28 also reflects such variation. The averaged intensity of the P0 (k) spectra over the 750- to 800nm range, hP0 (k)i of 0.186 mM HbO2 in PBS–CW versus either dry CW or PBS–CW (Fig. 2C) indeed depends linearly on the HbO2 concentration with high correlation coefficients of R = 0.973 and 0.981 for dry CW and PBS–CW, respectively. Therefore, P0 (k) obeys the Lambert–Beer law. The slopes of 1.73  103 mM1 nm1 are independent of the reference. However, the intercepts for both 9.3  105 and 5 1 1.8  10 nm are significantly different. POD determined versus dry CW contains both water absorption and light-scattering components hP0 dry(k) = l0w (k)L + dsdry/dki = 9.3  105 nm1, whereas the intercept determined versus PBS–CW reference consists of the light scattering only hP0 PBS(k) = dsPBS/dki = 1.8  105 nm1. Because dry and wet CW may have different light-scattering properties, dsdry/dk 6¼ dsPBS/dk. Indeed, assuming that the mean value of l0w (k) at 750–800 nm is hl0w (k)i = 1.14  104 cm1 nm1 as calculated from the water absorption spectrum [22], the difference between the intercept values for the two references reflects a significant difference in the light-scattering properties of dry CW and PBS–CW (dsdry/dkdsPBS/dk = hP0 dryihP0 PBSihl0w i L = 10.0  105 nm1, with L being estimated at 0.22 cm [see below]). The intercept for PBS–CW is close to zero [the standard deviation of 3.5  105 nm1 of hP0 dryi was higher than the intercept value of 1.8  105 nm1], reflecting the similarity of PBS–CW and HbO2– CW phantom structures. In general, either Mie or Rayleigh light scattering is nonlinear. It was assumed [5,7,8,29–32] that scattering in turbid media may be described by a power function l’s = bkn. The power n is supposed to be close to unity (n = 0.82 from Ref. [8] at 650–100 nm; n = 1.11 from Ref. [5] at 600–900 nm). Then a first approximation by the Taylor series l’s(k) may be presented by a linear function

0.05

0.10

0.15

0.20

[Hb] initial, mM Fig. 2. First derivative dP/dk = P0 (k) of POD spectrum of HbO2 (0.186 mM) in a 10.6% CW phantom determined when reference is dry CW (A) or PBS–CW (B). In panel A, the bold line (1) shows the spectrum of PBS, and the thin line (2) shows the spectrum of HbO2. In panel B, the thin line (1) shows the spectrum of 0.186 mM HbO2 in PBS–CW, and the bold line (2) shows a dA/dk = deHbO2/dk  [HbO2]  L  1.28, where deHbO2/dk is the first derivative of the HbO2 aqueous solution molar extinction coefficient determined elsewhere (see text). L = 2.2 mm (see text). A factor of 1.28 was used to adjust dA/dk to P0 (k) in the wavelength range of 750 to 800 nm (plateau). (C) Plot of the mean hP0 (k)i over the range of 750 to 800 nm at various concentrations of initial HbO2 loaded onto CW. Vertical bars show standard deviations. Filled circles and the thin line represent P0 (k) determined relative to dry CW (A). Open circles and the bold line represent P0 (k) determined relative to PBS– CW (B).

ð7Þ

when k 2 {650,1050}. A linear approximation of the light scattering in turbid medium ls0 = ak + b has been evaluated successfully [30,33–35]. The coefficient at k was found to be negative [26,30] as in s  bk. Then ds/dk = b. Therefore, Eq. (5) transforms to

P’ ðkÞ ¼ ½HbO2 

deHbO2 dl L þ w L  b; dk dk

ð8Þ

meaning that the light-scattering contribution to the first derivative is a wavelength-independent offset. deoHb in a CW phantom Hb was deoxygenated by the addition of dry dithionite to solution (see Materials and Methods). After loading deoHb into CW, reoxygenation appeared much faster than in solution, sometimes resulting in some HbO2 at the moment of the diffuse reflection

[Hb + Mb] and NIR light pathlength / E. Gussakovsky et al. / Anal. Biochem. 382 (2008) 107–115

measurement lasting 5 s. Therefore, it is not unreasonable to assume that the diffuse reflection spectrum may contain some portion of HbO2. Using the spectrum shape in the 500- to 600-nm region, we assigned the samples with a single band at 554– 556 nm to the deoxygenated form and samples with mainly two bands at approximately 540 and 575 nm to a mixture of HbO2 and deoHb. The NIR P0 (k) spectra of these two types of samples are shown in Fig. 3. Three bands of water were obvious in the spectra determined versus dry CW, whereas no water contribution was observed for the PBS–CW reference. Evidently, Eqs. (5), (6), and (8) are valid for deoHb if dedeoHb/dk substitutes for deHbO2/dk. Respectively, for deoHb, Eq. (8) transforms to

P’ ðkÞ ¼ ½deoHb

dedeoHb dl L þ w L  b; dk dk

ð9Þ

and for a mixture of HbO2 and deoHb Eq. (8) transforms to

P’ ðkÞ ¼ ½HbO2 

deHbO2 dedeoHb dl L þ ½deoHb L þ w L  b: dk dk dk

ð10Þ

111

where e0 HbO2, e0 deoHb, and l0 w are vectors–columns of n elements representing the first derivatives deHbO2/dk, dedeoHb/dk, and dlw/dk, respectively. Vector–column E has n elements equal to 1. Respectively, matrix M has four columns and n rows. The unknowns form a vector–column N = {n1, n2, n3, n4} of four elements: n1 = [HbO2]  L, n2 = [deoHb]  L, n3 = L, and n4 = b. Then Eq. (10) in the matrix form is

P ¼ M  N;

ð12Þ

where  denotes matrix multiplication. Solution of this equation gives all unknowns (n1, n2, n3, and n4) from which absolute concentrations of HbO2 and deoHb can be deduced easily as [HbO2] = n1/n3 and [deoHb] = n2/n3. Thus, the solution delivers absolute concentrations of HbO2, deoHb, and actual light pathlength L for this particular pair of sample plus optode as well as the scattering factor b. In practice, the MatLab software function lsqnonneg uses matrix M and vector P in Eq. (12) and provides the best least-squares solution N with a constraint that all unknowns are positive. Verification

Computational model If molar extinctions of the two forms of hemoglobin and the extinction of water are known, Eq. (10) may be considered as a linear combination of four components: [HbO2]  L, [deoHb]  L, L, and b with related factors. When P0 (k) is an n-component vector– column P (n is the number of wavelengths k taken in the P0 (k) spectrum), Eq. (10) becomes a system of linear equations of rank 4 with regard to four unknowns: [HbO2]  L, [deoHb]  L, L, and b with the matrix of

M ¼ ðe0HbO2 ; e0deoHb ; l0w ; EÞ;

ð11Þ

A

0.002

dP /d λ, nm -1

0.001 3

0.000 2

-0.001

1

-0.002 -0.003 650

dP /d λ or d A/d λ, nm-1

0.0010

B

750

850

950

1050

3

0.0005

Table 1 Composition and properties of Hb–CW phantoms

1

0.0000 -0.0005 -0.0010

2

-0.0015 -0.0020 650

Table 1 shows the results for different initial concentrations of HbO2 and deoHb in PBS–CW obtained with a homemade MatLab program based on Eq. (12). According to a v2 goodness-of-fit criterion, for all samples mentioned in Table 1, a difference between the fit and measured P0 (k) was insignificant because in all cases v2 < v2a . The HbO2 samples contained some deoHb but in negligible quantity of approximately 1–2% of the totHb pool. Because of this, we considered that the entire amount of Hb was in the oxygenated form only. Light pathlength varied from sample to sample of either HbO2 or deoHb, with a mean value of 2.2 ± 0.4 or 3.4 ± 0.9 mm, respectively, for the given optode geometry (DPFs = 2.6 ± 0.5 and 4.1 ± 1.0, respectively). A Student’s t-test indicates that the difference of L between HbO2–CW and deoHb–CW is confident (a < 0.05). The somewhat higher light pathlength in deoHb–CW phantom may result from the higher absorption of deoHb than of HbO2 (integral absorptions over 650–965 nm are 947 and 633 mM1cm1nm, respectively, according to the absorption spectra of the solutions [23]). We plotted the diffuse reflectance-measured concentrations of oxygenated [HbO2] and deoxygenated (dithionite-treated) [deoHb] hemoglobin as well as [totHb] = [HbO2] + [deoHb] versus total concentration of the initial hemoglobin, which was loaded onto the CW phantom. Such plots can directly verify the method if they

Parameter

HbO2–CW

deoHb–CW

[HbO2] (mM) [deoHb] (mM) [totHb] (mM) L (mm) DPF b  104

0.32–1.20 0.001–0.012 0.33–1.21 2.21 ± 0.48 2.60 ± 0.48 1.43 ± 0.51 36 ± 13 356 7

0 0.01–0.83 0.01–0.83 3.44 ± 0.86 4.05 ± 1.01 0.01 ± 0.04 33 ± 11 356 9

v2 750

850

950

1050

Wavelength, nm Fig. 3. First derivative dP/dk = P0 (k) of the POD spectrum of deoHb–CW with dry CW (A) or PBS–CW (B) as references. Thin curves 1 and 2 show measured representative spectra of deoHb–CW and partially oxygenated deoHb–CW, respectively. The bold curve 3 in panel A shows the spectrum of PBS–CW. The bold curve 3 in panel B is a deoHb P0 (k) spectrum calculated from the absorption spectrum of deoHb solution (see text).

Critical N

v2a

Note. Concentrations of Hb forms are in millimolars (mM) on a heme basis. HbO2, oxygenated Hb; deoHb, deoxygenated Hb; L, light pathlength in the 650- to 965-nm range. Differential pathlength factor (DPF) was calculated as a light pathlength per optode distance, DPF = L/0.85 (see Materials and methods). For the scattering parameter b, see Eqs. (8)–(10). The parameters were calculated from the P0 (k) spectra with dry CW as a reference. The v2 parameter and critical v2a values were calculated as described in Materials and methods.

[Hb + Mb] and NIR light pathlength / E. Gussakovsky et al. / Anal. Biochem. 382 (2008) 107–115

Applications to heart tissue The same type of analysis was applied to normal pig hearts in vivo where regional ischemia was induced (see Materials and methods for details). Cardiac tissue contains both deoxygenated and oxygenated Hb and Mb. Because Fe2+-containing heme determines the spectra of both Hb and Mb, their spectra differ insignificantly [36] and their distinction is nearly impossible. Therefore, in pig hearts, we consider a mixture of Hb and Mb as spectroscopically the same molecule (Hb + Mb). For the Hb–CW phantom, we used the Hb molar extinction spectra of the Hb tetramer, whereas myoglobin exists as a monomer. That is why in the case of heart tissue we should consider both Hb and Mb on the basis of heme content. The approach described above for the phantom now was applied for measurements of the absolute concentrations of HbO2 + MbO2, deo(Hb + Mb), and the light pathlength as well as the oxygen saturation parameter (OSP) = [HbO2 + MbO2]/[tot(Hb + Mb)] in control and damaged areas of pig hearts using the molar extinction coefficient of hemoglobin subunits containing a single heme [36]. Fe3+-containing MetHb may also occur in cardiac tissue in small concentrations. Fig. 5 shows the absorption spectrum of MetHb from Zijlstra and coworkers [24] and its first derivative. In the wavelength range of 650 to 700 nm, the derivative intensity of MetHb significantly exceeds the intensities of HbO2 and deoHb, and this may lead to measurable contributions of MetHb even at low concentrations. However, at wavelengths greater than 700 nm, the differential intensity vanishes. That is why we used the wavelength range of 700 to 965 nm in the cardiac studies instead of 650 to 965 nm for the phantom. Fig. 6 shows representative samples of both direct P(k) spectra and their first derivatives P0 (k) of intact and ischemic areas of pig hearts in vivo. The POD spectra indicate qualitatively that after occlusion a band at around 750 to 760 nm that belongs to deoHb increases, indicating a decrease in the tissue oxygen concentration because of interruption of O2 supply caused by artery occlusion. Differential spectra of intact and ischemic areas differ more significantly. The fitting procedure based on Eq. (12) revealed the HbO2 and deoHb concentrations as well as the light pathlength (Table 3). The v2 criterion of the goodness-of-fit indicated that the fit was satisfactory (v2 < v2a ). According to Table 3, occlusion resulted in an increase in the deoxygenated forms of Hb and Mb and in a reduction of the [tot(Hb + Mb)] (although the difference was found to be insignificant because of the data variation among different hearts, with the occluded/intact ratio definitely being < 1) and oxygen saturation parameter OSP. Light pathlength did not change with occlusion, probably because of the absence of the structural changes in cardiac tissue fol-

0.30

[HbO2] measured, mM

A 0.25 0.20 0.15 0.10 0.05 0.00 0.00

0.05

0.10

0.15

0.20

0.25

0.25

B [deoHb] measured, mM

are linear, have a slope equal to 1 and an intercept equal to zero because with these parameters of linear regression the y axis is identical to the x axis; that is, the concentration of Hb measured with the diffuse reflectance is equal to the initial concentration loaded onto the phantom. Fig. 4 and Table 2 show the results. In all cases, the linear regression had a high correlation coefficient and an intercept close to zero. The slope differed from unity by 19–28%. This may be caused by the effect of the phantom on the absorption spectrum of Hb at 650–965 nm. Such an effect probably is different for oxygenated and deoxygenated heme. It is obvious that to obtain the slope equal to unity, the P0 (k) spectra of HbO2 and deoHb should be divided by factors 1.28 and 0.81, respectively. Thus, the first derivative of the pseudo-absorbance spectrum allows using a Lambert–Beer law with respect to the light pathlength L and products [HbO2]  L and [deoHb]  L. Furthermore, the absolute concentrations of deoHb and HbO2 may be determined easily.

0.20

0.15

0.10

0.05

0.00 0.00

0.05

0.10

0.15

0.20

0.10

0.15

0.20

0.25

C [totHb] measured, mM

112

0.20

0.15

0.10

0.05

0.00 0.00

0.05

[Hb] total initial, mM Fig. 4. Concentrations of HbO2 (A), deoHb (B), and totHb (C) measured with a diffuse reflectance technique and the P0 (k) approach in HbO2–CW phantom, plotted versus initial [totHb] = [HbO2]. Initial concentrations were determined spectrophotometrically for the tetrameric form of Hb. P0 (k) was determined with dry CW as a reference. deoHb was obtained using sodium dithionite as described in Materials and methods. Open circles and dashed lines denote calculated values of the Hb concentration. Filled circles and solid lines represent calculated values corrected by the factors 1.28 for HbO2 (A) and 0.81 for deoHb (B). Panel C shows all samples of the dithionite-treated Hb pool that contained both oxygenated and deoxygenated Hb ([HbO2] + [deoHb]) (see Table 1). [HbO2] was corrected by the factor 1.28, and [deoHb] was corrected by the factor 0.81.

lowing several minutes of ligation. The POD intensity variation after the ligature was probably too small to affect the light pathlength. How reasonable are the heart tissue data? All findings mentioned above are typical for ischemic cardiac tissue when blood flow and oxygen delivery are reduced drasti-

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[Hb + Mb] and NIR light pathlength / E. Gussakovsky et al. / Anal. Biochem. 382 (2008) 107–115 Table 2 Parameters of linear regressions shown in Fig. 4 Hemoglobin

Correction

Factor(s)

Slope

Intercept

Correlation coefficient

HbO2 HbO2 DeoHb DeoHb TotHb

No Yes No Yes Yes

1 1.28 1 0.81 1.28 and 0.81

1.284 1.005 0.812 1.002 1.007

0.0007 0.0003 0.0075 0.0092 0.0089

0.991 0.995 0.994 0.994 0.995

Note. Regression for totHb includes both HbO2 and deoHb.

4

0.9

A

P (λ)

ε, mM-1cm-1

A 0.8

3

2

1

0.7 0.6

2

1 0.5 0 600

650

700

750

800

0.4 600

0.1

B

800

900

1000

1100

B 0.002

0

dP/d λ, nm-1

dε /d λ, mM-1cm-1nm-1

700

0.003

-0.1

α

0.001 1

-0.001 -0.2 600

β

650

700

750

800

-0.002 700

Wavelength, nm Fig. 5. Absorption spectrum (A) and its first derivative (B) of pig MetHb in solution. The direct spectrum was taken from Ref. [11]. A Savitsky–Golay moving average approach was applied before numerical differentiation. No smoothing was applied for the first derivative spectrum.

cally. After acute occlusion of the LAD branches, the downstream myocardium becomes immediately deoxygenated due to the depletion of oxygen by oxidative phosphorylation [37,38] and very low residual flow in pig hearts (collateral flow < 5% of the baseline [39]). Furthermore, blockage of the flow results in a dramatic decrease in blood pressure in the downstream vasculature, causing a decrease in blood volume [40]. This explains the observed trend of a decline in the [tot(Hb + Mb)] after artery blockage (Table 3). Absolute concentration of tot(Hb + Mb) in control areas in the heart samples was 1.2 mM heme. According to published data, the Mb content in pig hearts was estimated to be in the range of 0.36 to 0.39 mM [41,42] at a muscle density of 1.06 g/ml [43]. For other mammalian (e.g., rodent) hearts or cardiomyocytes, the Mb content was reported to vary in the same range of 0.15 to 0.32 mM [10,44–48]. In bird heart muscles, the Mb was determined to be in a range of 1 to 7 mg/g = 0.06 to 0.40 mM [49]. In skeletal muscles, the Mb concentration was measured to vary in the range of 0.5 to 4.7 mg/g = 0.03 to 0.26 mM, depending on the muscle type [50,51]. Based on NIR spectroscopy measurements [42], in pig hearts in vivo the Mb heme contribution to [tot(Hb + Mb)] was reported to be 46%. Thus, we have the total heme concentration of 0.8–0.9 mM in normal pig hearts, which is close to the data in Table 3 (1.2 mM).

750

2

800

850

900

950

1000

Wavelength, nm Fig. 6. (A) Representative P(k) spectra measured from intact areas (thin curve 1) and ischemic areas (bold curve 2) of pig hearts. (B) First derivative dP/dk (bold curves 2) and their best fit (thin curves 1) for intact areas (a) and ischemic areas (b).

Table 3 Parameters obtained by the fitting of the P0 (k) spectra measured in the wavelength range of 700 to 965 nm from the surface of five normal pig hearts in vivo Parameter

Intact area

Ischemic area

a

Ischemic/Intact ratio

[deo(Hb + Mb)] [HbO2 + MbO2] [tot(Hb + Mb)] OSP L (mm) DPF b  104

0.44 ± 0.23 0.78 ± 0.34 1.21 ± 0.40 0.63 ± 0.14 2.30 ± 0.42 2.71 ± 0.26 3.41 ± 2.06 112 ± 39 304 27

0.69 ± 0.15 0.26 ± 0.45 0.95 ± 0.45 0.17 ± 0.26 2.37 ± 0.60 2.79 ± 0.60 3.29 ± 1.84 89 ± 65 304 10

<0.01 <0.001 >0.05 <0.001 >0.05 >0.05

1.66 ± 0.45 0.23 ± 0.40 0.75 ± 0.21 0.24 ± 0.37 1.05 ± 0.20 1.05 ± 0.20 1.12 ± 0.69

v2 Critical N

v2a

5

Note. All concentrations of Hb are in mM of heme. [tot(Hb + Mb)] = [deo(Hb + Mb)] + [HbO2 + MbO2]. OSP = [HbO2 + MbO2]/[tot(Hb + Mb)] was calculated for each spectrum and then averaged. L, light pathlength; N, number of points on the surface of five hearts at which the P0 (k) spectra were measured. Differential pathlength factor (DPF) was calculated as a light pathlength per optode distance, DPF = L/0.85 (see Materials and methods). For scattering factor b, see Eq. (7). To obtain the ischemic/intact ratio, it was calculated for each of five hearts and then averaged. Parameter a is a significance level of the difference determined by a Student’s t-test (for a > 0.05, the difference is not significant).

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OSP determined as HbO2 + MbO2 per tot(Hb + Mb) was found to be at the 65–75% level for normal heart tissue. It depends on the intracellular Mb fraction and its oxygenation as well as the volume of arterial (>99% HbO2) and venous (50% HbO2) capillary blood. Assuming 50% oxygen saturation of the heart Mb [41] and 100/ 50% oxygenation of arterial/venous Hb in blood, a 70% OSP value in the intact area seems to be reasonable and agrees with the previously published data [15,40]. In the ischemic area, OSP was reduced to 0–30% due to very low blood flow [15,39] and hence oxygen delivery to the infarcted tissue, resulting in dissociation of O2 from Hb + Mb. Intraventricular blood did not interfere with the measurements because it was separated from the optode tip by the left ventricular wall thickness (>10 mm) exceeding the pathlength two- to fourfold. In addition, placement of the light guide away from the large vessels (2–3 mm diameter) eliminated potential spectra contamination from this source. Absolute values of light pathlength, L = 2.3 ± 0.4 mm in the intact area of the heart samples (Table 3), are close to the value measured for chicken breast muscles (L = 1.8 mm at 920–960 nm) [7], pig hearts (L = 4.4 ± 0.4 in the wavelength range of 680–975 nm at the emitting–collecting optode distance of 2 mm, DPF = 2.2) [6], and myocardium (L = 1.2–1.4 mm at 510–590 nm) [52]. Although the DPF in control areas of the heart is approximately two to three times lower than that reported for different horse muscles (DPF = 3.9–4.7 for forelimb, DPF = 5.6–6.2 for gluteal) [27], this difference may be caused by the different muscle structure of pig myocardium and horse leg muscles. Significant variations in the absolute concentration of tot(Hb + Mb), oxygenation, and light pathlength are possible, depending on many factors. Similarity of our data to those available in the literature (mentioned above) indicates that the proposed method gives reasonable results. Conclusion Application of the first derivative to the POD density spectrum of light diffuse reflectance from cardiac tissue in the wavelength range of 700 to 965 nm allows simultaneous determination of the oxygenated and deoxygenated [Hb + Mb], as well as light pathlength, when light is delivered to the tissue and collected by a fiber-optic probe. The approach was developed and verified using the CW phantom mimicking the muscle tissue using the same fiber-optic probe. Acknowledgments This work was partially supported by a Genomic and Health Initiative program, GHI-3 National Research Council Canada (NRCC). We are thankful to J.C.T. Rendell (Institute for Biodiagnostics, NRCC) for fruitful discussion. References [1] K.J. Jeon, S.J. Kim, K.K. Park, J.W. Kim, G. Yoon, Noninvasive total hemoglobin measurement, J. Biomed. Optics 7 (2002) 45–50. [2] L.S.L. Arakaki, M.J. Kushmerick, D.H. Burns, Myoglobin oxygen saturation measured independently of hemoglobin in scattering media by optical reflectance spectroscopy, Appl. Spectrosc. 50 (1996) 697–707. [3] A. Duncan, J.H. Meek, M. Clemence, C.E. Elwell, L. Tyszczuk, M. Cope, D.T. Delpy, Optical pathlength measurements on adult head, calf, and forearm and the head of newborn infant using phase resolved optical spectroscopy, Phys. Med. Biol. 40 (1995) 295–304. [4] D.A. Benaron, C.D. Kurth, J.M. Steven, M. Delivoria-Papadopoulos, B. Chance, Transcranal optical pathlength on infants by near-infrared phase-shift spectroscopy, J. Clin. Monit. 11 (1995) 109–117. [5] R.M.P. Doornbos, R. Lang, M.C. Aalders, F.W. Cross, H.J.C.M. Sterenborg, The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy, Phys. Med. Biol. 44 (1999) 967–981.

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