Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy in calves

Tobias Lindbergh; Marcus Larsson; Zoltán Szabó; Henrik Casimir-Ahn M.D.; Tomas Strömberg

doi:10.1117/1.3374050

1 March 2010 Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy in calves

Tobias Lindbergh, Marcus Larsson, Zoltán Szabó, Henrik Casimir-Ahn M.D., Tomas Strömberg

Author Affiliations +

Journal of Biomedical Optics, Vol. 15, Issue 2, 027009 (March 2010). https://doi.org/10.1117/1.3374050

Abstract

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.

1. Introduction

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.^{1, 2, 3} 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.^{4, 5, 6}

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.^{7, 8, 9, 10} 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,^{16, 17, 18} 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.

2. Material and Methods

Seven calves, $5 months$ old, body weight ranging from $75 to 85 kg$ , 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 $(0.15 mg ∕ kg)$ and atropine sulfate $(0.06 mg ∕ kg)$ . A central venous catheter was inserted into the external jugular vein for administration of fluids and medication. Pentobarbital sodium $(2 mg ∕ kg)$ was used for induction of anesthesia, and a tracheotomy was carried out to allow mechanical ventilation. Anesthesia was maintained with intravenous fentanyl $(10 μ g ∕ kg ∕ h)$ and pentobarbital sodium $(2 mg ∕ kg ∕ h)$ .

2.1.

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 $5 mm$ 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 $6000 rpm$ . The intramuscular fiber-optic probe was then positioned identically as in animals in group A. For details about the implantation, see Hübbert 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 .

Fig. 1

(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.

2.2.

Equipment

A multichannel spectrometer (AvaSpec 2048-5-RM, Avantes BV, Eerbeek, The Netherlands ) operating in the visible wavelength region ( $400 to 900 nm$ , grating: VB $600 lines ∕ mm$ ), 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 $200 ∕ 230 μ m$ and a numerical aperture of 0.37. The optical fibers were inserted into a slightly bent syringe cannula with a diameter of $800 μ m$ (Fig. 1, left panel). The receiving fiber was positioned adjacent to the illuminating fiber at a center–center separation of $230 μ m$ . 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.

2.3.

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 $200 ms to 1000 ms$ 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 $(Ba S O_{4})$ powder with a reflectivity of above 98% in the visible wavelength range was used. The probe was vertically lowered approximately $1 cm$ 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.

2.3.1.

Group A (provocations with changes in $F_{I, O 2}$ )

Five calves, denoted A1 to A5, were subjected to this protocol. After placement of the fiber-optic probe, at least $10 \min$ 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 $O_{2}$ $(F_{I, O 2})$ was varied in three different steps, 21%, 50%, and 100%, respectively, with $3 - \min$ duration per phase. Spectra were measured continuously during the $F_{I, O 2}$ variations. In cases A1 and A2, registrations of spectra during $3 to 4 \min$ after initiation of cardiac arrest in the end of the experiment were also performed.

2.3.2.

Group B (provocations with changes in LVAD speed and $F_{I, O 2}$ )

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

In calve B1, the $F_{I, O 2}$ was first held constant at 100%, while the speed of the LVAD was varied in three different steps, $6000 rpm$ , $7500 rpm$ , and $10,000 rpm$ , with $1 - \min$ duration per phase. After switching from $6000 rpm to 7500 rpm$ , and from $7500 rpm to 10,000 rpm$ , $30 s$ was allowed before spectra were measured.

After the $1 - \min$ duration with the LVAD speed at $10,000 rpm$ , the $F_{I, O 2}$ was then varied in four steps; 50%, 21%, 50%, and 100%, with $1 - \min$ duration per phase. During the different $F_{I, O 2}$ levels, spectra were measured continuously.

In calf B2, the LVAD speed was held constant at $7500 rpm$ throughout the experiment, and $F_{I, O 2}$ was varied in three different steps, 21%, 50%, and 100%, with $1 - \min$ duration per phase.

2.4.

Spectral Preprocessing and System Calibration

First, all unprocessed measurement spectra $M^{raw}$ were dark-corrected by subtracting the detector dark noise spectrum, $D$ , which was registered immediately after each measurement series. The dark-corrected spectra $(M^{raw} - D)$ were then filtered and resampled in three preprocessing steps: first, the spectrum was equidistantly up-sampled to a resolution of $0.1 nm$ ; 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 $1 nm$ and limited to the wavelength region $500 to 800 nm$ . 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 $(M_{white}^{raw})$ 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:

Eq. 1

M_{heart}^{norm} = \frac{(M_{heart}^{raw} - D_{heart} / M_{lamp, heart}^{raw} - D_{heart})}{{⟨ M_{white}^{raw} - D_{white} / M_{lamp, white}^{raw} - D_{white} ⟩}_{t}},

where

{⟨ \cdot ⟩}_{t}

denotes averaging over time. The preprocessed and normalized spectrum

M_{heart}^{norm}

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.^{22, 23} The details are described in Häggblad, 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:

Eq. 2

T (μ_{a}, μ_{s}^{'}) = K \cdot \exp (- μ_{a} \cdot L),

where

K = a + b \cdot μ_{s}^{'} + c \cdot μ_{s}^{' 2}

, and

L = d + e \cdot μ_{s}^{'} + f \cdot μ_{s}^{' 2}

, 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

μ_{s} = {[1 2 3 4 8]}_{λ = 632.8 nm} {mm}^{- 1}

,

μ_{a} = {[0 0.01 0.05 0.1 0.2 0.4 0.8 1.6]}_{λ = 632.8 nm} {mm}^{- 1}

. The anisotropy factor,

g

, of milk at

632.8 nm

was set to 0.84 according to a previous study,²⁴ resulting in

μ_{s}^{'} = {[0.16 0.32 0.64 1.28]}_{λ = 632.8 nm} {mm}^{- 1}

. The calibrated light transport model was denoted

T_{cal}

.

2.5.

Tissue Chromophore Selection and Spectral Analysis

The major chromophores in myocardial tissue are oxygenized and deoxygenized hemoglobin and myoglobin ( $Hb O_{2}$ , Hb, $Mb O_{2}$ , 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, $Hb O_{2}$ , Mb, $Mb O_{2}$ , 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 concentration^{26, 27} compared to the epicardial fat layer.²² According to several studies, the water content was set to 75% (Refs. 21, 22, 28). Because of the very similar absorption spectra of hemoglobin and myoglobin (Mb is red-shifted $2 to 4 nm$ 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 $\pm 5 nm$ , 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 $(μ_{a, heart})$ for model II. The $μ_{a}$ expression for model I is obtained by forcing $f_{cyt aa 3}$ and $f_{metHb}$ to be equal to zero.

Eq. 3

μ_{a, heart} (λ) = f_{Hb + Mb} \cdot [S_{Hb + Mb} \cdot μ_{a, Hb O_{2}} + (1 - S_{Hb + Mb}) \cdot μ_{a, Hb}] + f_{cyt aa 3} \cdot [O_{cyt aa 3} \cdot μ_{a, cyt aa 3, ox} + (1 - O_{cyt aa 3}) \cdot μ_{a, cyt aa 3, red}] + f_{metHb} \cdot μ_{a, metHb} + 0.75 \cdot μ_{a, W} .

In Eq. 3,

f_{Hb + Mb}

is the

Hb + Mb

tissue fraction,

S_{Hb + Mb}

is the

Hb + Mb

oxygen saturation,

f_{cyt aa 3}

is the cyt aa3 tissue fraction,

O_{cyt aa 3}

is the oxidation status of cyt aa3, and

f_{metHb}

is the metHb tissue fraction. It should be noted that absorption data is often provided in terms of the specific extinction coefficient,

μ_{e}

. The conversion from

μ_{e}

to

μ_{a}

can be found in Sec. 6.

The reduced scattering coefficient $(μ_{s}^{'})$ was modeled according to a previous study by Häggblad²² :

Eq. 4

μ_{s}^{'} (λ) = \frac{α \cdot λ^{- β}}{700^{- β}},

where

α

and

β

are the fitting parameters.

By combining $T_{cal}$ and Eq. 3, expressions for light transport in myocardial tissue are obtained for both models and are denoted $T_{cal, I}$ and $T_{cal, II}$ , respectively. The unknown parameters in Eqs. 3, 4 ( $f_{Hb + Mb}$ , $S_{Hb + Mb}$ , $f_{cyt aa 3}$ , $O_{cyt aa 3}$ , $f_{metHb}$ , $α$ , and $β$ ) were determined by minimizing the expressions $T_{cal, I} ∕ M_{heart}^{norm} - 1$ and $T_{cal, II} ∕ M_{heart}^{norm} - 1$ 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 $T_{cal, I}^{*}$ and $T_{cal, II}^{*}$ , respectively. For both models, visual inspection of $T_{cal}^{*} ∕ M_{heart}^{norm} - 1$ was performed, and the goodness of fit was evaluated by calculating the Pearson product-moment correlation coefficient $R^{2}$ . Visual inspection of $T_{cal}^{*} ∕ M_{heart}^{norm} - 1$ 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 and Buiteveld, ^{30, 31} 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 ³⁰ As the cyt aa3 absorption data were not available for wavelengths shorter than $520 nm$ (Ref. 19), while the sensitivity of the spectrometer was considered too poor above $800 nm$ , the spectral analysis was limited to the wavelength region $520 to 800 nm$ .

In group A, spectra from the last minute of each $F_{I, O 2}$ level were averaged over time, and the curve-fitting was applied on the resulting spectra. In group B, spectra from the last $10 s$ of each $F_{I, O 2}$ level and LVAD speed were averaged over time, and the curve-fitting was applied on the resulting spectra.

2.6.

Statistical Analysis

Summarized data from groups A and B are calculated from fitting an average spectrum over the recording interval. The effect of $F_{I, O 2}$ on $S_{Hb + Mb}$ (groups A and B) was evaluated on data from fitting individual spectra using an ANOVA repeated measures design, with calves and $F_{I, O 2}$ as factors. The effect of LVAD pump speed on $S_{Hb + Mb}$ (calf B1) was evaluated on data from fitting individual spectra using an ANOVA repeated measures design, with subject and LVAD pump speed as factors.

3. Results

3.1.

Spectral Fitting

To illustrate the effect of adding cyt aa3 and metHb as chromophores in the light transport model, two spectra with varying $S_{Hb + Mb}$ were selected. The curve-fits for model I (dashed black), model II (solid black), and the measured spectrum (solid gray) are shown in Figs. 2 and 3 .

Fig. 2

(a) Representative measured spectrum $(M_{heart}^{norm})$ and model spectra ( $T_{cal, I}^{*}$ and $T_{cal, II}^{*}$ ) from calf A4, 100% $F_{I, O 2}$ . (b) $T_{cal}^{*} ∕ M_{heart}^{norm} - 1$ .

Fig. 3

(a) Representative measured spectrum $(M_{heart}^{norm})$ and model spectra ( $T_{cal, I}^{*}$ and $T_{cal, II}^{*}$ ) from calf A4, 21% $F_{I, O 2}$ (gray). (b) $T_{cal}^{*} ∕ M_{heart}^{norm} - 1$ .

Model I yielded characteristic spectral misfits in the wavelength region $\sim 540 to \sim 620 nm$ . The use of model II resulted in improved spectral fitting, and the characteristic spectral misfits were eliminated. The calculated $S_{Hb + Mb}$ using model II, compared to $S_{Hb + Mb}$ from model I, differed only by $- 0.9 %$ in the low $S_{Hb + Mb}$ case (16.7% compared to 17.6%, respectively), and by 2.6% in the high $S_{Hb + Mb}$ case (37.7% compared to 35.1%, respectively). The corresponding values for differences in $S_{Hb + Mb}$ were 0.1% in both the high and low $f_{Hb + Mb}$ case. The $R^{2}$ -values for the two different curve-fits versus measured spectra from the last minute of phase $F_{I, O 2} = 21 %$ of group A calves showed that model II resulted in higher $R^{2}$ -values in all five cases $(R^{2} > 0.99)$ . Taken together, the improved $R^{2}$ -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 $2.2 nm$ , $2.0 nm$ , and $1.8 nm$ during $F_{I, O 2} = 21 %$ , 50%, and 100%, respectively. In group B, the average wavelength shift was $0.8 nm$ .

3.2.

Intramyocardial Light Scattering

The parameters $α$ and $β$ in Eq. 4 were averaged for each calf. In group A, $μ_{s}^{'}$ ranged from $0.17 {mm}^{- 1} to 2.28 {mm}^{- 1}$ , and $β$ was in the range 2.43 to 2.84. Corresponding values for group B were $0.35 {mm}^{- 1} to 2.28 {mm}^{- 1}$ $(μ_{s}^{'})$ and 2.18 to 3.91 $(β)$ . The average $μ_{s}^{'}$ calculated for both groups was $0.79 {mm}^{- 1}$ at $633 nm$ and $0.45 {mm}^{- 1}$ at $780 nm$ , which are both commonly used laser wavelengths in biomedical optics.

3.3.

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.

3.3.1.

Group A (provocations with changes in $F_{I, O 2}$ )

As a representative case, Fig. 4 shows the time-resolved $S_{Hb + Mb}$ for calf A2 during the variations in $F_{I, O 2}$ .

Fig. 4

$S_{Hb + Mb}$ in calf A2 as a function of time during three different $F_{I, O 2}$ and during cardiac arrest at the end of the experiment. The last minute in each $F_{I, O 2}$ phase is marked with vertical dashed lines.

As can be seen in Fig. 4, there is an increase in $S_{Hb + Mb}$ that follows the $F_{I, O 2}$ changes from 21% via 50% to 100%. Approximately $60 s$ after each change, the $S_{Hb + Mb}$ reached a stable value, suggesting that the $S_{Hb + Mb}$ during the last $60 s$ of each $F_{I, O 2}$ level is an accurate interval when calculating average $S_{Hb + Mb}$ values for each $F_{I, O 2}$ .

Cyclic variations in $S_{Hb + Mb}$ and $f_{Hb + Mb}$ 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, $f_{Hb + Mb}$ for the first $30 s$ of calf A1, is shown in the left panel of Fig. 5 . The right panel illustrates the correlation between $f_{Hb + Mb}$ and $S_{Hb + Mb}$ during the same period.

Fig. 5

(a) $f_{Hb + Mb}$ as a function of time during the first $30 s$ in calf A1. (b) Relationship between $f_{Hb + Mb}$ and $S_{Hb + Mb}$ including linear fitting $(R^{2} = 0.94)$ during the first $30 s$ in calf A1.

The left panel in Fig. 5 shows distinct periodical behavior of $f_{Hb + Mb}$ . The number of local maxima was determined by visual inspection to 34 during $30 s$ , giving a frequency of $68 \min^{- 1}$ . This was compared to the heart rate observed by the ECG monitor, which was $67 beats \cdot \min^{- 1}$ . The right panel displays an inverse relationship between $f_{Hb + Mb}$ and $S_{Hb + Mb}$ . The $R^{2}$ -value of the fitted straight line was 0.94. Negative correlations between $f_{Hb + Mb}$ and $S_{Hb + Mb}$ were found for four of five calves. Similarly, the relationship between the wavelength shift of the Hb spectrum and the $S_{Hb + Mb}$ 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 $S_{Hb + Mb}$ was slightly positive in calves A1 to A3, slightly negative in A4, and without any trend in A5.

$f_{Hb + Mb}$ , $S_{Hb + Mb}$ , $f_{metHb}$ , and $f_{cyt aa 3}$ average values (over the last minute) of each $F_{I, O 2}$ level are presented in Table 1 . $O_{cyt aa 3}$ was on average 97%, ranging from 82% to 100%, and displayed no correlations with $F_{I, O 2}$ . Thus, $O_{cyt aa 3}$ data were omitted from Table 1.

Table 1

Average chromophore tissue fractions and SHb+Mb for the last minute of every FI,O2 level.

FI,O2 [%]	[%]	Calves					Average
FI,O2 [%]	[%]	A1	A2	A3	A4	A5	Average
21	$f_{Hb + Mb}$	0.9	1.2	0.5	1.2	1.5	1.1
	$S_{Hb + Mb}$	22.8	20.0	22.6	14.7	15.6	19.1
	$f_{metHb}$	03	0.1	03	03	03	03
	$f_{cyt aa 3}$	1.5	1.7	1.3	1.9	2.0	1.7
50	$f_{Hb + Mb}$	0.9	1.3	0.5	1.2	1.6	1.1
	$S_{Hb + Mb}$	27.9	24.4	27.7	16.7	21.6	23.7
	$f_{metHb}$	03	0.1	03	03	03	03
	$f_{cyt aa 3}$	1.6	1.8	1.2	1.7	1.8	1.6
100	$f_{Hb + Mb}$	0.9	1.2	0.5	1.1	1.5	1.0
	$S_{Hb + Mb}$	33.3	30.4	32.5	31.1	13.8	28.2
	$f_{metHb}$	0.1	0.1	03	03	03	03
	$f_{cyt aa 3}$	1.4	1.9	1.2	1.4	2.0	1.6
211	$f_{Hb + Mb}$	1.4	1.1	—	—	—	—2
	$S_{Hb + Mb}$	3.7	1.8	—	—	—	—2
	$f_{metHb}$	03	0.1				—2
	$f_{cyt aa 3}$	1.4	2.0	—	—	—	—2

^aFor 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.

^bNo average values were calculated—only two values.

^cCalculated values were smaller than 0.05%.

As can be seen in Table 1, calves A1 to A4 responded with an increase in $S_{Hb + Mb}$ when $F_{I, O 2}$ increased. Increasing $F_{I, O 2}$ 21% to 50% to 100%, gave average values for $S_{Hb + Mb} = 19 \pm 4 %$ , $24 \pm 5 %$ , and $28 \pm 8 %$ , respectively. Hence, the average increases in $S_{Hb + Mb}$ were 4.6% and 4.5% when $F_{I, O 2}$ was increased from 21% to 50% and from 50% to 100%, respectively. The effect of $F_{I, O 2}$ on $S_{Hb + Mb}$ was significant ( $p < 0.001$ , ANOVA). The $S_{Hb + Mb}$ varied between calves ( $p < 0.001$ , ANOVA), as did the response to $F_{I, O 2}$ ( $p < 0.001$ , ANOVA). Calves A1 to A3 had a similar step-wise increase in their $S_{Hb + Mb}$ , while for A4, a larger response was seen when $F_{I, O 2}$ increased from 50% to 100% than from 21% to 50%. For A5, $S_{Hb + Mb}$ decreased when $F_{I, O 2}$ increased from 50% to 100%.

3.3.2.

Group B (provocations with changes in LVAD speed and $F_{I, O 2}$ )

The time-resolved $S_{Hb + Mb}$ for calf B1 is shown in Fig. 6 . It can be seen in Fig. 6 that the $S_{Hb + Mb}$ did not reach stable levels during the $O_{2}$ provocations $(180 to 480 s)$ . For this reason, spectra from the 10 last seconds for every $F_{I, O 2}$ level were averaged when calculating the tissue fractions and $S_{Hb + Mb}$ and $O_{cyt aa 3}$ levels of the chromophores. $O_{cyt aa 3}$ was on average 98%, ranging from 84% to 100% throughout measurements in calf B1, and displayed no correlations with $F_{I, O 2}$ . The time-resolved $S_{Hb + Mb}$ for calf B2 is shown in Fig. 7 .

Fig. 6

$S_{Hb + Mb}$ as a function of time during variations in LVAD speed and $F_{I, O 2}$ in calf B1. Note: Last $10 s$ in each $F_{I, O 2}$ phase are marked with vertical dashed lines.

Fig. 7

$S_{Hb + Mb}$ as a function of time during variations in $F_{I, O 2}$ during constant LVAD speed $(7500 rpm)$ in calf B2. Note: Last $10 s$ in each $F_{I, O 2}$ phase are marked with vertical dashed lines.

A similar oxygenation trend as in group A was observed during the $O_{2}$ variations. It should be noted that during the first $F_{I, O 2}$ level (21%; $0 to 60 s$ ), $S_{Hb + Mb}$ did not reach a stable level. As in calf B1, spectra from the last $10 s$ were averaged when calculating chromophore tissue fractions and $S_{Hb + Mb}$ and $O_{cyt aa 3}$ levels. The chromophore tissue fractions and $S_{Hb + Mb}$ oxygenation levels for both calves are summarized in Table 2 . $O_{cyt aa 3}$ was on average 96%, ranging from 85% to 100%, throughout the measurements in calf B2, and are omitted in Table 2.

Table 2

Average chromophore tissue fractions and SHb+Mb for the last 10s of every phase.

Calf
B1						B2
LVADspeed	FI,O2	fHb+Mb	SHb+Mb	fmetHb	fcytaa3	LVADspeed	FI,O2	fHb+Mb	SHb+Mb	fmetHb	fcytaa3
[rmp]	[%]			[%]		[rmp]	[%]	[%]
6000	100	0.8	18.8	0.2	1.8	7500	21	0.9	12.9	01	2.1
7500	100	0.9	20.7	0.2	1.9	7500	50	0.9	25.1	01	2.1
10,000	100	0.8	38.4	0.2	1.6	7500	100	0.9	44.3	01	1.9
10,000	50	0.8	36.3	0.2	1.6
10,000	21	0.8	27.1	0.2	1.6
10,000	50	0.8	30.0	0.2	1.6
10,000	100	0.8	36.5	0.2	1.6

^aCalculated values were smaller than 0.05%.

In calf B1, only a small increase from 18.8% to 20.7% was found in $S_{Hb + Mb}$ when increasing the LVAD speed from $6000 rpm$ $(0 to 60 s)$ to $7500 rpm$ $(90 to 150 s)$ . When increasing the LVAD speed from $7500 rpm$ $(90 to 150 s)$ to $10, 000 rpm$ $(180 to 240 s)$ , there was a larger $S_{Hb + Mb}$ increase, from 20.7% to 38.4%. The $S_{Hb + Mb}$ increased with LVAD pump speed ( $p < 0.001$ , ANOVA). During the following phases with constant LVAD speed and variations in $F_{I, O 2}$ 21%, $(300 to 360 s)$ , 50% $(360 to 420 s)$ , 100% $(420 to 480 s)$ , $S_{Hb + Mb}$ increased significantly ( $p < 0.001$ , ANOVA).

4. Discussion

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.