Amir H. Gandjbakhche, PhD, Head, Section on Biomedical Stochastic Physics
Franck Amyot, PhD, Postdoctoral Fellow
Moinuddin Hassan, PhD, Postdoctoral Fellow
Jason Riley, PhD, Postdoctoral Fellow
Alex Small, PhD, Postdoctoral Fellow
Victor Chernomordik, PhD, Staff Scientist
Sudeh Izadmehr, Summer Student ¹
Ali Shabestari, Summer Student ²
Zachary Ulissi, Summer Student ³
Alexander Sviridov, PhD, Guest Researcher ⁴
Abby Vogel, MS, Student ²

We devise quantitative theories, develop methodologies, and design instrumentation to study biological phenomena whose properties are characterized by elements of randomness in both space and time. Our research focuses on developing quantitative theories applicable to quantitative optical spectroscopy and tomographic imaging of tissues. Our work requires analysis of different optical sources of contrast such as endogenous or exogenous fluorescent labels, absorption (e.g., hemoglobin or chromophore concentration), and/or scattering. We design and conduct experiments and computer simulations to validate theoretical findings. In addition, collaborations with other scientists at the NIH and researchers around the country and world investigate physiological sites where optical techniques might be clinically practical and permit the acquisition of new diagnostic knowledge and/or less morbidity than that associated with existing diagnostic methods. A new project studies tumor-induced angiogenesis. Given that angiogenesis plays an essential role in establishing tumor malignancy, we study the mechanisms underlying angiogenesis through stochastic modeling and in vitro assays.

Quantitative characterization of tissue

Sviridov, Ulissi, Chernomordik, Gandjbakhche; in collaboration with Hebden, Smith, Weiss

Biological tissues often exhibit characteristic regular features or ornamental patterns. Transition from normal tissue function to diseased tissue can be detected by quantifying irregular patterns. The degree of statistical similarities in a region of interest can carry valuable comparative information about the structural features of a tissue and can help characterize it, i.e., disease localization and progression.

To visualize subsurface structural features of biological tissues, we have developed a user-friendly polarization imaging system that simultaneously images cross- and co-polarized light. We have also developed a quantitative statistical tool, based on Pearson correlation coefficient analysis, to enhance image quality and reveal regions of high statistical similarities within noisy tissue images. We have shown that, under certain conditions, such maps of the correlation coefficient are determined by the textural character of tissues and not by the choice of the reference image region, thereby providing information on tissue structure. As an example, we enhanced the subsurface texture of a demineralized tooth sample from a noisy polarized light image. We are moving to test this technique in a clinical setting and will investigate skin fibrosis and human teeth ex vivo.

Many biological tissues (muscle, skin, white matter in brain, and so forth) are known to be anisotropic, i.e., photons tend to migrate preferentially along fibers. While life-time fluorescence measurements have become a popular tool for assessing the characteristics of the fluorophore environment, we chose to consider the effects of tissue anisotropy on observed characteristics of fluorescent light by generalizing our random-walk analysis of light propagation in the anisotropic turbid media for the case of a deeply embedded small fluorophore or scattering inclusion, with special focus on the time-resolved measurement set-up. Our goal is to find an analytical expression for the expected change in the photon mean time-of-flight resulting from the presence of such an abnormality. The literature has discussed the chosen photon mean time-of-flight as a data type well suited for applications in reconstruction algorithms because of its robustness relative to noise. Obtained formulas can be used to separate variations in observed fluorescence lifetimes attributable to pH, temperature, and so forth from changes in the vicinity of the fluorophore and from effects of photon migration in anisotropic media.

Fluorescence lifetime imaging

Hassan, Riley, Chernomordik, Shabestari, Gandjbakhche; in collaboration with Capala, Gannot, Smith

Fluorophore lifetime imaging is a promising tool for studying tissue environment such as tumors. The lifetime (time for an electron to return from excited state to initial state) of a fluorophore can vary in response to changes in the immediate environment such as temperature, pH, tissue oxygen content, nutrient supply, and bioenergetic status. Mapping the lifetime and location of a fluorophore in tissue at different depths can be used to monitor such parameters.

To this end, we developed a time-resolved lifetime imaging system for in vivo small animal studies that maps fluorophore lifetimes. The system consists of a single source-multiple detector array that scans the surface of the tissue. The use of several source-detector separations makes it possible to probe different depths of the medium in two classes of experiments. In collaboration with Jacek Capala, who developed a pH-sensitive dye in the near-infrared region, we studied the tumor environment below the skin. A breast cancer cell line (SK-BR-3) was injected into the flank area of a female nude mouse; the cell line expresses high levels of the HER2 (HER2/neu, c-ErbB2) protein, which is a 185 kD trans-membrane receptor with tyrosine kinase activity that stimulates cell signaling pathways to increase cell proliferation, mobility, and survival. An infrared pH-sensitive dye, Alexa Fluor 750, was conjugated with Herceptin, a HER2-specific monoclonal antibody currently used for targeted therapy of HER2-overexpressing tumors.

We have demonstrated that, by using simplified back projections, we are able to map near-surface fluorescent lifetime in vivo. Combining the projections with the pre-calibrated lifetime response to pH, we have been able to perform biologically plausible, non-invasive quantification of pH in mouse tumors. We plan to continue these studies to investigate an Affibody-based molecular probe for imaging HER2 receptors and then validate our method by using other invasive pH-monitoring methods. The results show the method's potential for localizing the tumor and monitoring its status non-invasively in vivo.

For deep-tissue imaging, high scattering of biological tissue complicates matters. We have established that our existing analytical model can, with some minor extensions for generalization, accurately localize fluorophores and determine their lifetime in phantom experiments. Initial results show that we are moving toward developing deep-tissue lifetime maps. In one advance, we included a more realistic distribution of fluorophore lifetime, providing the inverse model with more flexibility to converge. At the same time, we have extended use of the analytical model as an integral component of an inverse model, allowing us to reconstruct the lifetime and location of a point source fluorophore. Further work is under way to extend the inverse model to handle distributed sources and hence extend current subsurface environmental maps of tissue behavior to deeper-tissue imaging. In other advances in studying the noise resistance of data types in fluorescence imaging, we have shown that a new local set of data types may provide more stability to noise than classical statistical (global) data types used in optical imaging.

Multimodality imaging techniques for monitoring tissue vasculature in Kaposi's sarcoma lesions

Hassan, Vogel, Gandjbakhche; in collaboration with Demos, Yarchoan

The oncology community is testing a number of novel targeted approaches such as anti-angiogenic, anti-vascular, immunological, and gene therapies against a variety of cancers. To monitor such therapies, it is desirable to establish non-invasive and quantitative techniques that, in assessing tumor vasculature and changes, can not only monitor structural changes but also assess the functional characteristics or metabolic status of the tumor. No such standard non-invasive techniques currently exist. For anti-angiogenic therapies, factors associated with blood flow are of particular interest.

We are testing three potential non-invasive imaging techniques to monitor patients undergoing an experimental therapy: infrared thermal imaging (thermography), laser Doppler imaging (LDI), and multispectral imaging. We are testing these techniques on subjects with Kaposi's sarcoma (KS), a highly vascular tumor that occurs frequently among patients with AIDS. Cutaneous KS lesions are easily accessible for non-invasive techniques that involve imaging of tumor vasculature and may thus represent a tumor model for assessing certain parameters of angiogenesis. Four NCI protocols are studying the effects of experimental anti-angiogenic therapies in KS.

Thermography graphically depicts temperature gradients over a given body surface area at a given time. It is used to study biological thermoregulatory abnormalities that directly or indirectly influence skin temperature. However, skin temperature is only an indirect measure of skin blood flow, and the superficial thermal signature of skin is also related to local metabolism. Thus, thermography is best used in conjunction with other techniques. LDI can more directly measure the net blood velocity of small blood vessels in tissue, which generally increases as blood supply increases during angiogenesis. We recorded thermal patterns by using an infrared camera with a uniform sensitivity in the wavelength range of 8-12 micrometers, and we acquired LDI images by scanning the lesion area of the KS patients at two wavelengths, 690 and 780 nm.

We have successfully used thermography and LDI to visualize KS lesions, and, though each measures an independent parameter, we observed a strong correlation in a group of 16 patients studied with both techniques. However, we detected some differences in individual lesions because LDI measured blood flow distribution in the superficial layer of the skin of the lesion, whereas the thermal signature provided a combined response of superficial vascularity and metabolic activities of deep tissue. Recently, we added to the clinical study near-infrared spectroscopy (NIRS), a non-contact and non-invasive method of monitoring changes in concentrations of blood volume and oxygenated and deoxygenated hemoglobin, and assessed the pathogenesis of the status and changes of KS lesions during therapy. Such an approach can be used to provide early markers for tumor responses and to learn about the pathophysiology of the disease and its changes in response to treatment.

NIRS is most closely related to visual assessment. In collaboration with Stavros Demos, we designed a portable spectral imaging system that captures images with a high-resolution CCD camera at six near-infrared wavelengths (700, 750, 800, 850, 900, and 1,000 nm). A white light held approximately 15 cm from tissue uniformly illuminates the surface. Using optical filters, we obtained images at the six wavelengths and used the intensity images in a mathematical optical model of skin containing two layers: an epidermis and a much thicker, highly scattering dermis. Each layer contains major chromophores that determine absorption in the corresponding layer, and the layers together determine the total reflectance of the skin. The effect of the thin epidermis layer on the intensity of the diffusely reflected light is determined by the effective attenuation of light where the epidermis absorption coefficient and the thickness of the epidermis must be taken into account. The influence of the much thicker, highly scattering dermis layer on skin reflectance should be estimated by a stochastic model of photon migration, e.g., random-walk theory. Multivariate analysis reconstructs local variations in melanin, oxygenated hemoglobin (HbO2), and blood volume.

Cellular dynamics of angiogenesis

Amyot, Small, Izadmehr, Ulissi, Gandjbakhche; in collaboration with Boukari, Camphausen, Neagu, Plant, Sackett

The process of tumor-induced angiogenesis, in which a growing tumor recruits new vasculature to increase nutrient intake, is a crucial part of tumor growth. We have developed a model of tumor-induced angiogenesis that includes the migratory response of endothelial cells (ECs) to tumor angiogenic factors and the interaction of ECs with the extracellular matrix (ECM). ECs switch between growth, differentiation, motility, or apoptotic behavior in response to the local topology and composition of the ECM. Considering the ECM as a statistically inhomogeneous two-phase random medium, we have shown that it can be a natural barrier to angiogenesis. We have studied vascular network formation for several ECM distributions and topologies and have found a correlation with percolation. A threshold exists under which sprouts cannot reach the tumor. During the growth of the vascular network, the attraction exerted by the tumor competes against the preferred path created by the ECM.

We have also examined the influence of branching on tumor vascularization. Branching is a natural phenomenon that helps the tumor become vascularized. By increasing the number of sprouts (i.e., capillaries), the vascular network increases the probability of reaching the tumor, as it can explore more pathways. Our simulations have shown that, after two branching events, the vascular network is very likely to reach the tumor.

In collaboration with Anne Plant's laboratory, which has designed thin films of highly oriented collagen fibers, we studied the local adhesion and orientation of ECs along collagen fibers. First, by using Fourier transform and Pearson correlation analysis, we were able to assess fiber orientation. Then we used an eccentricity model for cell orientation and morphology to study cell trajectory and shape as well as their correlation with the orientation of collagen fibers. We found high degrees of correlation, suggesting that our model can be used to study cell migrations in a controlled environment.

We are continuing our studies to characterize the physical and chemical proprieties of the ECM with fluorescence correlation spectroscopy (FCS). By measuring the diffusion coefficient of fluorescent molecules in ECM gels, FCS is able to measure the degradation of the gel by matrix metalloproteases (MMPs) released by cells. We plan to measure the interaction and stress generated between ECs and the ECM.

In another study, we investigate the directional guidance by growth factor gradients in angiogenesis. Large tumors become hypoxic and secrete a growth factor called vascular endothelial growth factor (VEGF). VEGF occurs in several common isoforms, in particular VEGF165 and VEGF189. The most significant difference between the two is that VEGF189 binds to the ECM more rapidly than does VEGF165. The uptake of VEGF by capillaries initiates a sequence of events that lead to the formation of a capillary network. This process is crucial to tumor growth and metastasis and therefore is of great clinical interest.

Much remains unknown about which form of VEGF guides chemotactic migration of cells to form a capillary network and the roles of the ECM and MMPs. Given that chemotactic migration is guided by growth-factor gradients, we devised a system of reaction-diffusion equations—with three adjustable parameters—to model the diffusion, binding, and cleavage of VEGF in vivo; the parameters are: (1) the rate constant for binding to the ECM; (2) the rate of VEGF production, which is known to vary in vivo; and (3) the rate of MMP production by cells proximal to capillaries, which is known to vary in vivo. Our simulations show that rapid binding to the ECM by VEGF₁₈₉ leads to short-range gradients of matrix-bound VEGF, whereas slower binding by VEGF₁₆₅ leads to longer-range gradients. The results are consistent with in vivo observations that the vasculature is particularly disorganized around tumors producing VEGF₁₈₉. Only VEGF₁₆₅ can produce long-range gradients that can guide cell migration to form an efficient and organized network.

We also found that the cleaved form of VEGF, removed from the matrix by the action of MMPs, is distributed with a gradient that points away from the tumor, calling into question whether the cleaved form of VEGF plays a chemotactic role in tumor-induced angiogenesis. Our observation is consistent with observations that cleaved VEGF molecules have a weaker chemotactic effect on receptors. Finally, our simulations show that, without MMPs, a gradient of matrix-bound VEGF cannot be sustained—an observation consistent with findings that the production of MMPs by cells near the parent capillary is necessary to initiate the formation of new vasculature.

Microscopy below the diffraction limit

Small, Chernomordik, Gandjbakhche; in collaboration with Ilev, Waynant

High-resolution confocal laser microscopy is an intensively active field in modern bioimaging. The technique provides sharp, high-magnification, three-dimensional imaging with submicron resolution by non-invasive optical sectioning and rejection of out-of-focus information. We have developed a simple fiber-optic confocal microscope with nano-scale depth resolution beyond the diffraction barrier. It combines the advanced properties of a simple apertureless single-mode-fiber confocal microscope, which provides a highly sensitive, diffraction-free Gaussian point light source/receiver, with a differential confocal microscope approach that exploits the sharp diffraction-free slope of the axial confocal response curve.

The method offers several advantages. First, apertureless fiber-optic confocal design provides higher spatial sensitivity and better submicron resolution, elimination of diffraction/aberration effects, flexibility, miniaturization, and scanning potential than conventional pinhole-based confocal systems. Second, the single-mode fiber coupler used as a key element serves simultaneously as a point light source and a point receiver, providing near-to-ideal conditions for forming and receiving the laser beam with a Gaussian mode distribution. Third, the design includes a high-NA (>0.8) confocal objective that provides high spatial discrimination. Fourth, the design involves tools and detecting techniques that possess high signal-to-noise potential. Fifth, by combining the advanced features of the fiber-optic confocal design and differential confocal pinhole microscope, ultrahigh-resolution confocal systems permit work in the subwavelength nanometric spatial range beyond the optical diffraction barrier. Finally, conventional optical microscopy cannot resolve features smaller than approximately half the wavelength of light, restricting lateral resolution to approximately 200 nanometers. Despite various efforts to overcome this limitation, most solutions are either computationally intensive or require elaborate and expensive equipment.

We have also developed an algorithm to enhance diffraction-limited images and obtain information on features smaller than the diffraction limit. Our algorithm tries to infer the best estimate of an object based on the diffraction-limited input image. Imaging an object with a diffraction-limited lens introduces a blurred image in which neighboring pixels on the camera are correlated. The point spread function (PSF) of a diffraction-limited lens determines the correlations between pixels. We exploit two key features of these correlations. In the first feature, the correlations have a finite range; thus, if a circle of pixels has a sufficiently large radius, the pixels do not record any information on the object conjugate to the center pixel. The pixels do, however, carry information about other objects that may be producing blur on the center pixel. We can therefore use the pixels along that circle to estimate the blur contribution to the signal recorded by the center pixel. As for the second feature, light detected near the center of the PSF is highly insensitive to displacements of the object while light detected away from the center (ideally where the PSF is at approximately half of its maximum value or where the slope is steepest) is highly sensitive to displacements of the object. We can therefore consider another circle of pixels, with a radius corresponding to the steepest slope of the PSF, and use the information encoded in those signals to calculate a better estimate of the intensity of the object conjugate to the center of the circle. Such an estimate is highly sensitive to small displacements of the object.

Applying the algorithm to simulated diffraction-limited images, we find that it is most effective for images of discrete point probes. Our algorithm enhances the blurry diffraction-limited image of the probes to reveal an elongated shape with a width that accurately tracks probe spacing at distances as low as 40 percent of the traditional diffraction limit. Our algorithm is robust against noise and can distinguish blur produced by a single bright probe from blur produced by two proximate dimmer probes. Our algorithm can also reveal the existence of a dim probe in proximity to a bright probe.

We are preparing to test the algorithm in experiments with fiber-optic nanoprobes, spacing and brightness of which can be easily controlled. After applying the algorithm to images acquired with real equipment and realistic noise, we envision applications in cell biology, where the ability to track small probes crossing membranes or probes aggregating or separating can be highly useful.

¹ Rutgers University
² University of Maryland at College Park
³ University of Delaware
⁴ Russian Academy of Science

COLLABORATORS

Hacène Boukari, PhD, Laboratory of Integrative and Medical Biophysics, NICHD, Bethesda, MD
Kevin Camphausen, MD, Radiation Oncology Branch, NCI, Bethesda, MD
Jacek Capala, PhD, Radiation Oncology Branch, NCI, Bethesda, MD
Stavros Demos, PhD, Lawrence Livermore National Laboratory, Livermore, CA
Israel Gannot, PhD, Tel Aviv University, Ramat Aviv, Israel
Jeremy Hebden, PhD, University College, London, UK
Ilko Ilev, PhD, Office of Science and Engineering Laboratories, FDA, Rockville, MD
Adrian Neagu, PhD, Victor Babes University of Medicine and Pharmacy, Timisoara, Romania
Anne Plant, PhD, NIST, Gaithersburg, MD
Dan Sackett, PhD, Laboratory of Integrative and Medical Biophysics, NICHD, Bethesda, MD
Paul Smith, PhD, Division of Bioengineering and Physical Science, ORS, NIH, Bethesda, MD
Ronald Waynant, PhD, Office of Science and Engineering Laboratories, FDA, Rockville, MD
George Weiss, PhD, Division of Computational Bioscience, CIT, NIH, Bethesda, MD
Robert Yarchoan, MD, HIV and AIDS Malignancy Branch, NCI, Bethesda, MD

For further information, contact amir@helix.nih.gov.