## An insight into statistical refractive index properties of cell internal structure via low-coherence statistical amplitude microscopy |

Optics Express, Vol. 18, Issue 21, pp. 21950-21958 (2010)

http://dx.doi.org/10.1364/OE.18.021950

Acrobat PDF (4664 KB)

### Abstract

Refractive index properties, especially at the nanoscale, have shown great potential in cancer diagnosis and screening. Due to the intrinsic complexity and weak refractive index fluctuation, the reconstruction of internal structures of a biological cell has been challenging. In this paper, we propose a simple and practical approach to derive the statistical properties of internal refractive index fluctuations within a biological cell with a new optical microscopy method – Low-coherence Statistical Amplitude Microscopy (SAM). We validated the capability of SAM to characterize the statistical properties of cell internal structures, which is described by numerical models of one-dimensional Gaussian random field. We demonstrated the potential of SAM in cancer detection with an animal model of intestinal carcinogenesis – multiple intestinal neoplasia mouse model. We showed that SAM-derived statistical properties of cell nuclear structures could detect the subtle changes that are otherwise undetectable by conventional cytopathology.

© 2010 OSA

## 1. Introduction

1. H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. **69**(13), 5357–5363 (2009). [CrossRef] [PubMed]

2. P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. **35**(17), 2840–2842 (2010). [CrossRef] [PubMed]

3. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. **29**(21), 2503–2505 (2004). [CrossRef] [PubMed]

4. N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. **34**(6), 767–769 (2009). [CrossRef] [PubMed]

3. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. **29**(21), 2503–2505 (2004). [CrossRef] [PubMed]

5. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. **30**(5), 468–470 (2005). [CrossRef] [PubMed]

6. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. **31**(6), 775–777 (2006). [CrossRef] [PubMed]

7. O. P. Bruno and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. **28**(21), 2049–2051 (2003). [CrossRef] [PubMed]

8. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods **4**(9), 717–719 (2007). [CrossRef] [PubMed]

9. F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. **31**(2), 178–180 (2006). [CrossRef] [PubMed]

## 2. Materials and methods

### 2.1 Statistical model of refractive index profile of a single biological cell

2. P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. **35**(17), 2840–2842 (2010). [CrossRef] [PubMed]

10. C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. **30**(16), 2131–2133 (2005). [CrossRef] [PubMed]

11. M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. **31**(10), 1462–1464 (2006). [CrossRef] [PubMed]

*n*= 1.52) as the top and bottom medium that sandwich the cell. For each GRF-modeled axial refractive index profile, a one-dimensional multilayer dielectric slab model that implements Fresnel reflection [13] is used to generate its backscattering spectrum. The backscattering spectrum from each pixel was numerically resampled to evenly spaced wavenumbers and multiplied by a Hanning window before applying a fast Fourier transform. The Fourier transformed data at the prominent peak corresponding to the optical path length of interest depth

*z*were selected for amplitude processing. After taking the discrete Fourier transform, a complex-valued

*F*is obtained, and the amplitude can be extracted by taking the absolute value of

### 2.3 Animal experiments

## 3. Results

### 3.1 Numerical experiments with gaussian random field model

*Section 2.1*. Additionally, due to the intrinsic variations of cell thickness

*L,*it is considered as another important variable in our numerical model. All values of these physical parameters were chosen to be within the cytologically relevant range, which is determined from our experimental data of cytological specimens from animal models and human patients.

*R*(

*L*with different spatial correlation length

*R*is moderately increased with the increase of

*R*, but it only weakly increase

*L*to the three SAM-derived parameters with fixed

### 3.2 Experiments with animal model of intestinal carcinogenesis

*adenomatous polyposis coli*(

*APC*) gene mutation that spontaneously develops multiple intestinal adenomas. We analyzed the normal-appearing epithelial cells from small intestine from wild-type and Min mice at four and a half months. At this time point, the Min mice have developed macroscopically visible multiple adenomatous polyps. We analyzed the histologically normal-appearing intestinal epithelial cells from Min mice and those from wild-type mice (control group). Figure 4 shows their representative Papanicolaou-stained cytological images obtained from a conventional bright-field microscope and the corresponding amplitude maps from the cell nuclei. Although the microscopic cytological images look similar (as confirmed by an expert cytopathologist), the amplitude maps that characterize the refractive index variation of cell internal structures exhibit distinct differences. The three statistical parameters from the cell nuclei were calculated from the amplitude maps: the average amplitude

*R*.

*R*is also substantially increased in the epithelial cell nuclei of Min mice (

*R*falls within the range from 0.1 to 0.2. Based on the lookup table created by the numerical simulation with a wide range of biologically relevant statistical properties of refractive index (

*L*), the correlation length

## 4. Discussion

*R*that are closely associated with the statistical properties of sub-cellular refractive index, characterized by

*L*. The results from the numerical simulation show that although the correlation between amplitude parameters and cell refractive index properties is rather complex, each of the amplitude parameter has a dominating contributor under the configuration emulating the cytology specimens. The average amplitude

*R*mainly arise from the changes in

*p*-value < 0.0001) has a much smaller

*p*-value than the average amplitude

*p*-value = 0.05) implying that the refractive index variation may be more sensitive than the average refractive index in detecting the carcinogenesis-associated structural changes. It is worth pointing out that both

*R*of axial refractive index can be used as a more experimentally robust parameter to minimize the effect of stain absorption. Such SAM-derived quantitative statistical information about the subtle alterations in nuclear architecture is otherwise undetectable with conventional optical microscopy. To confirm that these cells are truly indistinguishable with conventional microscopy, we performed the quantitative analysis on conventional bright-field cytology images and found that the intensity parameters (i.e., average intensity and standard deviation of intensity) cannot distinguish cytologically normal-appearing epithelial cell nuclei from the wild-type and Min mice (

*p*-value = 0.10 and 0.26, respectively).

## 5. Conclusions

1. H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. **69**(13), 5357–5363 (2009). [CrossRef] [PubMed]

## Acknowledgements

## References and links

1. | H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. |

2. | P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. |

3. | G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. |

4. | N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. |

5. | P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. |

6. | G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. |

7. | O. P. Bruno and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. |

8. | W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods |

9. | F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. |

10. | C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. |

11. | M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. |

12. | R. J. Adler, |

13. | U. S. Inan, and A. S. Inan, |

14. | Y. Liu, X. Li, Y. L. Kim, and V. Backman, “Elastic backscattering spectroscopic microscopy,” Opt. Lett. |

**OCIS Codes**

(110.0180) Imaging systems : Microscopy

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine

(290.1350) Scattering : Backscattering

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: August 30, 2010

Revised Manuscript: September 24, 2010

Manuscript Accepted: September 26, 2010

Published: September 30, 2010

**Virtual Issues**

Vol. 5, Iss. 14 *Virtual Journal for Biomedical Optics*

**Citation**

Pin Wang, Rajan K. Bista, Wei Qiu, Walid E. Khalbuss, Lin Zhang, Randall E. Brand, and Yang Liu, "An insight into statistical refractive index properties of cell internal structure via low-coherence statistical amplitude microscopy," Opt. Express **18**, 21950-21958 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-21-21950

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### References

- H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. 69(13), 5357–5363 (2009). [CrossRef] [PubMed]
- P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. 35(17), 2840–2842 (2010). [CrossRef] [PubMed]
- G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004). [CrossRef] [PubMed]
- N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34(6), 767–769 (2009). [CrossRef] [PubMed]
- P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005). [CrossRef] [PubMed]
- G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006). [CrossRef] [PubMed]
- O. P. Bruno and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28(21), 2049–2051 (2003). [CrossRef] [PubMed]
- W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007). [CrossRef] [PubMed]
- F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006). [CrossRef] [PubMed]
- C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. 30(16), 2131–2133 (2005). [CrossRef] [PubMed]
- M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. 31(10), 1462–1464 (2006). [CrossRef] [PubMed]
- R. J. Adler, The geometry of random fields (J. Wiley, Chichester Eng., New York, 1981).
- U. S. Inan, and A. S. Inan, Electromagnetic waves (Prentice Hall, Upper Saddle River, N.J., 2000).
- Y. Liu, X. Li, Y. L. Kim, and V. Backman, “Elastic backscattering spectroscopic microscopy,” Opt. Lett. 30(18), 2445–2447 (2005). [CrossRef] [PubMed]

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