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Research Papers: Sensing

Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy in calves

[+] Author Affiliations
Tobias Lindbergh, Marcus Larsson

Linköping University, Department of Biomedical Engineering, Division of Biomedical Instrumentation, Linköping, 58185 Sweden

Zoltán Szabó

Linköping University, Department of Medicine and Health Sciences, Division of Drug Research, Anesthesiology, Linköping, 58185 Sweden

Henrik Casimir-Ahn

Linköping University, Department of Medicine and Health Sciences, Division of Cardiovascular Medicine, Thoracic Surgery, Linköping, 58185 Sweden

Tomas Strömberg

Linköping University, Department of Biomedical Engineering, Division of Biomedical Instrumentation, Linköping, 58185 Sweden

J. Biomed. Opt. 15(2), 027009 (April 19, 2010). doi:10.1117/1.3374050
History: Received May 07, 2009; Revised February 08, 2010; Accepted February 10, 2010; Published April 19, 2010; Online April 19, 2010
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Open Access Open Access

* Address all correspondence to: Tobias Lindbergh, Linköping University, Department of Biomedical Engineering, Linköping, 58185 Sweden. Tel:13-22-21-13; Fax:13-1-19-02; E-mail: tobi@imt.liu.se.

Intramyocardial oxygen transport was assessed during open-chest surgery in calves by diffuse reflectance spectroscopy using a small intramuscular fiber-optic probe. The sum of hemo- and myoglobin tissue fraction and oxygen saturation, the tissue fraction and oxidation of cytochrome aa3, and the tissue fraction of methemoglobin were estimated using a calibrated empirical light transport model. Increasing the oxygen content in the inhaled gas, 21%–50%–100%, in five calves (group A) gave an increasing oxygen saturation of 19±4%, 24±5%, and 28±8% (p<0.001, ANOVA repeated measures design) and mean tissue fractions of 1.6% (cytochrome aa3) and 1.1% (hemo- and myoglobin). Cardiac arrest in two calves gave an oxygen saturation lower than 5%. In two calves (group B), a left ventricular assistive device (LVAD pump) was implanted. Oxygen saturation in group B animals increased with LVAD pump speed (p<0.001, ANOVA) and with oxygen content in inhaled gas (p<0.001, ANOVA). The cytochrome aa3 oxidation level was above 96% in both group A and group B calves, including the two cases involving cardiac arrest. In conclusion, the estimated tissue fractions and oxygenation/oxidation levels of the myocardial chromophores during respiratory and hemodynamic provocations were in agreement with previously presented results, demonstrating the potential of the method.

Figures in this Article

A common reason for myocardial ischemia in heart patients is atherosclerotic coronary heart disease. Treatment often involves medication and/or surgical interventions, such as coronary stent implants and coronary artery bypass grafting (CABG). During the CABG procedure, the blood flow in the grafted vessels can be monitored during the surgery with ultrasound techniques.13 However, for proper contractility in the myocardial cells, not only adequate coronary blood flow and release of hemoglobin-bound oxygen in capillaries, but also sufficient mitochondrial oxygen uptake has to be ensured.46

Optical steady-state diffuse reflectance spectroscopy (DRS) has been used in several in vitro studies to study myocardial tissue status via spectral changes that are linked to chromophores involved in myocardial oxygen transport.710 A chromophore that reveals information about the mitochondrial oxygen uptake is the cytochrome aa3 (cyt aa3), also known as cytochrome c oxidase. This is an enzyme found in the mitochondrial inner wall and is the final electron transporter in the mitochondrial respiratory chain.11 A reduction of the cyt aa3 oxidation status causes a decrease in cellular adenosine triphosphate (ATP) production. Therefore, monitoring of cyt aa3 oxidation status can be of vital importance in clinical cardiovascular medicine, since ATP production is a prerequisite for proper mechanical function in the myocardium.12 Since the optical absorbances of reduced and oxidized cyt aa3 differ, DRS is suitable for detecting changes in cyt aa3 oxidation status. However, it is a nontrivial challenge to separate the absorption effects of cyt aa3 tissue fraction from that of hemoglobin,13 although attempts have been made to measure the cyt aa3 oxidation status in the presence of hemoglobin.14

The redox state of nicotinamide adenine dinucleotide (NADH) has been described by Mayevsky and Chance as another marker in measuring mitochondrial function.15 In that study, it was concluded that the best way of monitoring the NADH redox state is by fluorometry, and that when measurements are performed on biological systems, monitoring of the NADH redox state alone is not sufficient when determining the tissue vitality.

Until today, DRS techniques have relied on physiological provocations to establish reference situations involving complete oxidation and reduction of the cyt aa3,1618 while only relative changes in the oxidation status have been measured. Obviously, extreme physiological provocations for reference measurements are not possible in clinical patient monitoring. However, publication19 of the specific extinction coefficients of cyt aa3 enables quantification of cyt aa3 tissue fraction and oxidation status without the need for physiological provocations.

The aim of this study was to determine the tissue fraction and oxygenation of the myocardial hemo- and myoglobin, the tissue fraction and oxidation of cytochrome aa3, and the tissue fraction of methemoglobin during hemodynamic and respiratory provocations in calves undergoing open-chest surgery. A small intramuscular fiber-optic probe and calibrated DRS was used for measurements during variations in the oxygen fraction of inhaled gas, when unloading the heart using a left ventricular assisting device (LVAD) and, in two calves, during cardiac arrest at the end of the experiment.

Seven calves, 5months old, body weight ranging from 75to85kg, were used in this study. The animals were primarily enrolled in two different studies performed at the Animal Research Laboratory, Linköping University Hospital. Both studies were approved by the regional animal ethic committee.

The main purpose of the first study (group A) was to provide open-chest situations for ablation surgery training.

The main purpose of the second study (group B) was to implant and evaluate the performance of a left ventricle assisting device (LVAD) to be used in humans suffering from severe left ventricle heart failure.

In both studies, the calves were premedicated with xylazine hydrochloride (0.15mgkg) and atropine sulfate (0.06mgkg). A central venous catheter was inserted into the external jugular vein for administration of fluids and medication. Pentobarbital sodium (2mgkg) was used for induction of anesthesia, and a tracheotomy was carried out to allow mechanical ventilation. Anesthesia was maintained with intravenous fentanyl (10μgkgh) and pentobarbital sodium (2mgkgh).

Surgical Technique

Exposure of the heart was performed with a midline sternotomy. In group A, immediately after the sternotomy, the intramuscular fiber-optic probe was placed at a depth of approximately 5mm in an area of the left ventricle wall supplied by the left anterior descending (LAD) artery. The probe was fixated by epicardial suturing in order to minimize movement artifacts.

In group B, extracorporeal circulation (ECC) was established after the sternotomy, and the aorta was cross-clamped together with antegrade cardioplegia infusion according to routine clinical procedures. The LVAD was implanted in the apex of the left ventricle. The aorta cross-clamp was then removed, and the LVAD was set to 6000rpm. The intramuscular fiber-optic probe was then positioned identically as in animals in group A. For details about the implantation, see Hübbert et al. 20 A schematic drawing of the probe, including the dimensions, and the probe placement in both group A and group B animals are shown in Fig. 1.

Grahic Jump LocationF1 :

(a) Probe design, indicating the dimensions of the probe tip. The hatched fiber indicates the emitting fiber. (b) Fiber-optic probe placement in animals from group A. (c) Fiber-optic probe placement in animals from group B, including the LVAD. The probe placement is highlighted with a white arrow.

Equipment

A multichannel spectrometer ( AvaSpec 2048-5-RM, Avantes BV, Eerbeek, The Netherlands ) operating in the visible wavelength region (400to900nm, grating: VB 600linesmm), was used. Access to the tissue was gained through a custom-built fiber-optic probe containing one emitting and one receiving step-index multimode fiber with a core/cladding diameter of 200230μm and a numerical aperture of 0.37. The optical fibers were inserted into a slightly bent syringe cannula with a diameter of 800μm (Fig. 1, left panel). The receiving fiber was positioned adjacent to the illuminating fiber at a center–center separation of 230μm. An additional fiber, guiding light directly from the lamp to the spectrometer, was used for registering the spectrum of the light source. In-house designed algorithms and software were developed for data recording and analysis, using LabView 6.1 (National Instruments, Austin, Texas), and MATLAB 7.5 (Mathworks, Inc., Natick, Massachusetts), respectively.

Protocols and Spectral Recordings

For each measured spectrum, a simultaneous registration of the lamp spectrum was performed. The integration time was not changed during each case, but varied from 200msto1000ms between calves.

After finishing the measurements on each subject, before disconnecting the probe from the spectroscope, three reference measurements were performed. As reference, a tightly packed sample of barium sulfate (BaSO4) powder with a reflectivity of above 98% in the visible wavelength range was used. The probe was vertically lowered approximately 1cm into the powder, allowing no surrounding light to enter. Three consecutive 10-s measurements were performed. Last, the lamp was turned off, and a dark spectrum (D) was registered.

Group A (provocations with changes in FI,O2)

Five calves, denoted A1 to A5, were subjected to this protocol. After placement of the fiber-optic probe, at least 10min was allowed to achieve stable heart rhythm as assessed by visual inspection of the ECG signal. In calves A1 and A2, the surgical training protocol was carried out before the spectroscopic measurements in order to enable measurements during cardiac arrest in the end of the experiment. In calves A3 to A5, measurements were performed immediately after the 10-min stabilization phase and before the surgical training.

The fraction of inspired O2(FI,O2) was varied in three different steps, 21%, 50%, and 100%, respectively, with 3-min duration per phase. Spectra were measured continuously during the FI,O2 variations. In cases A1 and A2, registrations of spectra during 3to4min after initiation of cardiac arrest in the end of the experiment were also performed.

Group B (provocations with changes in LVAD speed and FI,O2)

Two calves, denoted B1 and B2, were subjected to this protocol. Similar to the group A protocol, at least 10min of stable heart rhythm was allowed after placement of the fiber-optic probe.

In calve B1, the FI,O2 was first held constant at 100%, while the speed of the LVAD was varied in three different steps, 6000rpm, 7500rpm, and 10,000rpm, with 1-min duration per phase. After switching from 6000rpmto7500rpm, and from 7500rpmto10,000rpm, 30s was allowed before spectra were measured.

After the 1-min duration with the LVAD speed at 10,000rpm, the FI,O2 was then varied in four steps; 50%, 21%, 50%, and 100%, with 1-min duration per phase. During the different FI,O2 levels, spectra were measured continuously.

In calf B2, the LVAD speed was held constant at 7500rpm throughout the experiment, and FI,O2 was varied in three different steps, 21%, 50%, and 100%, with 1-min duration per phase.

Spectral Preprocessing and System Calibration

First, all unprocessed measurement spectra Mraw were dark-corrected by subtracting the detector dark noise spectrum, D, which was registered immediately after each measurement series. The dark-corrected spectra (MrawD) were then filtered and resampled in three preprocessing steps: first, the spectrum was equidistantly up-sampled to a resolution of 0.1nm; second, high-frequency noise and aliasing effects were removed using a phase-invariant low-pass filter (Butterworth of order 4) with a normalized cutoff frequency of 0.02; and third, the spectra was down-sampled to a resolution of 1nm and limited to the wavelength region 500to800nm. Visual inspection of the residuals when comparing unfiltered and filtered data displayed only stochastic noise with no trends or patterns. To eliminate influences from changes in lamp intensity and color, all preprocessed measurement spectra were normalized by simultaneously recorded and preprocessed lamp spectra. The unprocessed white reference measurements (Mwhiteraw) were identically preprocessed and normalized, and in addition, averaged over time in order to obtain a single white reference spectrum. Last, the lamp-normalized measurement spectra were white-corrected by dividing with the lamp-normalized time-averaged white spectra. The complete normalization process is described in Eq. 1:Display Formula

1Mheartnorm=(MheartrawDheart/Mlamp,heartrawDheart)MwhiterawDwhite/Mlamp,whiterawDwhitet,
where t denotes averaging over time. The preprocessed and normalized spectrum Mheartnorm was used in the analysis of myocardial tissue status.

The method used for calibration was originally described by Jacques21 and has, with some modifications, been used by other authors.2223 The details are described in Häggblad et al. ,22 and only a brief overview is given here. The method utilizes a modified Beer-Lambert model that takes both absorption and scattering into account when describing the light transport, T, in tissue. The expression is given in Eq. 2:Display Formula

2T(μa,μs)=Kexp(μaL),
where K=a+bμs+cμs2, and L=d+eμs+fμs2, with a to f being constants determined in a calibration procedure involving measurements on liquid optical phantoms based on milk (scatterer), ink (absorber), and distilled water. The optical properties of the phantom grid were μs=[12348]λ=632.8nmmm1, μa=[00.010.050.10.20.40.81.6]λ=632.8nmmm1. The anisotropy factor, g, of milk at 632.8nm was set to 0.84 according to a previous study,24 resulting in μs=[0.160.320.641.28]λ=632.8nmmm1. The calibrated light transport model was denoted Tcal.

Tissue Chromophore Selection and Spectral Analysis

The major chromophores in myocardial tissue are oxygenized and deoxygenized hemoglobin and myoglobin (HbO2, Hb, MbO2, and Mb, respectively), water (W), and fat (lipid).7,14,22 In addition to the major chromophores described earlier, it has been shown that methemoglobin (metHb) and changes in oxidation status of cyt aa3 in the myocardium can be detected by DRS.10,18,25 To investigate whether inclusion of these additional chromophores resulted in a substantially improved model, two different setups were evaluated: one with only the major chromophores (Hb, HbO2, Mb, MbO2, and W) included in the absorption model (model I); and one including, in addition to the major chromophores, metHb and the oxidized (cyt aa3,ox) and reduced (cyt aa3,red) form of cyt aa3 (model II). In this study, lipid absorption was not included in the light transport model because of its very low intramuscular concentration2627 compared to the epicardial fat layer.22 According to several studies, the water content was set to 75% (Refs. 2122,28). Because of the very similar absorption spectra of hemoglobin and myoglobin (Mb is red-shifted 2to4nm compared to Hb), only the sum of the tissue fractions of these two chromophores was determined. However, to account for this shift, hemoglobin absorption spectra, with an adaptive wavelength transition of ±5nm, was used in our absorption model [Eq. 3]. The adaptive transition was implemented as a fitting parameter when solving the inverse problem. Equation 3 shows the expression for the total myocardial tissue absorption (μa,heart) for model II. The μa expression for model I is obtained by forcing fcytaa3 and fmetHb to be equal to zero.Display Formula

3μa,heart(λ)=fHb+Mb[SHb+Mbμa,HbO2+(1SHb+Mb)μa,Hb]+fcytaa3[Ocytaa3μa,cytaa3,ox+(1Ocytaa3)μa,cytaa3,red]+fmetHbμa,metHb+0.75μa,W.
In Eq. 3, fHb+Mb is the Hb+Mb tissue fraction, SHb+Mb is the Hb+Mb oxygen saturation, fcytaa3 is the cyt aa3 tissue fraction, Ocytaa3 is the oxidation status of cyt aa3, and fmetHb is the metHb tissue fraction. It should be noted that absorption data is often provided in terms of the specific extinction coefficient, μe. The conversion from μe to μa can be found in Sec. 6.

The reduced scattering coefficient (μs) was modeled according to a previous study by Häggblad22:Display Formula

4μs(λ)=αλβ700β,
where α and β are the fitting parameters.

By combining Tcal and Eq. 3, expressions for light transport in myocardial tissue are obtained for both models and are denoted Tcal,I and Tcal,II, respectively. The unknown parameters in Eqs. 34 (fHb+Mb, SHb+Mb, fcytaa3, Ocytaa3, fmetHb, α, and β) were determined by minimizing the expressions Tcal,IMheartnorm1 and Tcal,IIMheartnorm1 in a least-squares sense using the Levenberg-Marquardt algorithm. The Levenberg-Marquardt algorithm has been shown useful when solving nonlinear systems in a least-squares sense.29

The model spectra giving the optimum solutions were denoted Tcal,I* and Tcal,II*, respectively. For both models, visual inspection of Tcal*Mheartnorm1 was performed, and the goodness of fit was evaluated by calculating the Pearson product-moment correlation coefficient R2. Visual inspection of Tcal*Mheartnorm1 is a very intuitive way of identifying wavelength interval where the model fails to fit the measured data. In turn, this reveals information about possible missing chromophores in the light transport model.

The absorption data of hemoglobin and water were compiled from Zijlstra et al. and Buiteveld et al. ,3031 respectively. The absorption data for cyt aa3,ox and cyt aa3,red were compiled from the BORL home page,19 and absorption data for metHb was compiled from Zijlstra et al. 30 As the cyt aa3 absorption data were not available for wavelengths shorter than 520nm (Ref. 19), while the sensitivity of the spectrometer was considered too poor above 800nm, the spectral analysis was limited to the wavelength region 520to800nm.

In group A, spectra from the last minute of each FI,O2 level were averaged over time, and the curve-fitting was applied on the resulting spectra. In group B, spectra from the last 10s of each FI,O2 level and LVAD speed were averaged over time, and the curve-fitting was applied on the resulting spectra.

Statistical Analysis

Summarized data from groups A and B are calculated from fitting an average spectrum over the recording interval. The effect of FI,O2 on SHb+Mb (groups A and B) was evaluated on data from fitting individual spectra using an ANOVA repeated measures design, with calves and FI,O2 as factors. The effect of LVAD pump speed on SHb+Mb (calf B1) was evaluated on data from fitting individual spectra using an ANOVA repeated measures design, with subject and LVAD pump speed as factors.

Spectral Fitting

To illustrate the effect of adding cyt aa3 and metHb as chromophores in the light transport model, two spectra with varying SHb+Mb were selected. The curve-fits for model I (dashed black), model II (solid black), and the measured spectrum (solid gray) are shown in Figs. 23.

Grahic Jump LocationF2 :

(a) Representative measured spectrum (Mheartnorm) and model spectra (Tcal,I* and Tcal,II*) from calf A4, 100% FI,O2. (b) Tcal*Mheartnorm1.

Grahic Jump LocationF3 :

(a) Representative measured spectrum (Mheartnorm) and model spectra (Tcal,I* and Tcal,II*) from calf A4, 21% FI,O2 (gray). (b) Tcal*Mheartnorm1.

Model I yielded characteristic spectral misfits in the wavelength region 540to620nm. The use of model II resulted in improved spectral fitting, and the characteristic spectral misfits were eliminated. The calculated SHb+Mb using model II, compared to SHb+Mb from model I, differed only by 0.9% in the low SHb+Mb case (16.7% compared to 17.6%, respectively), and by 2.6% in the high SHb+Mb case (37.7% compared to 35.1%, respectively). The corresponding values for differences in SHb+Mb were 0.1% in both the high and low fHb+Mb case. The R2-values for the two different curve-fits versus measured spectra from the last minute of phase FI,O2=21% of group A calves showed that model II resulted in higher R2-values in all five cases (R2>0.99). Taken together, the improved R2-values and the eliminated spectral misfit characteristics in the residuals supported the choice of model II for further analysis. The wavelength shift in the Hb spectrum was on average in group A 2.2nm, 2.0nm, and 1.8nm during FI,O2=21%, 50%, and 100%, respectively. In group B, the average wavelength shift was 0.8nm.

Intramyocardial Light Scattering

The parameters α and β in Eq. 4 were averaged for each calf. In group A, μs ranged from 0.17mm1to2.28mm1, and β was in the range 2.43 to 2.84. Corresponding values for group B were 0.35mm1to2.28mm1(μs) and 2.18 to 3.91 (β). The average μs calculated for both groups was 0.79mm1 at 633nm and 0.45mm1 at 780nm, which are both commonly used laser wavelengths in biomedical optics.

Intramyocardial Tissue Chromophores

The results for chromophore tissue fractions and oxygenation/oxidation status are presented for each group (A and B) separately. In addition, for group B, results for the two calves are presented as separate cases.

Group A (provocations with changes in FI,O2)

As a representative case, Fig. 4 shows the time-resolved SHb+Mb for calf A2 during the variations in FI,O2.

Grahic Jump LocationF4 :

SHb+Mb in calf A2 as a function of time during three different FI,O2 and during cardiac arrest at the end of the experiment. The last minute in each FI,O2 phase is marked with vertical dashed lines.

As can be seen in Fig. 4, there is an increase in SHb+Mb that follows the FI,O2 changes from 21% via 50% to 100%. Approximately 60s after each change, the SHb+Mb reached a stable value, suggesting that the SHb+Mb during the last 60s of each FI,O2 level is an accurate interval when calculating average SHb+Mb values for each FI,O2.

Cyclic variations in SHb+Mb and fHb+Mb were detected throughout the measurements for all cases, although with varying magnitude of the variation. As an illustrative example of a case with high variation, fHb+Mb for the first 30s of calf A1, is shown in the left panel of Fig. 5. The right panel illustrates the correlation between fHb+Mb and SHb+Mb during the same period.

Grahic Jump LocationF5 :

(a) fHb+Mb as a function of time during the first 30s in calf A1. (b) Relationship between fHb+Mb and SHb+Mb including linear fitting (R2=0.94) during the first 30s in calf A1.

The left panel in Fig. 5 shows distinct periodical behavior of fHb+Mb. The number of local maxima was determined by visual inspection to 34 during 30s, giving a frequency of 68min1. This was compared to the heart rate observed by the ECG monitor, which was 67beatsmin1. The right panel displays an inverse relationship between fHb+Mb and SHb+Mb. The R2-value of the fitted straight line was 0.94. Negative correlations between fHb+Mb and SHb+Mb were found for four of five calves. Similarly, the relationship between the wavelength shift of the Hb spectrum and the SHb+Mb was evaluated in order to determine whether the wavelength shift could be related to Mb during blood volume pulsations. However, the correlation between the wavelength shift and SHb+Mb was slightly positive in calves A1 to A3, slightly negative in A4, and without any trend in A5.

fHb+Mb, SHb+Mb, fmetHb, and fcytaa3 average values (over the last minute) of each FI,O2 level are presented in Table 1. Ocytaa3 was on average 97%, ranging from 82% to 100%, and displayed no correlations with FI,O2. Thus, Ocytaa3 data were omitted from Table 1.

Table Grahic Jump Location
Average chromophore tissue fractions and SHb+Mb for the last minute of every FI,O2 level.
Table Footer NoteaFor calves A1 and A2, FI,O2 was set to 21% during the process of cardiac arrest in the end of the experiment. The average SHb+Mb was calculated during the time interval 3to4min after initiation of cardiac arrest.
Table Footer NotebNo average values were calculated—only two values.
Table Footer NotecCalculated values were smaller than 0.05%.

As can be seen in Table 1, calves A1 to A4 responded with an increase in SHb+Mb when FI,O2 increased. Increasing FI,O2 21% to 50% to 100%, gave average values for SHb+Mb=19±4%, 24±5%, and 28±8%, respectively. Hence, the average increases in SHb+Mb were 4.6% and 4.5% when FI,O2 was increased from 21% to 50% and from 50% to 100%, respectively. The effect of FI,O2 on SHb+Mb was significant (p<0.001, ANOVA). The SHb+Mb varied between calves (p<0.001, ANOVA), as did the response to FI,O2 (p<0.001, ANOVA). Calves A1 to A3 had a similar step-wise increase in their SHb+Mb, while for A4, a larger response was seen when FI,O2 increased from 50% to 100% than from 21% to 50%. For A5, SHb+Mb decreased when FI,O2 increased from 50% to 100%.

Group B (provocations with changes in LVAD speed and FI,O2)

The time-resolved SHb+Mb for calf B1 is shown in Fig. 6. It can be seen in Fig. 6 that the SHb+Mb did not reach stable levels during the O2 provocations (180to480s). For this reason, spectra from the 10 last seconds for every FI,O2 level were averaged when calculating the tissue fractions and SHb+Mb and Ocytaa3 levels of the chromophores. Ocytaa3 was on average 98%, ranging from 84% to 100% throughout measurements in calf B1, and displayed no correlations with FI,O2. The time-resolved SHb+Mb for calf B2 is shown in Fig. 7.

Grahic Jump LocationF6 :

SHb+Mb as a function of time during variations in LVAD speed and FI,O2 in calf B1. Note: Last 10s in each FI,O2 phase are marked with vertical dashed lines.

Grahic Jump LocationF7 :

SHb+Mb as a function of time during variations in FI,O2 during constant LVAD speed (7500rpm) in calf B2. Note: Last 10s in each FI,O2 phase are marked with vertical dashed lines.

A similar oxygenation trend as in group A was observed during the O2 variations. It should be noted that during the first FI,O2 level (21%; 0to60s), SHb+Mb did not reach a stable level. As in calf B1, spectra from the last 10s were averaged when calculating chromophore tissue fractions and SHb+Mb and Ocytaa3 levels. The chromophore tissue fractions and SHb+Mb oxygenation levels for both calves are summarized in Table 2. Ocytaa3 was on average 96%, ranging from 85% to 100%, throughout the measurements in calf B2, and are omitted in Table 2.

Table Grahic Jump Location
Average chromophore tissue fractions and SHb+Mb for the last 10s of every phase.
Table Footer NoteaCalculated values were smaller than 0.05%.

In calf B1, only a small increase from 18.8% to 20.7% was found in SHb+Mb when increasing the LVAD speed from 6000rpm(0to60s) to 7500rpm(90to150s). When increasing the LVAD speed from 7500rpm(90to150s) to 10,000rpm(180to240s), there was a larger SHb+Mb increase, from 20.7% to 38.4%. The SHb+Mb increased with LVAD pump speed (p<0.001, ANOVA). During the following phases with constant LVAD speed and variations in FI,O2 21%, (300to360s), 50% (360to420s), 100% (420to480s), SHb+Mb increased significantly (p<0.001, ANOVA).

We have presented a calibrated diffuse reflectance spectroscopy method for in vivo determination of myocardial tissue light scattering properties and chromophore tissue fractions, as well as the sum of hemoglobin and myoglobin oxygenation and cytochrome oxidation. A custom-made fiber-optic probe was designed to enable intramyocardial probe placement. The method relies on an empirical light transport model together with calibration measurements on liquid optical phantoms,21 which previously has been found applicable for in vivo determination of myocardial oxygenation.22 The method was evaluated during hemodynamic and respiratory provocations in seven calves, enrolled in two different studies.

Spectral Fitting

In our previous study of myocardial oxygenation estimation with DRS,22 we found characteristic spectral misfits in model adaption to measured spectra. For model I, the lowest R2 value for the model adaption to measured spectra from group A, FI,O2=21%, was 0.954. The corresponding value for the model II was R2=0.994. Averaged over calves A1 to A5, the R2 value improved from 0.965 (model I) to R2=0.997 (model II). When using model II, the residual spectra, defined as Tcal,II*Mheartnorm1, displayed no systematic trends as function of wavelength. Furthermore, the introduction of a fitting parameter in the model allowing wavelength shifting (up to ±5nm) of hemoglobin absorption spectra, naturally contributed to the improved spectra fit compared to our previous study. When including additional chromophores, it is a necessity that their absorption spectra are unique for the chosen wavelength region. This means that none of the chromophores should have an absorption spectrum that could be expressed as a linear combination of other included chromophores. In this study, where the wavelength region 520to800nm was used, all included chromophores displayed unique absorption spectra.

Intramyocardial Light Scattering

The estimated average value for μs at 525nm of 1.34mm1 in this study is comparable to that in pig hearts by Gandjbakhche et al. 32 (μs=1.2to1.1mm1 at 540to590nm)32 Reported values by Häggblad et al. are in the range 0.42to1.3mm1 in wavelength region 530nmto585nm.22

Intramyocardial Tissue Chromophores
Hemo- and myoglobin

The fHb+Mb values reported in Table 1 and Table 2 varied from 0.5% to 1.6% and displayed very small and nonsystematic intraindividual variations during changes in FI,O2 and/or LVAD speed. The magnitude of fHb+Mb pulsations varied between cases, suggesting that large variations may indicate the presence of a large blood vessel, while smaller fHb+Mb variations may indicate a probe placement in an area dominated by capillaries. It should be noted that the magnitude of the variations in fHb+Mb may be affected by movement artifacts due to myocardial contractions, although it is fixated by epicardial suturing. Due to the contractile movement of the myocardium, it is likely that the pressure between the probe tip and the surrounding tissue varies. At such high pressure (contractile phase), Hb molecules in front of the probe may be forced away, causing fHb+Mb to drop.

When analyzing individual spectra, cyclic variations in fHb+Mb with identical frequency as the heart rate were observed. Since myoglobin is bound to muscle tissue,33 it is reasonable to assume that variations in fHb+Mb should be associated with changes mostly in hemoglobin tissue fraction. Moreover, myoglobin is nearly fully oxygenated at normal working conditions,18 and releases oxygen only at very low partial oxygen pressure,34 which is not the case during the conditions in this study. Our observed variations in SHb+Mb should therefore be interpreted as a change mostly in hemoglobin oxygenation. The relationship between the pulsatile variations in the wavelength shift of the Hb spectrum and the SHb+Mb did not support the idea that the relative Hb and Mb contributions can be determined from the wavelength shift. However, the red-shift of Mb is small (about 5nm), which demands very high wavelength accuracy in the recordings and also suggests that reference spectra obtained with the same spectrometer should be used.

We chose not to use more sophisticated methods for separation of hemoglobin and myoglobin oxygenation, despite the fact that other authors14,3536 have made successful attempts to distinguish between hemoglobin and myoglobin absorption influence on both in vitro and in vivo diffuse reflectance spectra recordings.

In the majority of cases, we observed a strong negative correlation between fHb+Mb and SHb+Mb If the assumptions of constant myoglobin tissue fraction and saturation (nearly 100%) holds true, a likely explanation for the negative SHb+Mb versus fHb+Mb correlation is that when fHb+Mb decreases, the relative influence of myoglobin absorption in the measured spectra increases, and since myoglobin is nearly fully oxygenated, SHb+Mb will increase. However, maximum SHb+Mb values of 33.3% (group A; A1) and 44.3% (group B; B2), respectively, suggest that the hemoglobin absorption contribution is predominant throughout the measurements.

In group A, 4 of 5 calves responded with increased SHb+Mb values when inspired FI,O2 was increased. During ventilation with room air (FI,O2=21%), the average SHb+Mb was 20.0%, which corresponds to an myocardial oxygen uptake of 80%, which is in agreement with findings from several other studies.3739

In calf B1, a small increase in SHb+Mb was found when increasing LVAD speed from 6000rpmto7500rpm. When the LVAD speed was further increased to 10,000rpm, SHb+Mb drastically increased. During all three LVAD speed settings, the FI,O2 was held at 100%. For the following changes in FI,O2 levels during constant LVAD speed, the SHb+Mb displayed the same trend as in calves A1 to A4.

When increasing FI,O2 in calf B2, SHb+Mb increased from 12.9% (FI,O2=21%) to 44.3% (FI,O2=100%).

The finding that SHb+Mb increased with LVAD pump speed was expected, since the purpose of the LVAD is to lower the amount of work needed (and hence lower the oxygen consumption) in the left ventricle, to maintain sufficient systemic and coronary circulation.

Cyt aa3 and metHb

The fcytaa3 values reported in Table 1 and Table 2 varied from 1.2% to 2.0% and displayed very small and nonsystematic intraindividual variations during changes in FI,O2 and/or LVAD speed. By assuming a molecular weight of 200kDa for cyt aa3 (Ref. 40), the findings for fcytaa3 gives a cyt aa3 tissue concentration ranging from 60to100nmolg1 tissue wet weight. Reported values for porcine heart in vitro are 30.5nmolg1 tissue wet weight.41

The findings of Ocytaa3 above 96% in both group A and group B, despite low SHb+Mb are compatible with findings in pig hearts during LAD occlusion.17 In Parson’s study, Ocytaa3 decreased only when LAD flow was reduced by more than 40% of resting flow.17 The nonrestricted coronary flow and normoxic conditions present throughout the measurements did not, as expected, display any reduction of the Ocytaa3.

The obtained fractions of methemoglobin were in the interval 0 to 0.2%, which is in agreement with values reported by Wright et al. 42

By using a calibrated intramuscular probe, the tissue chromophore fractions and the hemoglobin+myoglobin oxygenation and cyt aa3 oxidation status of the myocardial chromophores during respiratory and hemodynamic provocations can be monitored. The presented DRS analysis algorithm is capable of delivering results that are physiologically reasonable and in agreement with others. Model inclusion of the chromophores metHb, cyt aa3, ox, and cyt aa3, red, in addition to Hb, HbO2, and W, resulted in nonsystematic residual spectra.

The presented diagnostic tool follows the way of the oxygen from hemo- and myoglobin to the last step of the oxidative phosphorylation and has the potential for enabling early detection of tissue hypoxia in the heart. However, future studies should include coronary flow provocations and pharmaceutically induced alterations of the mitochondrial ability to utilize oxygen in the ATP formation process. Furthermore, in these future studies, it would be advisable to include, in addition to the presented DRS technique, additional measurement techniques such as microdialysis for cellular metabolism analysis43 and intermittent coronary sinus blood samples for global in vitro analysis of hemoglobin oxygenation.

Appendix

The absorption data for all chromophores are given in specific extinction coefficients (μe)[mM1cm1]. To be included in the light transport model, μe has to be translated into the absorption coefficient μa[mm1]. A general description of this conversion has been described by Prahl44 and is shown in Eq. 5;Display Formula

5μa=100ln(10)μeρmw,
where ρ is the substance density [gL1], and mw is the molecular weight [gmol1] of the specific substance.

For the hemoglobin protein, consisting of four heme units, the molecular weight was set to 64,500gmol1. For cyt aa3, where each functional unit consists of 13 subunit enzymes containing haem a, haem a3, CuA, and CuB, the molecular weight was set to 200,000gmol1. To convert the specified tissue fractions to a molecular amount (e.g., mol per gram tissue), simply divide the fraction by the corresponding molecular weight.

This study was financed by VINNOVA and Perimed AB through the SAMBIO research collaboration program between companies and academia within bioscience (VINNOVA, D. no. 2008-00149), by the Swedish Research Council (D. no. 2005-3934), and by NovaMedTech (supported by the European union Regional Development Fund). The authors would also like to thank the staff at the Laboratory for Experimental Animal Studies, Faculty of Health Sciences, Linköping University.

Williams  R. I., , Haaverstad  R., , Sianos  G., , Vourvouri  E., , and Fraser  A. G., “ Perioperative tissue Doppler echocardiography and bypass graft flowmetry in patients undergoing coronary revascularization: predictive power for late recovery of regional myocardial function. ,” J. Am. Soc. Echocardiogr.  0894-7317 15, (10, II ), 1202–1210  ((2002)).
Haaverstad  R., , Vitale  N., , Tjomsland  O., , Tromsdal  A., , Torp  H., , and Samstad  S. O., “ Intraoperative color Doppler ultrasound assessment of LIMA-to-LAD anastomoses in off-pump coronary artery bypass grafting. ,” Ann. Thorac. Surg..  0003-4975 74, (4 ), 1390–1394  ((2002)).
Lovstakken  L., , Ibrahim  K. S., , Vitale  N., , Henriksen  S. T., , Kirkeby-Garstad  I., , Torp  H., , and Haaverstad  R., “ Blood flow imaging: a new two-dimensional ultrasound modality for enhanced intraoperative visualization of blood flow patterns in coronary anastomoses. ,” J. Am. Soc. Echocardiogr.  0894-7317 21, (8 ), 969–975  ((2008)).
Parsons  W. J., , Rembert  J. C., , Bauman  R. P., , Greenfield  J. C.  Jr., , and Piantadosi  C. A., “ Dynamic mechanisms of cardiac oxygenation during brief ischemia and reperfusion. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 259, (5 ), 1477–1485  ((1990)).
Al-Obaidi  M. K., , Etherington  P. J., , Barron  D. J., , Winlove  C. P., , and Pepper  J. R., “ Myocardial tissue oxygen supply and utilization during coronary artery bypass surgery: evidence of microvascular no-reflow. ,” Clin. Sci..  0323-5084 98, (3 ), 321–328  ((2000)).
Chung  Y., “ Oxygen reperfusion is limited in the postischemic hypertrophic myocardium. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 290, (5 ), H2075–H2084  ((2006)).
Heineman  F. W., , Kupriyanov  V. V., , Marshall  R., , Fralix  T. A., , and Balaban  R. S., “ Myocardial oxygenation in the isolated working rabbit heart as a function of work. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 262, (1 ), 255–267  ((1992)).
Leisey  J. R., , Scott  D. A., , Grotyohann  L. W., , and Scaduto  R. C.  Jr., “ Quantitation of myoglobin saturation in the perfused heart using myoglobin as an optical inner filter. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 267, (2 ), 645–653  ((1994)).
Zijp  J. R., and Ten Bosch  J. J., “ Optical properties of bovine muscle tissue in vitro: a comparison of methods. ,” Phys. Med. Biol..  0031-9155 43, (10 ), 3065–3081  ((1998)).
Schenkman  K. A., “ Cytochrome c oxidation determined by multiwavelength optical spectral analysis in the isolated perfused heart. ,” Proc. SPIE.  0277-786X 4613, , 278–285  ((2002)).
Ribacka  C., “ Redox-linked proton transfer by cytochrome c oxidase. ,” PhD Thesis, Department of Biological and Environmental Sciences, University of Helsinki ((2007)), p. 64 .
Opie  L. H.,  Heart Physiology from Cell to Circulation. , 4th ed.,  Lippincott, Williams & Wilkins ,  Philadelphia, PA  ((2004)).
Cooper  C. E., and Springett  R., “ Measurement of cytochrome oxidase and mitochondrial energetics by near-infrared spectroscopy. ,” Philos. Trans. R. Soc. London, Ser. B.  0962-8436 352, (1354 ), 669–676  ((1997)).
Schenkman  K. A., , Marble  D. R., , Feigl  E. O., , and Burns  D. H., “ Near-infrared spectroscopic measurement of myoglobin oxygen saturation in the presence of hemoglobin using partial least-squares analysis. ,” Appl. Spectrosc..  0003-7028 53, (3 ), 325–331  ((1999)).
Mayevsky  A., and Chance  B., “ Oxidation-reduction states of NADH in vivo: from animals to clinical use. ,” Mitochondrion.  1567-7249 7, (5 ), 330–339  ((2007)).
Jöbsis  F. F., , Keizer  J. H., , LaManna  J. C., , and Rosenthal  M., “ Reflectance spectrophotometry of cytochrome aa3 in vivo. ,” J. Appl. Physiol.: Respir., Environ. Exercise Physiol..  0161-7567 43, (5 ), 858–872  ((1977)).
Parsons  W. J., , Rembert  J. C., , Bauman  R. P., , Duhaylongsod  F. G., , Greenfield  J. C.  Jr., , and Piantadosi  C. A., “ Myocardial oxygenation in dogs during partial and complete coronary artery occlusion. ,” Circ. Res..  0009-7330 73, (3 ), 458–464  ((1993)).
Arai  A. E., , Kasserra  C. E., , Territo  P. R., , Gandjbakhche  A. H., , and Balaban  R. S., “ Myocardial oxygenation in vivo: optical spectroscopy of cytoplasmic myoglobin and mitochondrial cytochromes. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 277, (2 ), 683–697  ((1999)).
“ BORL Tissue Spectra. ,” available at http:www.medphys.ucl.ac.uk/research/borl/research/NIR_topics/spectra/spectra.htm (retrieved 10 June (2009)).
Hübbert  L., , Peterzén  B., , Träff  S., , Janerot-Sjöberg  B., , and Ahn  H., “ Axial flow pump treatment during myocardial depression in calves: an invasive hemodynamic and echocardiographic tissue Doppler study. ,” ASAIO J..  1058-2916 54, , 367–371  ((2008)).
Jacques  S. L., “ Optical fiber reflectance spectroscopy. ,” available at http://omlc.ogi.edu/news/oct03/saratov/index.htm (retrieved 10 June (2009)).
Häggblad  E., , Lindbergh  T., , Karlsson  M. G. D., , Casimir-Ahn  H., , Salerud  E. G., , and Strömberg  T., “ Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting. ,” J. Biomed. Opt..  1083-3668 13, (5 ), 054030  ((2008)).
Bargo  P. R., , Prahl  S. A., , Goodell  T. T., , Sleven  R. A., , Koval  G., , Blair  G., , and Jacques  S. L., “ In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy. ,” J. Biomed. Opt..  1083-3668 10, (3 ), 034018  ((2005)).
Lindbergh  T., , Fredriksson  I., , Larsson  M., , and Strömberg  T., “ Spectral determination of a two-parametric phase function for polydispersive scattering media. ,” Opt. Express.  1094-4087 17, (3 ), 1610–1621  ((2009)).
Lee  J., , El-Abaddi  N., , Duke  A., , Cerussi  A. E., , Brenner  M., , and Tromberg  B. J., “ Noninvasive in vivo monitoring of methemoglobin formation and reduction with broadband diffuse optical spectroscopy. ,” J. Appl. Phys..  0021-8979 100, (2 ), 615–622  ((2006)).
Fleischer  S., , Rouser  G., , Fleischer  B., , Casu  A., , and Kritchevsky  G., “ Lipid composition of mitochondria from bovine heart, liver, and kidney. ,” J. Lipid Res..  0022-2275 8, (3 ), 170–180  ((1967)).
Fei  D. Y., and Shung  K. K., “ Ultrasonic backscatter from bovine tissues. ,” in  IEEE Ultrasonics Symposium. , pp. 677–680 ,  IEEE ,  Piscataway, NJ  ((1984)).
Wittenberg  B. A., , Wittenberg  J. B., , and Katz  I. R., “ Oxygen transport in isolated cardiac myocytes. ,” Basic Res. Cardiol..  0300-8428 80, , 75–77  ((1985)).
Nocedal  J., and Wright  S. J., “ Algorithms for nonlinear least-squares problems. ,” Chapter 10.3, in  Numerical Optimization. , Mikosh  T. V., Robinson  S. M., and Resnick  S. I., Eds., pp. 258–262 ,  Springer Science and Business Media , New York ((2008)).
Zijlstra  W. G., , Buursma  A., , and van Assendelft  O. W., “ Definitions and terminology. ,” Chapter 2, in  Visible and Near Infrared Absorption Spectra of Human and Animal Haemoglobin–Determination and Application. , pp. 9–16 ,  VSP ,  Ridderkerk, The Netherlands  ((2000)).
Buiteveld  H., , Hakvoort  J. M. H., , and Donze  M., “ The optical properties of pure water. ,” in Ocean Optics XII, Jaffe  J. S., Ed., Proc. SPIE.  0277-786X 2258, , 174–183  ((1994)).
Gandjbakhche  A. H., , Bonner  R. F., , Arai  A. E., , and Balaban  R. S., “ Visible-light photon migration through myocardium in vivo. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 277, (2 ), 698–704  ((1999)).
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Citation

Tobias Lindbergh ; Marcus Larsson ; Zoltán Szabó ; Henrik Casimir-Ahn and Tomas Strömberg
"Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy in calves", J. Biomed. Opt. 15(2), 027009 (April 19, 2010). ; http://dx.doi.org/10.1117/1.3374050


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Figures

Grahic Jump LocationF1 :

(a) Probe design, indicating the dimensions of the probe tip. The hatched fiber indicates the emitting fiber. (b) Fiber-optic probe placement in animals from group A. (c) Fiber-optic probe placement in animals from group B, including the LVAD. The probe placement is highlighted with a white arrow.

Grahic Jump LocationF2 :

(a) Representative measured spectrum (Mheartnorm) and model spectra (Tcal,I* and Tcal,II*) from calf A4, 100% FI,O2. (b) Tcal*Mheartnorm1.

Grahic Jump LocationF3 :

(a) Representative measured spectrum (Mheartnorm) and model spectra (Tcal,I* and Tcal,II*) from calf A4, 21% FI,O2 (gray). (b) Tcal*Mheartnorm1.

Grahic Jump LocationF4 :

SHb+Mb in calf A2 as a function of time during three different FI,O2 and during cardiac arrest at the end of the experiment. The last minute in each FI,O2 phase is marked with vertical dashed lines.

Grahic Jump LocationF5 :

(a) fHb+Mb as a function of time during the first 30s in calf A1. (b) Relationship between fHb+Mb and SHb+Mb including linear fitting (R2=0.94) during the first 30s in calf A1.

Grahic Jump LocationF6 :

SHb+Mb as a function of time during variations in LVAD speed and FI,O2 in calf B1. Note: Last 10s in each FI,O2 phase are marked with vertical dashed lines.

Grahic Jump LocationF7 :

SHb+Mb as a function of time during variations in FI,O2 during constant LVAD speed (7500rpm) in calf B2. Note: Last 10s in each FI,O2 phase are marked with vertical dashed lines.

Tables

Table Grahic Jump Location
Average chromophore tissue fractions and SHb+Mb for the last minute of every FI,O2 level.
Table Footer NoteaFor calves A1 and A2, FI,O2 was set to 21% during the process of cardiac arrest in the end of the experiment. The average SHb+Mb was calculated during the time interval 3to4min after initiation of cardiac arrest.
Table Footer NotebNo average values were calculated—only two values.
Table Footer NotecCalculated values were smaller than 0.05%.
Table Grahic Jump Location
Average chromophore tissue fractions and SHb+Mb for the last 10s of every phase.
Table Footer NoteaCalculated values were smaller than 0.05%.

References

Williams  R. I., , Haaverstad  R., , Sianos  G., , Vourvouri  E., , and Fraser  A. G., “ Perioperative tissue Doppler echocardiography and bypass graft flowmetry in patients undergoing coronary revascularization: predictive power for late recovery of regional myocardial function. ,” J. Am. Soc. Echocardiogr.  0894-7317 15, (10, II ), 1202–1210  ((2002)).
Haaverstad  R., , Vitale  N., , Tjomsland  O., , Tromsdal  A., , Torp  H., , and Samstad  S. O., “ Intraoperative color Doppler ultrasound assessment of LIMA-to-LAD anastomoses in off-pump coronary artery bypass grafting. ,” Ann. Thorac. Surg..  0003-4975 74, (4 ), 1390–1394  ((2002)).
Lovstakken  L., , Ibrahim  K. S., , Vitale  N., , Henriksen  S. T., , Kirkeby-Garstad  I., , Torp  H., , and Haaverstad  R., “ Blood flow imaging: a new two-dimensional ultrasound modality for enhanced intraoperative visualization of blood flow patterns in coronary anastomoses. ,” J. Am. Soc. Echocardiogr.  0894-7317 21, (8 ), 969–975  ((2008)).
Parsons  W. J., , Rembert  J. C., , Bauman  R. P., , Greenfield  J. C.  Jr., , and Piantadosi  C. A., “ Dynamic mechanisms of cardiac oxygenation during brief ischemia and reperfusion. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 259, (5 ), 1477–1485  ((1990)).
Al-Obaidi  M. K., , Etherington  P. J., , Barron  D. J., , Winlove  C. P., , and Pepper  J. R., “ Myocardial tissue oxygen supply and utilization during coronary artery bypass surgery: evidence of microvascular no-reflow. ,” Clin. Sci..  0323-5084 98, (3 ), 321–328  ((2000)).
Chung  Y., “ Oxygen reperfusion is limited in the postischemic hypertrophic myocardium. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 290, (5 ), H2075–H2084  ((2006)).
Heineman  F. W., , Kupriyanov  V. V., , Marshall  R., , Fralix  T. A., , and Balaban  R. S., “ Myocardial oxygenation in the isolated working rabbit heart as a function of work. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 262, (1 ), 255–267  ((1992)).
Leisey  J. R., , Scott  D. A., , Grotyohann  L. W., , and Scaduto  R. C.  Jr., “ Quantitation of myoglobin saturation in the perfused heart using myoglobin as an optical inner filter. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 267, (2 ), 645–653  ((1994)).
Zijp  J. R., and Ten Bosch  J. J., “ Optical properties of bovine muscle tissue in vitro: a comparison of methods. ,” Phys. Med. Biol..  0031-9155 43, (10 ), 3065–3081  ((1998)).
Schenkman  K. A., “ Cytochrome c oxidation determined by multiwavelength optical spectral analysis in the isolated perfused heart. ,” Proc. SPIE.  0277-786X 4613, , 278–285  ((2002)).
Ribacka  C., “ Redox-linked proton transfer by cytochrome c oxidase. ,” PhD Thesis, Department of Biological and Environmental Sciences, University of Helsinki ((2007)), p. 64 .
Opie  L. H.,  Heart Physiology from Cell to Circulation. , 4th ed.,  Lippincott, Williams & Wilkins ,  Philadelphia, PA  ((2004)).
Cooper  C. E., and Springett  R., “ Measurement of cytochrome oxidase and mitochondrial energetics by near-infrared spectroscopy. ,” Philos. Trans. R. Soc. London, Ser. B.  0962-8436 352, (1354 ), 669–676  ((1997)).
Schenkman  K. A., , Marble  D. R., , Feigl  E. O., , and Burns  D. H., “ Near-infrared spectroscopic measurement of myoglobin oxygen saturation in the presence of hemoglobin using partial least-squares analysis. ,” Appl. Spectrosc..  0003-7028 53, (3 ), 325–331  ((1999)).
Mayevsky  A., and Chance  B., “ Oxidation-reduction states of NADH in vivo: from animals to clinical use. ,” Mitochondrion.  1567-7249 7, (5 ), 330–339  ((2007)).
Jöbsis  F. F., , Keizer  J. H., , LaManna  J. C., , and Rosenthal  M., “ Reflectance spectrophotometry of cytochrome aa3 in vivo. ,” J. Appl. Physiol.: Respir., Environ. Exercise Physiol..  0161-7567 43, (5 ), 858–872  ((1977)).
Parsons  W. J., , Rembert  J. C., , Bauman  R. P., , Duhaylongsod  F. G., , Greenfield  J. C.  Jr., , and Piantadosi  C. A., “ Myocardial oxygenation in dogs during partial and complete coronary artery occlusion. ,” Circ. Res..  0009-7330 73, (3 ), 458–464  ((1993)).
Arai  A. E., , Kasserra  C. E., , Territo  P. R., , Gandjbakhche  A. H., , and Balaban  R. S., “ Myocardial oxygenation in vivo: optical spectroscopy of cytoplasmic myoglobin and mitochondrial cytochromes. ,” Am. J. Physiol. Heart Circ. Physiol..  0363-6135 277, (2 ), 683–697  ((1999)).
“ BORL Tissue Spectra. ,” available at http:www.medphys.ucl.ac.uk/research/borl/research/NIR_topics/spectra/spectra.htm (retrieved 10 June (2009)).
Hübbert  L., , Peterzén  B., , Träff  S., , Janerot-Sjöberg  B., , and Ahn  H., “ Axial flow pump treatment during myocardial depression in calves: an invasive hemodynamic and echocardiographic tissue Doppler study. ,” ASAIO J..  1058-2916 54, , 367–371  ((2008)).
Jacques  S. L., “ Optical fiber reflectance spectroscopy. ,” available at http://omlc.ogi.edu/news/oct03/saratov/index.htm (retrieved 10 June (2009)).
Häggblad  E., , Lindbergh  T., , Karlsson  M. G. D., , Casimir-Ahn  H., , Salerud  E. G., , and Strömberg  T., “ Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting. ,” J. Biomed. Opt..  1083-3668 13, (5 ), 054030  ((2008)).
Bargo  P. R., , Prahl  S. A., , Goodell  T. T., , Sleven  R. A., , Koval  G., , Blair  G., , and Jacques  S. L., “ In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy. ,” J. Biomed. Opt..  1083-3668 10, (3 ), 034018  ((2005)).
Lindbergh  T., , Fredriksson  I., , Larsson  M., , and Strömberg  T., “ Spectral determination of a two-parametric phase function for polydispersive scattering media. ,” Opt. Express.  1094-4087 17, (3 ), 1610–1621  ((2009)).
Lee  J., , El-Abaddi  N., , Duke  A., , Cerussi  A. E., , Brenner  M., , and Tromberg  B. J., “ Noninvasive in vivo monitoring of methemoglobin formation and reduction with broadband diffuse optical spectroscopy. ,” J. Appl. Phys..  0021-8979 100, (2 ), 615–622  ((2006)).
Fleischer  S., , Rouser  G., , Fleischer  B., , Casu  A., , and Kritchevsky  G., “ Lipid composition of mitochondria from bovine heart, liver, and kidney. ,” J. Lipid Res..  0022-2275 8, (3 ), 170–180  ((1967)).
Fei  D. Y., and Shung  K. K., “ Ultrasonic backscatter from bovine tissues. ,” in  IEEE Ultrasonics Symposium. , pp. 677–680 ,  IEEE ,  Piscataway, NJ  ((1984)).
Wittenberg  B. A., , Wittenberg  J. B., , and Katz  I. R., “ Oxygen transport in isolated cardiac myocytes. ,” Basic Res. Cardiol..  0300-8428 80, , 75–77  ((1985)).
Nocedal  J., and Wright  S. J., “ Algorithms for nonlinear least-squares problems. ,” Chapter 10.3, in  Numerical Optimization. , Mikosh  T. V., Robinson  S. M., and Resnick  S. I., Eds., pp. 258–262 ,  Springer Science and Business Media , New York ((2008)).
Zijlstra  W. G., , Buursma  A., , and van Assendelft  O. W., “ Definitions and terminology. ,” Chapter 2, in  Visible and Near Infrared Absorption Spectra of Human and Animal Haemoglobin–Determination and Application. , pp. 9–16 ,  VSP ,  Ridderkerk, The Netherlands  ((2000)).
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