## Fraction estimation of small, dense LDL using autocorrelation function of dynamic light scattering

Optics Express, Vol. 18, Issue 6, pp. 6315-6326 (2010)

http://dx.doi.org/10.1364/OE.18.006315

Acrobat PDF (233 KB)

### Abstract

Small, dense low-density lipoprotein (sdLDL) in total LDL is strongly related with the cardiovascular risk level. An optical technique using dynamic light scattering (DLS) measurement is useful for point-of-care testing of sdLDL. However, the sdLDL fraction estimated from the particle size distribution in DLS data is sensitive to noise and artifacts. Therefore, we derived analytical solutions in a closed form to estimate the fraction of scatterers using the autocorrelation function of scattered light from a polydisperse solution. The effect of the undesired large particles can be eliminated by the pre-processing of the autocorrelation function. The proposed technique was verified using latex standard particles and LDL solutions. Results suggest the feasibility of this technique to estimate the sdLDL fraction using optical scattering measurements.

© 2010 OSA

## 1. Introduction

1. Y. Hirowatari, H. Yoshida, H. Kurosawa, K. I. Doumitu, and N. Tada, “Measurement of cholesterol of major serum lipoprotein classes by anion-exchange HPLC with perchlorate ion-containing eluent,” J. Lipid Res. **44**(7), 1404–1412 (2003). [CrossRef] [PubMed]

4. J. B. German, J. T. Smilowitz, and A. M. Zivkovic, “Lipoproteins: When size really matters,” Curr. Opin. Colloid Interface Sci. **11**(2–3), 171–183 (2006). [CrossRef] [PubMed]

1. Y. Hirowatari, H. Yoshida, H. Kurosawa, K. I. Doumitu, and N. Tada, “Measurement of cholesterol of major serum lipoprotein classes by anion-exchange HPLC with perchlorate ion-containing eluent,” J. Lipid Res. **44**(7), 1404–1412 (2003). [CrossRef] [PubMed]

2. S. Akita, F. M. Sacks, L. P. Svetkey, P. R. Conlin, and G. KimuraS. AkitaF. M. SacksL. P. SvetkeyP. R. ConlinG. KimuraDASH-Sodium Trial Collaborative Research Group, “Effects of the Dietary Approaches to Stop Hypertension (DASH) diet on the pressure-natriuresis relationship,” Hypertension **42**(1), 8–13 (2003). [CrossRef] [PubMed]

5. W. Ensign, N. Hill, and C. B. Heward, “Disparate LDL phenotypic classification among 4 different methods assessing LDL particle characteristics,” Clin. Chem. **52**(9), 1722–1727 (2006). [CrossRef] [PubMed]

5. W. Ensign, N. Hill, and C. B. Heward, “Disparate LDL phenotypic classification among 4 different methods assessing LDL particle characteristics,” Clin. Chem. **52**(9), 1722–1727 (2006). [CrossRef] [PubMed]

5. W. Ensign, N. Hill, and C. B. Heward, “Disparate LDL phenotypic classification among 4 different methods assessing LDL particle characteristics,” Clin. Chem. **52**(9), 1722–1727 (2006). [CrossRef] [PubMed]

8. H. Campos, E. Blijlevens, J. R. McNamara, J. M. Ordovas, B. M. Posner, P. W. Wilson, W. P. Castelli, and E. J. Schaefer, “LDL particle size distribution. Results from the Framingham Offspring Study,” Arterioscler. Thromb. **12**(12), 1410–1419 (1992). [CrossRef] [PubMed]

9. T. Hirano, Y. Ito, H. Saegusa, and G. Yoshino, “A novel and simple method for quantification of small, dense LDL,” J. Lipid Res. **44**(11), 2193–2201 (2003). [CrossRef] [PubMed]

10. F. Gonzalez, J. M. Saiz, F. Moreno, and P. J. Valle, “Application of a Laplace Transform Method to Binary-Mixtures of Spherical-Particles in Solution for Low Scattered Intensity,” J. Phys. D Appl. Phys. **25**(3), 357–361 (1992). [CrossRef]

15. H. Ruf and B. J. Gould, “Size distributions of chylomicrons from human lymph from dynamic light scattering measurements,” Eur. Biophys. J. Biophy. **28**(1), 1–11 (1998). [CrossRef]

14. M. Schneider and T. F. McKenna, “Comparative study of methods for the measurement of particle size and size distribution of polymeric emulsions,” Part. Part. Syst. Char. **19**(1), 28–37 (2002). [CrossRef]

17. M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle characterization by PCS: The analysis of bimodal distributions,” Particul. Sci. Technol. **26**(5), 413–437 (2008). [CrossRef]

16. M. P. Cagigal, M. A. Rebolledo, and F. Moreno, “Determination of the radii and the concentration ratio in binary mixtures of spherical macromolecules from the measurement of n^{(2)}(T),” Appl. Opt. **23**(13), 2091–2096 (1984). [CrossRef] [PubMed]

17. M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle characterization by PCS: The analysis of bimodal distributions,” Particul. Sci. Technol. **26**(5), 413–437 (2008). [CrossRef]

17. M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle characterization by PCS: The analysis of bimodal distributions,” Particul. Sci. Technol. **26**(5), 413–437 (2008). [CrossRef]

## 2. Theoretical derivation of the weight fraction

### 2.1 Dynamic light scattering

*g*

^{(1)}(

*τ*) of scattered electric field

*E*(

*t*) is given as [18]where

*τ*is the correlation time. The decay constant Γ is given as Γ =

*q*, where

^{2}D*D*is the translational diffusion coefficient and

*q*is the magnitude of the scattering vector given as

*q*= (4

*πn*/

*λ*)sin(

*θ*/2), where

*n*,

*λ*, and

*θ*respectively signify the refractive index of the medium, the wavelength of light, and the scattering angle.

*d*of the sphere is obtained from the Stokes–Einstein equation aswhere

_{h}*k*,

*T*, and

*η*are, respectively, the Boltzmann’s constant, the absolute temperature and the viscosity of the medium.

*g*

^{(2)}(

*τ*) of the scattered intensity

*I*(

*t*) instead of

*g*

^{(1)}(

*τ*), where

*g*

^{(1)}(

*τ*) is obtained from the measured

*g*

^{(2)}(

*τ*) using the Siegert relation as

*g*

^{(1)}(

*τ*) is given as the weighted mean of the size distribution function as [16

16. M. P. Cagigal, M. A. Rebolledo, and F. Moreno, “Determination of the radii and the concentration ratio in binary mixtures of spherical macromolecules from the measurement of n^{(2)}(T),” Appl. Opt. **23**(13), 2091–2096 (1984). [CrossRef] [PubMed]

19. A. Flamberg and R. Pecora, “Dynamic Light-Scattering Study of Micelles in a High Ionic-Strength Solution,” J. Phys. Chem. **88**(14), 3026–3033 (1984). [CrossRef]

*α=q*6

^{2}kT/*πη*and

*r*represents the size of the scatterer, i.e. a radius of a spherical particle. Furthermore,

*i*(

*r*) signifies the intensity size distribution or the amplitude distribution of scattered light intensity with respect to size

*r*. In the measurement of DLS, the size distribution

*i*(

*r*) is obtainable using conventional data processing algorithms such as CONTIN and NNLS [20

20. A. Lomakin, G. B. Benedek, and D. B. Teplow, “Monitoring protein assembly using quasielastic light scattering spectroscopy,” Methods Enzymol. **309**, 429–459 (1999). [CrossRef] [PubMed]

*i*(

*r*) is available, it is not difficult to obtain the fraction of specific scatterers in a known size range. However, the size distribution obtained with these techniques is often unstable and non-repeatable, particularly in the polydisperse case, as described above. Therefore, we have attempted to develop a different technique to obtain the fraction of one kind of scatterers in a bimodal size distribution.

### 2.2 Fraction estimation methods

#### 2.2.1 Fraction for narrow size distributions

*r*and

_{s}*r*denote the typical sizes of small and large components of scatterers. Subscripts

_{l}*s*and

*l*hereinafter represent the small and the large components of scatterers. The intensity weights

*I*and

_{s}*I*are given as

_{l}*r*≤ b and c ≤

_{s}*r*. Then, using Eq. (5) the autocorrelation function of the electric field scattered from the mixed scatterers is given as [13

_{l}≤ d13. M. Shibayama, T. Karino, and S. Okabe, “Distribution analyses of multi-modal dynamic light scattering data,” Polymer (Guildf.) **47**(18), 6446–6456 (2006). [CrossRef]

16. M. P. Cagigal, M. A. Rebolledo, and F. Moreno, “Determination of the radii and the concentration ratio in binary mixtures of spherical macromolecules from the measurement of n^{(2)}(T),” Appl. Opt. **23**(13), 2091–2096 (1984). [CrossRef] [PubMed]

*X*=

_{I}*I*/(

_{s}*I*), then Eq. (7) reduces toand the fraction is obtainable as

_{s}+I_{l}*g*

_{sl}^{(1)}(

*τ*) and the typical sizes of the two scatterer components:

*r*and

_{s}*r*.

_{l}*r*and

_{s}*r*are sufficiently close ((

_{l}*r*−

_{l}*r*)/ (

_{s}*r*+

_{l}*r*) << 1) such as in the LDL case, the autocorrelation function can be approximated as

_{s}*r*is the typical size of the two-component scatterers, or

_{sl}*r*≤

_{s}*r*≤

_{sl}*r*. In the case of LDL,

_{l}*τ*. Then Eq. (9) can be approximated in a much simpler form as

*X*=

_{W}*W*/(

_{s}*W*),

_{s}+W_{l}*W*and

*w*(

*r*) respectively represent the mass-weight and the size distribution of weight. The LDL particles are much smaller than the wavelength of light. Therefore, the scattered light shows the characteristics of the Rayleigh scattering. The scattered intensity of the Rayleigh scattering is proportional to the square of the particle’s volume [20

20. A. Lomakin, G. B. Benedek, and D. B. Teplow, “Monitoring protein assembly using quasielastic light scattering spectroscopy,” Methods Enzymol. **309**, 429–459 (1999). [CrossRef] [PubMed]

*X*can be estimated from

_{W}*X*as

_{I}21. R. S. Stock and W. H. Ray, “Interpretation of photon correlation spectroscopy data: A comparison of analysis methods,” J. Polym. Sci., Polym. Phys. Ed. **23**(7), 1393–1447 (1985). [CrossRef]

22. P. A. Hassan and S. K. Kulshreshtha, “Modification to the cumulant analysis of polydispersity in quasielastic light scattering data,” J. Colloid Interface Sci. **300**(2), 744–748 (2006). [CrossRef] [PubMed]

*r*and

_{s}*r*as the mean sizes

_{l}*m*and

_{s}*m*in the DLS measurement using pure samples of small and large scatterers. Then, the weight fraction can be estimated aswhere

_{l}*m*is the mean size evaluated in the DLS measurement with the sample solution of interest.

_{sl}#### 2.2.2 Fraction for rectangular size distribution

*u*(

*r*) is a unit step function, and where [

*a*,

*b*] and [

*c*,

*d*] respectively denote the size ranges of small and large scatterers. In most cases,

*b*is smaller than or equal to

*c*, but the following formulae are also valid in the case of

*b*>

*c*.

*i*(

*r*),

*w*(

*r*), and

*n*(

*r*) respectively signify size distributions of scattered intensity, scatterers’ weight and scatterers’ number.

## 3. Method of experiment

### 3.1 Polystyrene latex beads

### 3.2 Lipoprotein

*d*= 1.019–1.044 kg/L) and sdLDL (

*d*= 1.044–1.063 kg/L) were separated from human serum by sequential ultracentrifugation (Optima

^{TM}Max ultracentrifuge; Beckman Coulter Inc.) with a near vertical tube rotor (MLN-80; Beckman Coulter Inc.). Serum (2 ml) was mixed with 6 ml KBr solution (

*d*= 1.023 kg/L); the mixture was centrifuged at 40,000 rpm for 20 h at 15°C. The 2.5 ml supernatant containing lipoproteins (

*d*< 1.019 kg/L) was removed and 2.5 ml KBr solution (

*d*= 1.099 kg/L) was added to the infranatant. After centrifugation at 50,000 rpm for 18 h at 15°C, 2.5 ml supernatant (

*d*< 1.044 kg/L) containing large LDL was obtained. Then, 2.5 ml of the KBr solution (

*d*=1.105 kg/L) was added to the infranatant. It was centrifuged at 50,000 rpm for 18 h at 15°C. Finally, 2.5 ml supernatant (

*d*< 1.063 kg/L) containing sdLDL was obtained, and the infranatant was used as the sample solution that contains HDL and the smaller proteins with higher density. The accuracy of these processes was confirmed using polyacrylamide gel electrophoresis (LipoPhor; Quantimetrix Corp.) as the purity of each separated fraction. Furthermore, serum lipids were measured using automated enzymatic method with a commercial kit (Denka Seiken Co., Ltd., Tokyo, Japan): T-CHO(S) for total cholesterol (TC). After this separation process, both sdLDL and large LDL were diluted with sterile 0.9% saline solution to make their concentrations equal. Then, they were mixed to prepare the LDL samples in different weight fractions.

### 3.3 Dynamic light scattering system

*g*

^{(2)}(

*τ*) was measured using a DLS system (FDLS-3000; Otsuka Electronics Co., Ltd.). The laser power was 100 mW and the wavelength was 532 nm. The scattered light was detected at

*θ*= 90°. The DLS system temperatures were respectively set to 25°C and at 37°C for the latex particles and the LDL experiments. The sample solution was contained in a 178 mm × 5 mmϕ glass tube (Optima USA, Inc.). A water bath was used to keep the temperature of the samples constant. Measurement of the scattered intensity fluctuation was repeated 100 times with each sample.

## 4. Elimination of large scatterer effect

*g*

_{m}^{(1)}(

*τ*) is the measured autocorrelation function, and

*S*and

*N*respectively denote the signal and the noise components. In practice,

*g*

_{m}^{(1)}(

*τ*) is obtained from the measured intensity autocorrelation function

*g*

_{m}^{(2)}(

*τ*) using Eq. (4).

*g*

^{(1)}(

*τ*) is divisible into two parts. According to a report of an earlier study [17

**26**(5), 413–437 (2008). [CrossRef]

*g*

_{S}^{(1)}(

*τ*) from

*g*

_{N}^{(1)}(

*τ*) using the curve fitting technique with two exponential components. In the following experiments, the

*g*

_{sl}^{(1)}(

*τ*) in the previous chapter was extracted as the

*g*

_{S}^{(1)}(

*τ*) in Eq. (22) from the measured autocorrelation function

*g*

_{m}^{(1)}(

*τ*) using the curve fitting technique with Eq. (22). The curve was fitted using nonlinear least squares fitting [23].

*g*

_{m}^{(1)}(

*τ*) of a monodisperse solution of 28 nm latex spheres in the DLS measurement. Deviation from the theoretical straight line is evident. This figure shows that the curve fitting with two exponential components yielded satisfactory agreement. By subtracting the component of large scatterers according to Eq. (22), we were able to extract the major component (thick dotted line) for the desired autocorrelation function

*g*

_{sl}^{(1)}(

*τ*).

24. D. O’Neal, P. Harrip, G. Dragicevic, D. Rae, and J. D. Best, “A comparison of LDL size determination using gradient gel electrophoresis and light-scattering methods,” J. Lipid Res. **39**(10), 2086–2090 (1998). [PubMed]

25. J. A. Chouinard, A. Khalil, and P. Vermette, “Method of imaging low density lipoproteins by atomic force microscopy,” Microsc. Res. Tech. **70**(10), 904–907 (2007). [CrossRef] [PubMed]

## 5. Experimental verification

### 5.1 Fraction estimation with standard particles

*g*

_{m}^{(1)}(

*τ*) was obtained from the measured intensity autocorrelation function

*g*

_{m}^{(2)}(

*τ*) in DLS measurement according to the Siegert relation in Eq. (4). Then

*g*

_{sl}^{(1)}(

*τ*) was obtained from the

*g*

_{m}^{(1)}(

*τ*) by the elimination process using Eq. (22).

*m*of the testing solution was estimated from the

_{sl}*g*

_{sl}^{(1)}(

*τ*) using the common cumulant method. The weight fraction

*X*was estimated using Eq. (12) using this

_{W}*m*and the known mean sizes

_{sl}*m*and

_{s}*m*.

_{l}*a*,

*b*] and [

*c*,

*d*] for small and large scatterers. We assumed the size ranges using the standard deviation of the size distribution. That is

*a*=

*m*−

_{s}*σ*,

_{s}*b*=

*m*+

_{s}*σ*,

_{s}*c*=

*m*−

_{l}*σ*,

_{l}*d*=

*m*+

_{l}*σ*, where

_{l}*m*and

*σ*respectively represent the mean and the standard deviation of the particle size distribution. The values of

*m*and

*σ*were provided by the manufacturer. The weight fraction

*X*was estimated from the

_{W}*g*

_{sl}^{(1)}(

*τ*) using Eq. (21).

21. R. S. Stock and W. H. Ray, “Interpretation of photon correlation spectroscopy data: A comparison of analysis methods,” J. Polym. Sci., Polym. Phys. Ed. **23**(7), 1393–1447 (1985). [CrossRef]

26. V. M. Gun’ko, A. V. Klyueva, Y. N. Levchuk, and R. Leboda, “Photon correlation spectroscopy investigations of proteins,” Adv. Colloid Interface Sci. **105**(1-3), 201–328 (2003). [CrossRef] [PubMed]

*f*(

_{est}*r*) estimated using the CONTIN algorithm. Using the curve fitting technique [23], this distribution

*f*(

_{est}*r*) is resolved into the sum of the two Gaussian distributions, orwhere

*m*,

_{s}*m*and

_{l}*σ*,

_{s}*σ*respectively signify means and standard deviations of the normal distribution. An example of curve fitting with two normal distributions of fixed means and standard deviations is presented in Fig. 2.

_{l}*I*and

_{s}*I*was estimated with the parameters 2

_{l}*m*= 21 nm, 2

_{s}*m*= 28 nm, 2

_{l}*σ*= 5.7 nm, and 2

_{s}*σ*= 6.1 nm. The intensity fraction

_{l}*X*was estimated as

_{I}*X*=

_{I}*I*/(

_{s}*I*+

_{s}*I*), and the weight fraction

_{l}*X*was obtained with Eq. (12), which is shown in the open circles in Fig. 3. More estimation processes were involved in this indirect estimation. Therefore, the agreement between the given and the estimated fraction was poor.

_{W}*m*<

_{sl}*m*, then

_{s}*m*=

_{sl}*m*and if

_{s}*m*>

_{sl}*m*, then

_{l}*m*=

_{sl}*m*in the Method#1. If

_{l}*X*< 0, then

_{w}*X*= 0, and if

_{w}*X*> 1, then

_{w}*X*= 1 in Method#2. Except for a few corrected points, both results show good agreement. As expected, the result by Method#2 was much closer than that by Method#1 to the correct value shown in the broken line in Fig. 4. This is the size distributions of 21 nm and 28 nm particles were too wide to be approximated as the Dirac’s delta function, and the assumption for Method#2 holds well.

_{w}### 5.2 Fraction estimation of sdLDL

21. R. S. Stock and W. H. Ray, “Interpretation of photon correlation spectroscopy data: A comparison of analysis methods,” J. Polym. Sci., Polym. Phys. Ed. **23**(7), 1393–1447 (1985). [CrossRef]

24. D. O’Neal, P. Harrip, G. Dragicevic, D. Rae, and J. D. Best, “A comparison of LDL size determination using gradient gel electrophoresis and light-scattering methods,” J. Lipid Res. **39**(10), 2086–2090 (1998). [PubMed]

*r*−

_{l}*r*)/(

_{s}*r*+

_{l}*r*) ≈0.1) than in the standard particle case ((

_{s}*r*−

_{l}*r*)/(

_{s}*r*+

_{l}*r*) ≈0.35). This made the autocorrelation functions for each component more similar in the LDL case. The estimated result was more vulnerable to noise and artifacts in the measurement of the autocorrelation function than in the standard particle case.

_{s}## 6. Conclusion

## Acknowledgements

## References and links

1. | Y. Hirowatari, H. Yoshida, H. Kurosawa, K. I. Doumitu, and N. Tada, “Measurement of cholesterol of major serum lipoprotein classes by anion-exchange HPLC with perchlorate ion-containing eluent,” J. Lipid Res. |

2. | S. Akita, F. M. Sacks, L. P. Svetkey, P. R. Conlin, and G. KimuraS. AkitaF. M. SacksL. P. SvetkeyP. R. ConlinG. KimuraDASH-Sodium Trial Collaborative Research Group, “Effects of the Dietary Approaches to Stop Hypertension (DASH) diet on the pressure-natriuresis relationship,” Hypertension |

3. | F. M. Sacks and H. Campos, “Clinical review 163: Cardiovascular endocrinology: Low-density lipoprotein size and cardiovascular disease: a reappraisal,” J. Clin. Endocrinol. Metab. |

4. | J. B. German, J. T. Smilowitz, and A. M. Zivkovic, “Lipoproteins: When size really matters,” Curr. Opin. Colloid Interface Sci. |

5. | W. Ensign, N. Hill, and C. B. Heward, “Disparate LDL phenotypic classification among 4 different methods assessing LDL particle characteristics,” Clin. Chem. |

6. | M. Rizzo and K. Berneis, “Low-density lipoprotein size and cardiovascular risk assessment,” QJM |

7. | H. Wang, H. M. Wang, Q. H. Jin, H. Cong, G. S. Zhuang, J. L. Zhao, C. L. Sun, H. W. Song, and W. Wang, “Microchip-based small, dense low-density lipoproteins assay for coronary heart disease risk assessment,” Electrophoresis |

8. | H. Campos, E. Blijlevens, J. R. McNamara, J. M. Ordovas, B. M. Posner, P. W. Wilson, W. P. Castelli, and E. J. Schaefer, “LDL particle size distribution. Results from the Framingham Offspring Study,” Arterioscler. Thromb. |

9. | T. Hirano, Y. Ito, H. Saegusa, and G. Yoshino, “A novel and simple method for quantification of small, dense LDL,” J. Lipid Res. |

10. | F. Gonzalez, J. M. Saiz, F. Moreno, and P. J. Valle, “Application of a Laplace Transform Method to Binary-Mixtures of Spherical-Particles in Solution for Low Scattered Intensity,” J. Phys. D Appl. Phys. |

11. | J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. |

12. | C. B. Frantzen, L. Ingebrigtsen, M. Skar, and M. Brandl, “Assessing the accuracy of routine photon correlation spectroscopy analysis of heterogeneous size distributions,” AAPS PharmSciTech |

13. | M. Shibayama, T. Karino, and S. Okabe, “Distribution analyses of multi-modal dynamic light scattering data,” Polymer (Guildf.) |

14. | M. Schneider and T. F. McKenna, “Comparative study of methods for the measurement of particle size and size distribution of polymeric emulsions,” Part. Part. Syst. Char. |

15. | H. Ruf and B. J. Gould, “Size distributions of chylomicrons from human lymph from dynamic light scattering measurements,” Eur. Biophys. J. Biophy. |

16. | M. P. Cagigal, M. A. Rebolledo, and F. Moreno, “Determination of the radii and the concentration ratio in binary mixtures of spherical macromolecules from the measurement of n |

17. | M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle characterization by PCS: The analysis of bimodal distributions,” Particul. Sci. Technol. |

18. | B. J. Berne, and R. Pecora, |

19. | A. Flamberg and R. Pecora, “Dynamic Light-Scattering Study of Micelles in a High Ionic-Strength Solution,” J. Phys. Chem. |

20. | A. Lomakin, G. B. Benedek, and D. B. Teplow, “Monitoring protein assembly using quasielastic light scattering spectroscopy,” Methods Enzymol. |

21. | R. S. Stock and W. H. Ray, “Interpretation of photon correlation spectroscopy data: A comparison of analysis methods,” J. Polym. Sci., Polym. Phys. Ed. |

22. | P. A. Hassan and S. K. Kulshreshtha, “Modification to the cumulant analysis of polydispersity in quasielastic light scattering data,” J. Colloid Interface Sci. |

23. | A. Milat, |

24. | D. O’Neal, P. Harrip, G. Dragicevic, D. Rae, and J. D. Best, “A comparison of LDL size determination using gradient gel electrophoresis and light-scattering methods,” J. Lipid Res. |

25. | J. A. Chouinard, A. Khalil, and P. Vermette, “Method of imaging low density lipoproteins by atomic force microscopy,” Microsc. Res. Tech. |

26. | V. M. Gun’ko, A. V. Klyueva, Y. N. Levchuk, and R. Leboda, “Photon correlation spectroscopy investigations of proteins,” Adv. Colloid Interface Sci. |

**OCIS Codes**

(170.1470) Medical optics and biotechnology : Blood or tissue constituent monitoring

(290.5850) Scattering : Scattering, particles

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: November 30, 2009

Revised Manuscript: February 12, 2010

Manuscript Accepted: February 22, 2010

Published: March 12, 2010

**Virtual Issues**

Vol. 5, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Suchin Trirongjitmoah, Toshihiro Sakurai, Kazuya Iinaga, Hitoshi Chiba, and Koichi Shimizu, "Fraction estimation of small, dense LDL using autocorrelation function of dynamic light scattering," Opt. Express **18**, 6315-6326 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-6315

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### References

- Y. Hirowatari, H. Yoshida, H. Kurosawa, K. I. Doumitu, and N. Tada, “Measurement of cholesterol of major serum lipoprotein classes by anion-exchange HPLC with perchlorate ion-containing eluent,” J. Lipid Res. 44(7), 1404–1412 (2003). [CrossRef] [PubMed]
- S. Akita, F. M. Sacks, L. P. Svetkey, P. R. Conlin, G. Kimura, and DASH-Sodium Trial Collaborative Research Group, “Effects of the Dietary Approaches to Stop Hypertension (DASH) diet on the pressure-natriuresis relationship,” Hypertension 42(1), 8–13 (2003). [CrossRef] [PubMed]
- F. M. Sacks and H. Campos, “Clinical review 163: Cardiovascular endocrinology: Low-density lipoprotein size and cardiovascular disease: a reappraisal,” J. Clin. Endocrinol. Metab. 88(10), 4525–4532 (2003). [CrossRef] [PubMed]
- J. B. German, J. T. Smilowitz, and A. M. Zivkovic, “Lipoproteins: When size really matters,” Curr. Opin. Colloid Interface Sci. 11(2–3), 171–183 (2006). [CrossRef] [PubMed]
- W. Ensign, N. Hill, and C. B. Heward, “Disparate LDL phenotypic classification among 4 different methods assessing LDL particle characteristics,” Clin. Chem. 52(9), 1722–1727 (2006). [CrossRef] [PubMed]
- M. Rizzo and K. Berneis, “Low-density lipoprotein size and cardiovascular risk assessment,” QJM 99(1), 1–14 (2005). [CrossRef] [PubMed]
- H. Wang, H. M. Wang, Q. H. Jin, H. Cong, G. S. Zhuang, J. L. Zhao, C. L. Sun, H. W. Song, and W. Wang, “Microchip-based small, dense low-density lipoproteins assay for coronary heart disease risk assessment,” Electrophoresis 29(9), 1932–1941 (2008). [CrossRef] [PubMed]
- H. Campos, E. Blijlevens, J. R. McNamara, J. M. Ordovas, B. M. Posner, P. W. Wilson, W. P. Castelli, and E. J. Schaefer, “LDL particle size distribution. Results from the Framingham Offspring Study,” Arterioscler. Thromb. 12(12), 1410–1419 (1992). [CrossRef] [PubMed]
- T. Hirano, Y. Ito, H. Saegusa, and G. Yoshino, “A novel and simple method for quantification of small, dense LDL,” J. Lipid Res. 44(11), 2193–2201 (2003). [CrossRef] [PubMed]
- F. Gonzalez, J. M. Saiz, F. Moreno, and P. J. Valle, “Application of a Laplace Transform Method to Binary-Mixtures of Spherical-Particles in Solution for Low Scattered Intensity,” J. Phys. D Appl. Phys. 25(3), 357–361 (1992). [CrossRef]
- J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. 261(1), 74–81 (2003). [CrossRef] [PubMed]
- C. B. Frantzen, L. Ingebrigtsen, M. Skar, and M. Brandl, “Assessing the accuracy of routine photon correlation spectroscopy analysis of heterogeneous size distributions,” AAPS PharmSciTech 4(3), 62 (2003). [CrossRef]
- M. Shibayama, T. Karino, and S. Okabe, “Distribution analyses of multi-modal dynamic light scattering data,” Polymer (Guildf.) 47(18), 6446–6456 (2006). [CrossRef]
- M. Schneider and T. F. McKenna, “Comparative study of methods for the measurement of particle size and size distribution of polymeric emulsions,” Part. Part. Syst. Char. 19(1), 28–37 (2002). [CrossRef]
- H. Ruf and B. J. Gould, “Size distributions of chylomicrons from human lymph from dynamic light scattering measurements,” Eur. Biophys. J. Biophy. 28(1), 1–11 (1998). [CrossRef]
- M. P. Cagigal, M. A. Rebolledo, and F. Moreno, “Determination of the radii and the concentration ratio in binary mixtures of spherical macromolecules from the measurement of n(2)(T),” Appl. Opt. 23(13), 2091–2096 (1984). [CrossRef] [PubMed]
- M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle characterization by PCS: The analysis of bimodal distributions,” Particul. Sci. Technol. 26(5), 413–437 (2008). [CrossRef]
- B. J. Berne, and R. Pecora, Dynamic light scattering: with applications to chemistry, biology, and physics, Dover ed. (Dover Publications, Mineola, N.Y., 2000).
- A. Flamberg and R. Pecora, “Dynamic Light-Scattering Study of Micelles in a High Ionic-Strength Solution,” J. Phys. Chem. 88(14), 3026–3033 (1984). [CrossRef]
- A. Lomakin, G. B. Benedek, and D. B. Teplow, “Monitoring protein assembly using quasielastic light scattering spectroscopy,” Methods Enzymol. 309, 429–459 (1999). [CrossRef] [PubMed]
- R. S. Stock and W. H. Ray, “Interpretation of photon correlation spectroscopy data: A comparison of analysis methods,” J. Polym. Sci., Polym. Phys. Ed. 23(7), 1393–1447 (1985). [CrossRef]
- P. A. Hassan and S. K. Kulshreshtha, “Modification to the cumulant analysis of polydispersity in quasielastic light scattering data,” J. Colloid Interface Sci. 300(2), 744–748 (2006). [CrossRef] [PubMed]
- A. Milat, MATLAB: an introduction with applications, 3rd ed. (Wiley Publications, N.Y., 2008).
- D. O’Neal, P. Harrip, G. Dragicevic, D. Rae, and J. D. Best, “A comparison of LDL size determination using gradient gel electrophoresis and light-scattering methods,” J. Lipid Res. 39(10), 2086–2090 (1998). [PubMed]
- J. A. Chouinard, A. Khalil, and P. Vermette, “Method of imaging low density lipoproteins by atomic force microscopy,” Microsc. Res. Tech. 70(10), 904–907 (2007). [CrossRef] [PubMed]
- V. M. Gun’ko, A. V. Klyueva, Y. N. Levchuk, and R. Leboda, “Photon correlation spectroscopy investigations of proteins,” Adv. Colloid Interface Sci. 105(1-3), 201–328 (2003). [CrossRef] [PubMed]

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