Time-resolved Stokes vectors of transmitted optical signals were measured to differentiate normal and stunned myocardium tissues. The corresponding Mueller matrices were calculated based on the Stokes-Mueller formalism. Our experimental results indicated that the time-resolved Mueller matrices could provide information about myocardial architectural alteration in stunned myocardium. Thus, the Stokes-Mueller measurement can be a useful method in cardiovascular research.
© 2002 Optical Society of America
Altered structures in biological tissues, either in the macroscopic, microscopic or molecule level, can reflect different biological functions. Exploring the tissue structures of heart is of special interest because of potential application to the diagnosis of related diseases. The major component of heart is bulky myocardium, which is composed of quasi-regularly arranged muscle fibers. It attaches to a fibrous skeleton and twists roughly in a manner of figure “8” to form the wall of ventricles. Individual cardiomyocytes connect each other in an end-to-end pattern to form muscle fibers. The estimate of the average width of normal human ventricular muscle fibers is around 23 μm . The diameter of typical rat cardiac muscle fibers is around 12 μm . Most heart diseases are associated with structural changes, either in composition or in the arrangement of muscle fibers within the myocardium. For example, after acute myocardial infarction, damaged myocardium is replaced by randomly oriented fibrous tissue within six weeks. Further pathological remodeling would result in disarrayed fiber orientation in the remaining working myocardium. Stunned myocardium, resulted from ischemia-reperfusion injuries, was also found with structural changes. Stunned myocardium can be seen in various clinical scenarios such as percutaneous transluminal coronary angioplasty, unstable angina and stress-induced ischemia. It can also be seen on patients after thrombolysis and after cardiopulmonary bypass . Tissue edema, contracture and disrupted orientation of muscle fibers scattered in the stunned area all contribute to mechanical dysfunction . To determine the optimal treatment strategy with such injuries, it is important for cardiovascular specialists to know the distributions as well as the sizes of lesions. Therefore, any information that characterizes myocardial tissue structures can be of great help.
Recently, the quasi-coherent photon imaging method becomes attractive as a promising noninvasive technique for biological tissue characterization [5–7]. In such an ultra-fast optics technique, short optical pulses are applied to biological tissues. The photons travel with nearly straight line trajectories with fewer random scattering events are collected as quasi-coherent photons or snake photons. Because the snake photons pass through biological tissues with weaker scattering, they carry direct information about histological characteristics of tissues. Because of the quasi-regular arrangement in myocardial muscle fibers, deterministic optical birefringence effect is expected [8,9]. In this situation, all the elements of polarization state must be considered for observing the polarization evolution and hence providing information of histological structure in myocardium. To observe the polarization properties in myocardial tissues, the Stokes-Mueller formalism was adopted to provide a complete representation of the polarization states [10–12]. In this paper, we measured the time-resolved Stokes vectors of normal and stunned myocardium from rats and compared their differences. Structural alterations in these specimens were also evaluated with the standard H&E staining process. The 4×4 full Mueller matrices of samples were evaluated from the measured Stokes vectors with time-gating processes. In section 2 of this paper, we describe the experimental procedures. The time-resolved Stokes-Mueller formalism is briefly introduced in section 3. The measurement results and discussions are given in section 4. Finally, conclusions are drawn in section 5.
2. Experimental Procedures
The work was conducted in accordance with the R.O.C. Animal Protection Law (Scientific Application of Animals), 1998. In this research, we adopted stunned myocardium of rats and cardiomyopathic myocardium of hamsters for optical measurements. Normal myocardial tissues in each case were also prepared for comparison.
In the case of stunned myocardium study, six adult male WKY rats were randomly assigned into either control (C) or stunned (S) group. Left thoracotomy after generalized anaethesia (sodium pentobarbital, 30 mg/kg i.p.) was performed. For rats in the S group (stunned myocardium), we ligated left anterior descending artery at its proximal part under adequate ventilation support. Ischemia was monitored with electrocardiography tracing as depression of ST segment in lead II. After 30 minutes, the ligature was released. The animals were then allowed reperfusion for another 180 minutes. For rats in the C group (normal myocardium), a sham operation was performed. To harvest myocardial tissues, lethal dose of sodium pentobarbital was administered. Animals were retrogradely perfused with heparinized PBS (10 units/ml) for 15 minutes followed by 2 % paraformaldehyde (pH 7.4) for another 15 minutes. Then, hearts were removed quickly and stored in 10 % formaldehyde till the optical experiments.
Bio14.6 hamster is another widely used animal model for autosomal recessive cardiomyopathy . Such an animal dies prematurely from progressive myocardial necrosis and heart failure due to a genetic defect leading to total absence of delta-sarcoglycan, which contributes significantly to stablizing cell membrane in striated muscle cells. The myocardium of the Bio14.6 cardiomyopathic hamster was obtained from Biobreeders Inc., Watertown, MA, USA. The heart was extracted and fixated in 10% formaldehyde after retrograde perfusion from ascending aorta. All other procedures of sample preparation are the same as those for the rat experiment.
The optical experiment setup is shown in Fig. 1. A Verdi-laser-pumped mode-locked Ti:sapphire laser was used to provide 76 MHz, around 100 fs laser pulses at 800 nm. The laser beam was split into two branches, one for triggering the used streak camera and another for propagating through tissue sample. About 100-mW average power of laser pulses was applied to the samples. The diameter of the sample beam was slightly smaller than 1 mm. The samples were submerged in water to avoid thermal damage. In positioning the samples, care was taken to ensure that laser pulses traveled through the middle segment of the left ventricle free wall. We positioned the heart as described to minimize the possibility that laser pulses past through valves, papillary muscles or intraventricular septum. Complex fiber orientation in these intracardiac structures adds uncertainties in output polarization state and may introduce errors.
According to the Stokes-Mueller formalism, we need to prepare four different polarization states of incident photons, including the horizontal polarization component, the vertical polarization component, the 45° linear polarization component, and the right-hand circular polarization component. In experiments, such polarization control was accomplished through adjusting the used polarizers, half-wave plates and quarter-wave plates. Here, the horizontal and vertical polarization directions are referred to the coordinate of the laboratory. The transmitted signals of samples were directed to the streak camera with a fiber bundle for each of the 16 combinations of the polarization states. The temporal resolution of the operation mode of the streak camera was about 20 ps due to the temporal limitation of the streak camera and the group-velocity dispersion effect in the fiber bundle. The quasi-coherent photon data were obtained through the integration of the time-resolved intensity profiles with the duration of 50 ps from the leading edges of the profiles. After the measurements, specimens were processed for standard H&E staining.
3. Stokes-Mueller Formalism
The Stokes components, generally denoted by S0, S1, S2 and S3, form a sufficient set for describing the amplitude, phase and polarization of a light wave. To express the Stokes vector S in terms of our experimental data, the following relation is needed:
Here, H, V, P, and R are the measured quantities of the polarization components, vertical polarization component, 45° linear polarization component, and right-hand circular polarization component, respectively. In experiments, the Stokes vectors of transmitted photons corresponding to the four incident polarization states H, V, P, and R are denoted, respectively, by S H, S V, S P, and S R. According to the Stokes-Mueller formalism, the Mueller matrix M can be evaluated from the output Stokes vectors as
4. Experimental Results
Figure 2 shows the time-resolved intensity profiles of the four polarization components of normal cardiac muscle tissue with horizontal polarization inputs. The middle segment of left ventricle free wall of a myocardium sample was used for obtaining the data. The narrow width (~70 ps) of the co-polarized component H and the weak intensity of the cross-polarized component V indicate the weak random scattering in the myocardial tissue. However, the small difference between the components P and R in the quasi-coherent part implies the polarization coupling effect due to the anisotropic structure of myocardial muscle fibers.
Figure 3 shows the histological images of normal and stunned myocardium. The wall thicknesses in both samples were about 3 mm with a left ventricle dimension of 4 mm. Under microscopic examination, hearts from the C group (as shown in Fig. 3 (a)) show a regular arrangement of muscle fibers. On the contrary, hearts from the S group show pronounced contraction band necrosis, myocyte contracture (arrowheads) and muscle fiber derangement (arrows) in putative regions through which the laser beam passed (Fig. 3 (b)). We believe that the loss of regularly arranged contractile proteins, degradation of bundle structures and disarrayed muscle fibers all contribute to the changes of birefringence effect in myocardium.
Based on the measured polarization components, the time-resolved Stokes elements of normal and stunned myocardium with horizontally polarized incident pulses can be obtained and shown in Figs. 4 (a) and (b), respectively. The measurement results of myocardial samples in each group (S or C) have similar patterns. The S0 profile represents the total intensity of measured signal through the myocardium samples. The S1 profile indicates the portion of transmitted quasi-coherent photons. The information of coupled polarization components was furnished with the quasi-coherent parts of S2 and S3. In Fig. 4 (a), the depression features of S2 and S3 near the leading edges of the time-resolved profiles should result from optical birefringence with the regular fiber architecture of normal myocardium. After ischemia-reperfusion, the altered tissue structure led to the changes of S2 and S3 (as shown in Fig. 4 (b)).
For further understanding of polarization evolution in myocardial tissues, the complete polarization elements of Mueller matrices are needed. Based on the Stokes-Mueller formalism with our experimental data, the Mueller matrices of normal and stunned myocardium are shown in Figs. 5 (a) and (b), respectively. The time-gated data was obtained by the integration of the time-resolved intensity profiles with duration of about 50 ps from the leading edges (~ 220 ps in Fig. 2) of the profiles. The 3-D mapping image represents a 4 × 4 full Mueller matrix with a linear interpolation surface. The quantities of diagonal elements in the Mueller matrices stand for the intensities of preserved original polarization states from various polarization inputs. The quantities of diagonal elements (the red region) in Fig. 5 (b) are lower than those of Fig. 5 (a) that reveals the larger polarization changes in the damaged fiber architecture. Meanwhile, the pattern in Fig. 5 (b) manifests the difference of polarization evolution with compare to Fig. 5 (a). The strength of circular polarization coupling (the violet region at the right corner) in Fig. 5 (b) is higher than (a) that again is attributed to the histological alterations of the fibrous structure in stunned myocardium. The clear difference in experimental results between normal and stunned myocardium implies different polarization evolution due to the altered structures.
The histological features of hearts from Bio14.6 hamsters include central nucleation, wide variation in muscle fiber diameter, and necrosis (see Fig. 6). Besides, in Fig. 6 we can see that muscle fibers are no longer regularly arranged and infiltration of scar tissue is evident. All these features contribute to the enhanced photon scattering and reduced degree of polarization of transmitted light. Fig. 7 (a) shows the Mueller matrix of hamster’s normal myocardium. The result of cardiomyopathic myocardium is shown in Fig. 7 (b). The significant difference between the two samples can be clearly seen. Because the cardiomyopathic myocardium tissue (about 5 mm in wall thickness) is thicker than normal myocardium tissue, the average level of matrix element values is relatively lower due to stronger scattering.
5. Discussions and Conclusions
The results of time-resolved Stokes-Mueller experiments have demonstrated that optical measurements using the time gating of transmitted light was a promising method for characterizing myocardial tissues. Altered birefringence signals could be utilized to differentiate stunned or cardiomyopathic from normal myocardium. The underlying mechanism was assumed to be the loss of optical anisotropy, both in the subcellular and tissue levels. Optical characterization based on time-resolved Stokes-Mueller measurements is a diagnostic tool of great potential, which can be a great assistance to the management of cardiovascular diseases. The full 4×4 time-gated Mueller matrix can reflect altered structures in myocardial tissues. Time-gated signals will be helpful in reducing the depolarization effect of random scattering in biological tissues. The transmission measurements were used for the first-step characterization of such tissues because they are supposed to provide more information than the reflection measurements. Since it is difficult to conductor the optical transmission measurements in in vivo experiments, the reflection type of measurement based on the technique of optical coherence tomography is currently under development.
This research was supported by National Health Research Institute, The Republic of China, under the grant of NHRI-GT-EX89E819L. L.S.L. is a recipient of NHRI MDPhD/DDSPhD Predoctoral Fellowship from the National Health Research Institute.
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