When a coherent beam illuminates spatially disordered particles, speckle patterns are formed due to interference of the scattered light waves. Speckle patterns from biological tissues using synchrotron phase contrast X-ray imaging can provide functional information about micro-scale morphological structures of the tissues. In this study, we investigated the size and contrast variations of the speckles of aggregated red blood cells (RBCs) suspensions with varying the degree of RBC aggregation. Results show that the degree of RBC aggregation is a governing parameter on the change of speckle characteristics. This blood speckle analysis method can be used as a novel modality for monitoring RBC aggregation.
© 2010 OSA
When a coherent light illuminates spatially disordered structures, such as porous membrane and particles in medium, random fluctuations of light intensity called speckles are formed due to interference of the scattered light waves. These speckle patterns contain the physicochemical and structural information of the illuminated samples. Numerous works on speckle patterns have been performed to measure surface roughness [1–3], particles size, and concentration in a medium [4–7] using the statistical analysis of the spatial distribution of speckle patterns (size, intensity, contrast, and polarization).
Speckle patterns are also appeared in X-ray images. The scattering angle of X-ray through an object is very small due to very short wavelength of the X-ray beam. Thus, the speckle image is not clearly visible when an image detector is situated near the sample. However, the interference effect of disturbed X-ray waves becomes dominant in the image by placing the detector far from the sample. This imaging method is called the propagation-based phase-contrast imaging technique. It employs Fresnel diffraction of partially coherent monochromatic X-ray beam by increasing the distance between the detector and the sample. The resultant edge-enhanced image can be utilized to investigate microstructure changes in biological tissues. Most biological tissues have similar X-ray absorption coefficients, making it difficult to visualize these samples if only the absorption-based imaging method is used. Various X-ray speckle images of biological samples such as an air-filled alveolar structure in a lung tissue [8,9] and red blood cells (RBCs) in plasma [10–13] are observed using phase-contrast imaging technique. However, the speckle characteristics of blood samples according to the RBC aggregation have not been investigated in detail.
RBCs suspended in plasma are not well dispersed compared to polystyrene particles in water. RBCs in plasma or solutions of high molecular weight polymers aggregate and form rouleaux and rouleaux networks (Fig. 1 ). RBC aggregation is a shear-dependent, dynamic, and reversible process. RBC forms rouleaux at a low shear rate and breaks up at a high shear rate. This phenomenon affects the non-Newtonian characteristics of blood because blood viscosity is varied with the degree of RBC aggregation, which is dependent on the shear force exerted on blood . Furthermore, RBC aggregation affects blood flow resistance in venous vasculatures  and increases arterial pressure by blocking pre-capillary vessels , so it plays important roles in pathophysiology.
RBC aggregation can be observed with various methods, such as direct optical imaging, optical transmission or scattering, and ultrasound backscattering method. However, direct in vivo access of RBC aggregation in a blood flow is difficult. In this study, the effect of RBC aggregation on the speckle characteristics of samples was investigated using X-ray phase-contrast imaging.
2. Materials and methods
2.1 Preparation of blood samples
The Declaration of Helsinki was followed in this study and volunteers gave informed consent prior to participation. Whole blood samples from three healthy male volunteers (age 25, 28, and 43) were taken and stored in anti-coagulated Vacutainer® tubes (BD, Franklin Lakes, NJ, USA). Blood was immediately centrifuged to separate RBCs and plasma. The concentrated RBCs were washed twice with an isotonic phosphate buffered saline (PBS, Ph = 7.4, 290 mOsmol/kg) and resuspended in PBS, autologous plasma, and 0.75% (wt/vol) polyvinylpyrrolidone 360 (PVP 360) in PBS at different hematocrit levels. All experiments were performed within four hours after collecting the blood samples. RBC suspensions in PBS, autologous plasma and 0.75% PVP 360 in PBS are hereafter referred as RBC-PBS, RBC-Plasma, and RBC-PVP, respectively.
2.2 Synchrotron radiation X-ray imaging
Experiments were carried out at the 1B2 beamline of the third generation synchrotron radiation source at Pohang Accelerator Laboratory (PAL; Pohang, Republic of Korea). A schematic diagram of the experimental set-up is shown in Fig. 2 . The X-ray beam is monochromatized by a W/B4C double-multilayer monochromator with peak energy at 10keV. The X-ray beam passes through a mechanical shutter and the blood sample. The X-ray beam through the sample is converted to visible light by a CdWO4 scintillator crystal and images of 512 x 512 pixels resolution are finally captured by an EM-CCD camera (Xion + , Andor Technologies) with a 10x objective lens. The corresponding field of view is 583 x 583μm (1.14μm/pixel). The distance from the sample to the scintillator was set to 40cm to acquire contrast-enhanced blood speckle pattern from propagation-based phase contrast effect.
2.3 Speckle pattern monitoring
Two separate experiments were conducted in this study. In the first experiment, the speckle patterns of various blood samples under static condition were compared. RBCs were placed in three different suspensions (PBS, autologous plasma, and PVP 0.75% in PBS) at different hematocrit levels (10%, 25%, 40%, 60%, 80%). Blood samples were gently shaken and loaded in a static sample holder of 1 mm thickness. Speckle images were then captured with an exposure time of 0.3 s. In the second experiment, we investigated the temporal variation of speckle patterns during the RBC aggregation process after stopping blood flow. Blood samples (40% RBC-PBS, RBC-Plasma, and RBC-PVP) were circulated in a closed loop with an inner diameter of 1mm by a peristaltic pump to keep RBCs flowing without sedimentation at a certain location. The average shear rate acting on the blood sample was about 106 s−1. A mechanical vibrator was installed below the tube to enhance RBC disaggregation. To monitor the variation of speckle pattern during RBC aggregation, the speckle images were recorded as a function of time from the stoppage of blood flow and mechanical vibration. Images were captured at a frame rate of 3.51 frames per second (fps) with exposure time of 0.2 s. The measurement section of 228 x 228μm for speckle analysis was located at the center of the tube to minimize the effect of sample thickness on speckle size.
To analyze the dynamic variation of speckle size during RBC aggregation, an exponential fitting curve was established, which has been commonly adopted to analyze RBC aggregation process using the visible light-transmission or backscattering method [17,18] and ultrasonic backscattering method . The initial speckle size at t = 0 was set to Sizeinitial and the temporal evolution curves of the speckle size were fitted with the exponential function of Eq. (1), which started from Sizeinitial and reached a maximum value at the equilibrium state as follows:Eq. (1), the time elapsed for reaching the half value of Sizegrowth (Thalf) was derived using Eq. (2). These parameters are shown in Fig. 6(b) .
2.4 Speckle image analysis
To analyze the main features of speckle patterns, the speckle size of RBCs in X-ray image was calculated using the normalized autocovariance function of the speckle intensity distribution in the detection plane (x,y). The normalized autocovariance function is denoted as cI(Δx, Δy).4–7]. In addition, the image contrast of speckle patterns was investigated to correlate the image contrast with the speckle size. Image contrast was calculated using Eq. (4). This equation has been used to calculate local or temporal contrast from laser speckle image [5,20,21].
3.1 Effect of RBC aggregation on speckle patterns
Figure 3 shows typical speckle images of RBCs suspended in different media (PBS, autologous plasma, and PVP 0.75% in PBS) at different hematocrit levels (10%, 25%, 40%, 60%, and 80%). The size and contrast of the blood speckles in each suspension are clearly distinguishable. The images obtained from RBC-PBS exhibit faint speckle patterns, while the images of RBC-Plasma show bigger speckle patterns with clearer image contrast. Addition of PVP 360 in PBS increased the size and contrast of speckle patterns. Statistical analysis was carried out for the blood speckles and the results are shown in Fig. 4 . Maximum speckle size for RBC-PBS is 50.26 ± 2.26 μm2 at 10% hematocrit and then decreases to a minimum size of 40.32 ± 2.44 μm2 at 60% hematocrit. Maximum speckle sizes for RBC-Plasma and RBC-PVP solutions are 60.92 ± 1.01 μm2 and 77.21 ± 3.49 μm2 at a hematocrit of 25% and 40%, respectively. Almost no speckle pattern is induced from the concentrated RBCs at 100% hematocrit (data not shown).
The size and contrast of speckle patterns is shown in Fig. 5 . In general, the speckle size is closely correlated with speckle contrast. The speckle contrast of X-ray images varies largely as the degree of RBC aggregation increases (RBC-PVP>RBC-Plasma>RBC-PBS). The fitting curve in Fig. 5 shows that the image contrast and speckle size have a proportional relation under various aggregation conditions. Statistical analysis shows that the coefficient of determination of the polynomial fitting curve is about r2 = 0.7 and p-value is less than 0.05. This indicates that the fitting equation is statistically significant and it represents well the experimental data of the present study
To estimate the uncertainties in the measurements of size and contrast of blood speckles, we captured 10 speckle images from the same blood sample and measured their size and contrast carefully. The standard error in the mean values of the speckle size and contrast was evaluated to be 0.57μm2 and 0.0003, respectively. This implies that the size and contrast of blood samples were measured accurately with high confidence and the possible errors in the obtained individual data are nearly negligible. Therefore, we compared the mean value ± standard deviation of 3 different RBC suspensions and their mean values are clearly distinguished as shown in Fig. 4,
3.2 Variation of speckle patterns during RBC aggregation process
Figure 6(a) shows a typical temporal variation of speckle size after stopping both blood flow and mechanical vibration. Results for the blood samples from three volunteers are summarized in Table 1 . While the initial speckle sizes among the RBC suspensions in three different media are not so different, the temporal variations of speckle size during RBC aggregation were noticeably different, depending on the suspension solution. The main parameters of speckle variation are summarized in Table 1. There is nearly no temporal variation for speckle patterns of RBC-PBS; the slope of the fitting curve is about −0.01 with the initial speckle size of 38.55 ± 2.52 μm2. On the other hand, the speckle size of RBC-plasma and RBC-PVP solution increase exponentially with time. Even though there are deviations caused by individual differences of the blood donors, the increasing rate of speckle size is higher at initial stage and the speckle size at steady state is consistently larger in the RBC-PVP solution compared to RBC-Plasma. As summarized in Table 1, the aggregation rate constant k of RBC-PVP solution (0.19 ± 0.12) is about 2.8-fold higher than 0.08 ± 0.07 of RBC-Plasma. The speckle size at steady state in the RBC-PVP solution is 69.98 ± 7.22 μm2, which is larger than the value of 61.81 ± 5.52 μm2 for RBC-Plasma.
This study was aimed to investigate the variation of speckle patterns of human blood using synchrotron X-ray imaging technique. Blood samples suspended in various solution media at different hematocrit levels were examined under static and flowing conditions. In this study, we analyzed the speckle size and contrast in synchrotron X-ray images of RBCs captured with varying the degree of RBC aggregation in blood samples. The experimental results show that the size and image contrast of blood speckles are largely affected by the degree of RBC aggregation. Furthermore, dynamic variation of speckle size after flow stoppage indicates the disaggregation and aggregation phenomena of RBCs, which is in agreement with previous results [19,22].
Previous studies [6,7] revealed that the decrease of particle number and the increase of aggregate diameter during particle aggregation result in increased speckle size. In the present study, the speckle size of blood increases in proportion to the aggregation-enhancing ability of RBC suspending media. It becomes smaller at high shear rate condition and recovers at static condition. The speckle size in RBC-PBS is smallest over the whole range of hematocrit and almost constant for three minutes after flow stoppage. This indicates no RBC aggregates in this medium because of the absence of aggregation-enhancing macromolecules. For the case of RBC-Plasma, the speckle size is bigger than that of RBC-PBS due to the formation of RBC aggregation mediated mainly by fibrinogen. In addition, the augmentation of speckle size is remarkable in the PVP 360 solution under both static and sudden flow stoppage conditions.
RBC aggregation has been investigated by many researchers during last several decades and there are many literatures dealing with the degree of RBC aggregation in various suspensions. Two mechanisms were proposed to explain the RBC aggregation phenomena. One is the bridging model and another is the depletion model [23,24]. Both models are based on the fact that fibrinogen or other macromolecules in blood mainly contribute to induce RBC aggregation. RBCs suspended in PBS solution do not aggregate and disperse separately . On the other hand, fibrinogen in blood sample (RBC-Plasma) induces RBC aggregation as shown in Fig. 1. The effect of various factors, such as donor, age, cellular and plasmatic factors, on the degree of RBC aggregation have been extensively studied . Artificial media such as dextran, PVP, poly (ethylene glycol) (PEG) were also found to enhance RBC aggregation [19,24]. This indicates that the degree of RBC aggregation also depends on the suspending media. Especially, 0.75% PVP 360 solution was observed to induce stronger RBC aggregation (see Fig. 4 and Table 1), compared to plasma. Therefore, it can be used to enhance RBC aggregation effectively [19,24].
Kim and Lee (2009)  showed that the speckle contrast of a blood sample under static condition is high when its hematocrit is in the range of 20%–80% and explained that the underlying reason results from the ratio of plasma and RBC. In the present study, we showed that the results from RBC-Plasma and RBC-PVP are similar in general tendency to the previous results based on the speckle pattern of blood at various hematocrit levels. However, the speckle size of RBC-PBS without aggregation is quite different from those in aggregating media. The speckle size in RBC-PBS is biggest at the lowest hematocrit level (10%). It is reduced by increasing hematocrit to 60%, and then increased at 80% hematocrit. Therefore, it is clear that RBC aggregation also affects the speckle size in RBC samples aside from the ratio of RBC and suspending medium. Furthermore, RBC aggregation is the main factor determining the speckle size.
In this study, we also analyzed the dynamic variation of speckle size in different medium by measuring not only the speckle size at steady state, but also the rate of RBC aggregation process. As expected, RBC-PBS does not show any temporal variation in speckle size because RBCs do not aggregate and change their size in PBS solution as shown in Fig. 6(a). In contrast, RBC-Plasma and RBC-PVP exhibited dynamic variation of speckle sizes. By comparing the dynamic aggregation parameters as shown in Fig. 6(b), it is possible to investigate quantitatively the effects of various factors, such as suspending media and donors, on the rate of RBC aggregation.
In our previous study, we investigated the X-ray image contrast of RBC speckle patterns under various experimental conditions to find the optimal condition for which velocity field information can be extracted using X-ray PIV technique . However, we did not consider the effect of RBC aggregation on the image contrast of RBC speckles. As shown in Figs. 4 and 5, the image contrast and speckle size are affected by the degree of RBC aggregation. They are increased along with the degree of RBC aggregation. This indicates that the degree of RBC aggregation should be taken into consideration in in vivo X-ray PIV measurements using speckle patterns of RBCs in blood flows. In addition, since various laboratory animals have different degrees of RBC aggregation, we have to consider this aspect in experiments using those animals.
Piederriere et al., investigated successfully the speckle patterns formed by laser illumination [4–7]. In the present study, sychrotron X-ray was used as a light source. The synchrotron X-ray imaging technique has several advantages over the optical microscopy. The most distinct merit is the penetration feature coming from transmission-type light source. It is possible to visualize internal structures of opaque bio-samples noninvasively under in vivo condition. Using this advantage, the sychrotron X-ray imaging techniuqe has been employed to visualize morphological structure, function and physiology of in vivo samples . The speckle imaging techniuqe developed in this study can be used to observe the degree of RBC aggregation under in vivo condition. In addition, by combining this method to the velocity field measurement techniuqes such as X-ray PIV/PTV [10–13,28], the degree of RBC aggregation and velocity field of blood flows can be measured simultaneously and these information would be helpful to understand the RBC aggregation phenomena in a blood flow.
RBC aggregation has been known to play an important pathological role by changing hemorheology such as blood viscosity and local hematocrit. This implies that the RBC aggregation has an influence on the flow resistance and shear stress in blood vessels [29,30]. Since the increase of RBC aggregation is highly related to many vascular diseases such as sepsis , diabetes [32,33], atherosclerosis [34,35], RBC aggregation has been receiving large attention. Various methodologies have been developed to measure RBC aggregation, such as erythrocyte sedimentation rate, microscopy, photometry, ultrasound backscatter. Optical techniques, such as LORCA (Mechatronics, The Netherlands) , Erythro-aggregometer (Regulest, France) , and Myrenne-aggregometer (Myrenne, GmbH, Germany)  are commonly used nowadays. Intravital microscopy and whole-organ perfusion methods have been used to observe RBC aggregation in a blood flow. However, it can be utilized to measure RBC aggregation only in thin transparent blood vessels . In addition, the ultrasound backscattering technique has poor spatial resolution and tissue-attenuation problem. However, it is so far the only means to measure the RBC aggregation in a blood flow passing through an opaque conduit. The in vivo measurement of RBC aggregation using X-ray radiography can be used as an alternative method to get detailed information on RBC aggregation of live bio-samples. Especially, the X-ray imaging technique makes it possible to observe relatively thick blood vessels in the range from millimeter to centimeter for which the intravital microscopy technique is infeasible to apply. The measurement of RBC speckles using X-ray radiography may provide exclusive information on RBC aggregation in large blood vessels.
In this study, the image contrast and size of RBC speckles in synchrotron phase contrast X-ray images of blood samples were found to be closely related to the RBC aggregation. The present phase-contrast X-ray imaging technique can be used effectively to investigate the physiological and pathological functions of RBC aggregation and its relationship with hemodynamic characteristics of live animals, especially in deep-seated large blood vessels.
This work is financed by the Creative Research Initiatives (Diagnosis of Biofluid Flow Phenomena and Biomimic Research) of MEST/NRF of Korea. X-ray imaging experiments were performed at the 1B2 beamline of Pohang Accelerator Laboratory (PAL), Pohang, Korea.
References and links
2. P. Lehmann, “Surface-roughness measurement based on the intensity correlation function of scattered light under speckle-pattern illumination,” Appl. Opt. 38(7), 1144–1152 (1999). [CrossRef]
3. R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. 39(31), 5811–5819 (2000). [CrossRef]
4. Y. Piederrière, F. Boulvert, J. Cariou, B. Le Jeune, Y. Guern, and G. Le Brun, “Backscattered speckle size as a function of polarization: influence of particle-size and- concentration,” Opt. Express 13(13), 5030–5039 (2005). [CrossRef] [PubMed]
5. Y. Piederrière, J. Cariou, Y. Guern, G. Le Brun, B. Le Jeune, J. Lotrian, J. F. Abgrall, and M. T. Blouch, “Evaluation of blood plasma coagulation dynamics by speckle analysis,” J. Biomed. Opt. 9(2), 408–412 (2004). [CrossRef] [PubMed]
6. Y. Piederrière, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lortrian, “Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,” Opt. Express 12(1), 176–188 (2004). [CrossRef] [PubMed]
7. Y. Piederrière, J. Le Meur, J. Cariou, J. Abgrall, and M. Blouch, “Particle aggregation monitoring by speckle size measurement; application to blood platelets aggregation,” Opt. Express 12(19), 4596–4601 (2004). [CrossRef] [PubMed]
8. M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008). [CrossRef] [PubMed]
9. M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004). [CrossRef] [PubMed]
10. S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008). [CrossRef]
11. S. C. Irvine, D. M. Paganin, A. Jamison, S. Dubsky, and A. Fouras, “Vector tomographic X-ray phase contrast velocimetry utilizing dynamic blood speckle,” Opt. Express 18(3), 2368–2379 (2010). [CrossRef] [PubMed]
12. G. B. Kim and S. J. Lee, “X-ray PIV measurements of blood flows without tracer particles,” Exp. Fluids 41(2), 195–200 (2006). [CrossRef]
15. M. Cabel, H. J. Meiselman, A. S. Popel, and P. C. Johnson, “Contribution of red blood cell aggregation to venous vascular resistance in skeletal muscle,” Am. J. Physiol. 272(2 Pt 2), H1020–H1032 (1997). [PubMed]
16. G. Mchedlishvili, L. Gobejishvili, and N. Beritashvili, “Effect of intensified red blood cell aggregability on arterial pressure and mesenteric microcirculation,” Microvasc. Res. 45(3), 233–242 (1993). [CrossRef] [PubMed]
17. E. Kaliviotis and M. Yianneskis, “Fast response characteristics of red blood cell aggregation,” Biorheology 45(6), 639–649 (2008). [PubMed]
18. J. H. Nam, Y. Yang, S. Chung, and S. Shin, “Comparison of light-transmission and -backscattering methods in the measurement of red blood cell aggregation,” J. Biomed. Opt. 15(2), 027003 (2010). [CrossRef] [PubMed]
19. K. H. Nam, D. G. Paeng, and M. J. Choi, “Ultrasonic backscatter from rat blood in aggregating media under in vitro rotational flow,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(2), 270–279 (2009). [CrossRef] [PubMed]
21. M. Draijer, E. Hondebrink, T. Leeuwen, and W. Steenbergen, “Review of laser speckle contrast techniques for visualizing tissue perfusion,” Lasers Med. Sci. 24(4), 639–651 (2009). [CrossRef]
22. Z. Qin, L. G. Durand, L. Allard, and G. Cloutier, “Effects of a sudden flow reduction on red blood cell rouleau formation and orientation using RF backscattered power,” Ultrasound Med. Biol. 24(4), 503–511 (1998). [CrossRef] [PubMed]
24. M. W. Rampling, H. J. Meiselman, B. Neu, and O. K. Baskurt, “Influence of cell-specific factors on red blood cell aggregation,” Biorheology 41(2), 91–112 (2004). [PubMed]
25. D. Fatkin, T. Loupas, J. Low, and M. Feneley, “Inhibition of red cell aggregation prevents spontaneous echocardiographic contrast formation in human blood,” Circulation 96(3), 889–896 (1997). [PubMed]
26. H. J. Meiselman, “Red blood cell aggregation: 45 years being curious,” Biorheology 46(1), 1–19 (2009). [PubMed]
27. M. W. Westneat, J. J. Socha, and W. K. Lee, “Advances in biological structure, function, and physiology using synchrotron X-ray imaging*,” Annu. Rev. Physiol. 70(1), 119–142 (2008). [CrossRef] [PubMed]
28. S. J. Lee and S. Kim, “Simultaneous measurement of size and velocity of microbubbles moving in an opaque tube using an X-ray particle tracking velocimetry technique,” Exp. Fluids 39(3), 492–495 (2005). [CrossRef]
30. J. J. Bishop, A. S. Popel, M. Intaglietta, and P. C. Johnson, “Rheological effects of red blood cell aggregation in the venous network: a review of recent studies,” Biorheology 38(2-3), 263–274 (2001). [PubMed]
31. O. K. Baskurt and H. J. Meiselman, “RBC aggregation: more important than RBC adhesion to endothelial cells as a determinant of in vivo blood flow in health and disease,” Microcirculation 15(7), 585–590 (2008). [CrossRef] [PubMed]
32. C. Le Devehat, M. Vimeux, G. Bondoux, and T. Khodabandehlou, “Red blood cell aggregation in diabetes mellitus,” Int. Angiol. 9(1), 11–15 (1990). [PubMed]
33. S. M. MacRury, S. E. Lennie, P. McColl, R. Balendra, A. C. MacCuish, and G. D. Lowe, “Increased red cell aggregation in diabetes mellitus: association with cardiovascular risk factors,” Diabet. Med. 10(1), 21–26 (1993). [CrossRef] [PubMed]
35. S. Berliner, D. Zeltser, R. Rotstein, R. Fusman, and I. Shapira, “A leukocyte and erythrocyte adhesiveness/aggregation test to reveal the presence of smoldering inflammation and risk factors for atherosclerosis,” Med. Hypotheses 57(2), 207–209 (2001). [CrossRef] [PubMed]
36. M. R. Hardeman, J. G. Dobbe, and C. Ince, “The Laser-assisted Optical Rotational Cell Analyzer (LORCA) as red blood cell aggregometer,” Clin. Hemorheol. Microcirc. 25(1), 1–11 (2001).
37. M. Donner, M. Siadat, and J. F. Stoltz, “Erythrocyte aggregation: approach by light scattering determination,” Biorheology 25(1-2), 367–375 (1988). [PubMed]
38. H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schönbein, “Microrheology and light transmission of blood. I. The photometric effects of red cell aggregation and red cell orientation,” Pflugers Arch. 333(2), 126–139 (1972). [CrossRef] [PubMed]