Stochastic Modeling of Biological Processes: Quantitative Optical Imaging and
Tumor-Induced Angiogenesis
Photo of Dr. Amir Gandjbakhche

Amir H. Gandjbakhche, PhD, Head, Section on Biomedical Stochastic Physics

Franck Amyot, PhD, Visiting Fellow

Moinuddin Hassan, PhD, Visiting Fellow

Victor Chernomordik, PhD, Staff Scientist

Asmaneh Siavosh, BS, Postbaccalaureate Fellow

Israel Gannot, PhD, Guest Researcher1

Alexander Sviridov, PhD, Guest Researcher2

Abby Vogel, MS, Student3

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 in vivo quantitative optical spectroscopy and tomographic imaging of tissues. We analyze optical sources of contrast such as endogenous or exogenous fluorescent labels, absorption, and/or scattering. We design and conduct experiments and computer simulations to validate theoretical findings. In addition, in collaboration with other scientists at the NIH and researchers around the country and world, we investigate physiological sites where optical techniques might be clinically practical while offering the potential of new diagnostic knowledge and/or less morbidity as compared 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

Many biological tissue components, such as collagen, muscle fibers, and keratin, as well as the retina and glucose possess polarization properties. Depolarization of polarized light depends strongly on the bulk optical properties of the tissue (absorption and scattering coefficients) and optical anisotropy. To visualize structural information about skin, we map its degree of polarization. We also study the propagation of polarized light in tissue and tissue-like phantoms and the possible application of polarized light for tissue diagnostics.

Mapping the degree of polarization may carry valuable information about the superficial and subsurface structures of the skin and other tissues and may provide information that cannot be obtained visually or photographically. A statistical analysis and methodology of noise filtering enhances detection of hidden structures and allows estimates of the characteristic sizes and directionality of possible structures.

We conducted experiments by irradiating the skin of athymic nude mice with a single dose of x-ray irradiation that initiated fibrosis. We took digital photographs of the irradiated mice by illuminating the mouse skin with a linearly polarized probe light of 650 nm. The specific pattern of the surface distribution of the degree of polarization allowed us to detect initial skin fibrosis structures that were not visually apparent. Data processing of the raw spatial distributions of the degree of polarization based on Fourier filtering of the high-frequency noise improved subjective perception of the revealed structure in the images. In addition, Pearson correlation analysis provided information about skin structural size and directionality.

We used polarized videoreflectometry to investigate the anisotropy of mouse and human skin in vivo. With an incident beam (linearly polarized, wavelength 650 nm) focused at the sample surface, we used two types of tissue-like media as controls to verify the technique: isotropic delrin and highly anisotropic demineralized bone with a priori knowledge of the preferential orientation of collagen fibers. Equi-intensity profiles of light, backscattered from the sample, were fitted with ellipses that appeared to follow the orientation of the collagen fibers. The ratio of the ellipse semiaxes correlated well with the ratio of reduced scattering coefficients obtained from radial intensity distributions. We analyzed the variation of equi-intensity profiles as a function of the distance from the incident beam for the initial polarization states of the light and the relative orientation of polarization filters for incident and backscattered light. For the anisotropic media (demineralized bone and human and mouse skin), we observed a qualitative difference between intensity distributions for cross- and co-polarized orientations of the polarization analyzer up to 1.5 to 2.5 mm from the entry point. The polarized videoreflectometry of the skin may be a useful tool for assessing skin fibrosis resulting from radiation treatment.

We continued collaborating with University College, London, to substantiate obtained random walk formulas describing light propagation in anisotropic media by phantom experiments for transmission and reflection geometries. We also applied random walk methodology based on time-dependent contrast functions to quantify optical properties of breast tumors for a sample of patients with invasive ductal carcinoma observed at two projections (craniocaudal and mediolateral). Using the Physikalisch-Technische Bundesanstalt’s time-domain scanning optical mammography, we recorded distributions of times-of-flight of photons through the breast in vivo at 670 nm and 785 nm. We reconstructed lateral dimensions of the tumors, their optical properties, and those of the surrounding tissue at both wavelengths for both projections. Research has shown that estimates of absorption coefficients are usually consistent for both projections while values of scattering coefficients often demonstrate large discrepancies. Using the absorption coefficients at both wavelengths, we estimated total blood volume and oxygen saturation for the tumors and the surrounding tissues.

Dudko OK, Weiss GH, Chernomordik V, Gandjbakhche A. photon migration in turbid media with anisotropic optical properties. Phys Med Biol 2004;49:3979-3989.

Hattery D, Hattery B, Chernomordik V, Smith P, Loew M, Mulshine J, Gandjbakhche A. Differential oblique angle spectroscopy of the oral epithelium. J Biomed Opt 2004;9:951-960.

Hebden JC, Guerrero JJ, Chernomordik V, Gandjbakhche A. Experimental evaluation of an anisotropic scattering model of a slab geometry. Opt Lett 2004;29:2518-2520.

Sviridov A, Chernomordik V, Hassan M, Russo A, Eidsath A., Smith P, Gandjbakhche A. Intensity profiles of linearly polarized light backscattered from skin and tissue-like phantoms. J Biomed Opt 2005;10:14012.

Sviridov A, Chernomordik V, Hassan M, Russo A, Smith P, Gandjbakhche A. Enhancement of hidden structures of early skin fibrosis using polarization degree patterns and Pearce correlation analysis. J Biomed Opt 2005; 10:51706.

Fluorescence

Deep-tissue optical imaging is of particular interest, as equipment costs are lower than for competing technologies such as MRI. For this purpose, the development of novel contrast agents with near-infrared fluorescence is especially important. We have been collaborating with Wei Chen, with whom we have entered into a nondisclosure agreement. We grew semiconductor nanocrystals of CdMnTe/Hg in aqueous solution and then coated them with bovine serum albumin. The nanocrystals are approximately 5 nm in diameter and have a broad fluorescence peak in the near-infrared (770 nm). We then injected the nanocrystals either subcutaneously or intravenously into athymic NCR NU/NU and C3H/HENCR MTV mice and excited the crystals with a spatially broad 633 nm source; a sensitive CCD (charge-coupled device) camera captured the resulting fluorescence.

We have demonstrated that the nanocrystals are a useful angiographic contrast agent for vessels surrounding and penetrating a murine squamous cell carcinoma in a C3H mouse. We conducted a preliminary assessment of the depth of penetration for excitation and emission by imaging a beating mouse heart both through an intact thorax and after a thoracotomy. We addressed the temporal resolution associated with imaging the nanocrystals in circulation and measured the blood clearance for the contrast agent.

In a study with researchers at Washington University, we were able to synthesize a novel near-infrared dye-labeled glycine-arginine-aspartic acid (Cyp-GRD) pentapeptide. The GRD peptide possesses amino acids similar to, but in a different sequence than, arginine-glycine-aspartic acid peptides known to target integrin receptors. In vitro, Cyp-GRD internalized in non–small-cell lung cancer cells (A549) without observable cytotoxic or proliferative effects on the cells at a concentration of up to 1x10-4 M. Time domain fluorescence intensity and lifetime imaging of the probe injected into A549 tumor-bearing mice revealed that the probe preferentially accumulated in the tumor and the major excretion organs (liver and kidneys). We mapped the fluorescence lifetime of the conjugate at the tumor site, showing the spatial distribution of the lifetime related to its environment. In addition, fluorescence intensity image reconstruction obtained by integrating the time-resolved intensities enabled us to display the contrast ratios of tumor-to-kidney or tumor-to-liver in slices at different depths. The study clearly demonstrated the feasibility of whole-body fluorescence lifetime imaging for tumor localization and its spatial functional status in living small animals. This imaging strategy could enhance the specificity and sensitivity of tumor detection by complementing intensity images in the diagnosis of diseases.

Fluorophore lifetime imaging is a promising tool for early detection of 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. The heterogeneity in tumor vascularity can be visualized as changes in pH and temperature. We established an Advanced Time-Correlated Single Photon Counting (ATCSPC) fluorescence life-time measurement system that was suitable for measuring the fluorescence lifetime in the experimental context of the application. We collected data regarding the behavior of decay shapes with respect to the position of the fluorophore and the surrounding pH value and correlated them with theoretical simulations; satisfying results from this step should provide the basis for the analytic solutions to the inverse image reconstruction. The next steps are to scan a sample in the XY plane and synchronize the scanning coordinates with the ATCSPC system, thus obtaining a two-dimensional lifetime map from every sample. The map will then be translated into a pH-values map according to scaling measurements. Once we are ready to implement the first analytic solutions, we will make in vivo measurements and compare the results with histopathological analysis.

Bloch S, Lesage F, McIntosh L, Gandjbakhche A, Liang K, Achilefu S. Whole-body fluorescence lifetime imaging of a tumor-targeted near infrared molecular probe in mice. J Biomed Opt 2005;10:54003.

Gannot I, Garashi A, Chernomordik V, Gandjbakhche A. Quantitative optical imaging of the pharmacokinetics of fluorescent-specific antibodies to tumor markers through tissuelike turbid media. Opt Lett 2004;29:742-744.

Gannot I, Izhar R, Hekmat F, Chernomordik V, Gandjbakhche A. Functional optical detection based on pH dependent fluorescence lifetime. Lasers Surg Med 2004;35:342-348.

Hassan M, Klaunberg BA. Biomedical applications of fluorescence imaging in vivo. Comp Med 2004;54:635-644.

Morgan N, English S, Chen W, Chernomordik V, Russo A, Smith PD, Gandjbakhche A. Real time in vivo non-invasive optical imaging using near-infrared fluorescent quantum dots. Acad Radiol 2005;12:313-323.

Monitoring blood circulation in Kaposi’s sarcoma and complex regional pain syndrome type I

Researchers continue to develop novel targeted therapies for use in a variety of diseases. To monitor cancer therapy, for example, patients normally undergo surgical biopsies or limited radiological evaluations. Noninvasive, quantitative techniques that not only can monitor structural changes but that can also assess the functional characteristics or metabolic status of the tissue are needed.

Interest abounds in developing therapies to treat cancer through inhibition of new blood vessel formation. AIDS-associated Kaposi’s sarcoma (KS) is a useful model for studying anti-angiogenesis approaches and imaging of such therapies. In ongoing clinical trials under three NCI protocols, we have developed and established three noninvasive techniques for studying angiogenesis in KS patients undergoing an experimental anti–KS therapy: thermography, laser Doppler imaging (LDI), and multispectral imaging. We record images of the lesion and compare them with those of normal skin either adjacent to the lesion or on the contralateral side, both before therapy and after a regimen of liposomal doxorubicin and interleukin-12 for 18 and 42 weeks.

Through an NIDCR protocol, we also study complex regional pain syndrome type I (CRPS-I), formerly known as reflex sympathetic dystrophy. The disorder has long been recognized clinically, but the pathogenesis is not clear. It appears as a regional disorder of a limb characterized by burning pain; edema; autonomic dysfunction such as altered skin color, temperature, or pseudomotor activity, a movement disorder; or tropic changes such as muscle or skin atrophy. All subjects with CRPS-I receive an individualized regime of physical therapy and standard treatment to control their pain. In addition, they receive an experimental drug for five weeks and then placebo tablets for five weeks. Given that the clinical trial is ongoing, we have not yet unblinded the results and have not yet assessed the effect of the drug as compared with the placebo.

For both the KS and CRPS-I clinical protocols, multispectral images show local variations in skin analyte concentrations such as oxy- and deoxy-hemoglobin and blood volume. LDI measures the blood velocity of small blood vessels, which generally increases as the demand for blood supply increases. Combining multispectral imaging and LDI allows us to determine changes in blood volume, oxygenation state, and blood velocity of the microvasculature and the location of the abnormality. However, the two techniques are limited because they can detect only that vasculature information located near the skin’s surface. By contrast, thermography, the third imaging technique, uses temperature to assess blood flow. Thermographic patterns in medical diagnostic applications may be related to blood flow changes associated with changes in metabolic activity. Thermography provides information from greater depths in the skin than multispectral imaging and LDI and may be used for continuously monitoring changes in the vascular patterns of tissue.

Results from the KS studies show that, compared with normal skin, lesions generally evidence increased blood volume, deoxy-hemoglobin levels, temperature, and blood velocity. We found a strong correlation between temperature and blood velocity and blood volume. After 18 weeks of anti-angiogenesis drug treatment, we observed a significant reduction in the blood volume, deoxy-hemoglobin, temperature, and blood velocity of the lesions. Further analysis of the data promises to promote our understanding of tumor angiogenesis and the effects of specific anti-angiogenic treatment.

Hassan M, Little R, Vogel A, Aleman K, Wyvill K, Yarchoan R, Gandjbakhche A. Use of noninvasive imaging techniques to assess tumor vasculature and response to therapy in Kaposi’s sarcoma. Tech Cancer Res Treat 2004;3:451-458.

Cellular dynamics of angiogenesis

Angiogenesis, the transient formation of new blood vessels, is mainly observed under certain physiological conditions in the adult. Although recent in vitro models have been crucial in determining the effects of growth factors and inhibitors on cell migration and sprouting, the fundamental processes of cell adhesion kinetics and the interaction between endothelial cells (ECs) and extracellular matrix (ECM) during tumor-induced angiogenesis have not been quantified. During early stages of angiogenesis, ECs migrate from pre-existing vessels through the ECM, adhere to each other, and form a specific pattern. Following this initial event, many ECs form new, small, finger-like capillaries. The sprouts grow in length with the migration and further recruitment of endothelial cells and move toward the tumor.

To study the network formation of ECs in an ECM environment, we devised an EC aggregation-type model based on a diffusion-limited-cluster-aggregation model (DLCA), where clusters of particles diffuse and stick together on contact. We use the model to quantify EC differentiation into cord-like-structures by comparing experimental and simulation data. Approximations made with the DLCA model, when combined with experimental kinetics and cell concentrations, not only allow us to quantify cell differentiation by a pseudo-diffusion coefficient but also permit us to measure the effects of tumor angiogenic factors (TAF) on the formation of cord-like structures by ECs.

We tested our model in an in vitro assay. We recorded EC aggregation by analyzing time-lapse images that provided us with the evolution of the fractal dimension measure through time. We performed the experiments for various cell concentrations and TAF (e.g., EVG, FGF-b, and VEGF). During the first six hours of an experiment, ECs aggregate quickly. The value of the measured fractal dimension decreases with time until reaching an asymptotic value that depends solely on the EC concentration. In contrast, the kinetics depends on the nature of TAF. The experimental and simulation results correlated with each other with respect to the fractal dimension and kinetics, allowing us to quantify the influence of each TAF by a pseudo-diffusion coefficient.

We showed that the shape, kinetic aggregation, and fractal dimension of the EC aggregates fit into an in vitro model capable of reproducing the first stage of angiogenesis. We concluded that the DLCA model, combined with experimental results, is a highly effective assay for the quantification of the kinetics and network characteristics of ECs embedded in ECM proteins. Finally, we presented a new method that can be used for studying the effect of angiogenic drugs in vitro.

In another project, we use stochastic modeling to analyze the influence of the ECM’s heterogeneity on tumor-induced angiogenesis. Cell migration during angiogenesis guides the formation of new blood vessels and is mainly directed by a chemotactic flux via a gradient of growth factors between the tumor and the cell. New studies have demonstrated that the ECM substrate can influence cell migration and apoptosis. We performed experiments showing the correlation between endothelial cell migration and the fiber distribution in the ECM. The endothelial cells follow the pathways created by the fibers in the ECM. Through stochastic modeling, we determined that the heterogeneity of the fibers in the ECM creates obstacles for the blood vessels to perfuse the tumor.

We are currently using fluorescence correlation spectroscopy (FCS) to measure locally the degradation of the ECM due to the ECs. During angiogenesis, when ECs migrate through the tumor to form new blood vessels, the ECs degrade the ECM by cell locomotion and the release of matrix metalloproteinase (MMP). FCS measures tiny variations in gel structures by determining the diffusion coefficient. Some preliminary experiments have shown promising results. We plan to undertake a cord-like structure assay to measure how the cell migration and aggregation locally change the structure of the gel. Our preliminary results show a variation in the gel structure during cell aggregation. In the future, we intend to study how MMP and anti–MMP could affect the degradation of the gel and to quantify the cause of degradation (cell locomotion and MMP).

Amyot F, Camphausen K, Siavosh A, Sackett D, Gandjbakhche A. Quantitative method to study the network formation of endothelial cells in response to tumor angiogenic factors. IEE Proc–Systems Biology 2005;152:61-66.

1Associate Professor, Tel Aviv University, Israel  

2Russian Academy of Sciences, Moscow

3University of Maryland at College Park

Collaborators

Samuel Achilefu, PhD, Washington University School of Medicine, St. Louis, MO

Kevin Camphausen, MD, Radiation Oncology Branch, NCI, Bethesda, MD

Wei Chen, PhD, Nomadics, Stillwater, OK

Rinaldo Cubeddu, PhD, Politecnico di Milano, Milan, Italy

Raymond Dionne, DDS, PhD, Pain and Neurosensory Mechanisms Branch, NIDCR, Bethesda, MD

Gallya Gannot, DDS, PhD, Laboratory of Pathology, Center for Cancer Research, NCI, Bethesda, MD

Jeremy Hebden, PhD, University College, London, United Kingdom

Herbert Rinneberg, PhD, Physikalisch-Technische Bundesanstalt, Berlin, Germany

Paul Smith, PhD, Division of Bioengineering and Physical Science, ORS, NIH, Bethesda, MD

George Weiss, PhD, Center for Information Technology, NIH, Bethesda, MD

Robert Yarchoan, MD, HIV and AIDS Malignancy Branch,NCI, Bethesda, MD

Giovanni Zaccanti, PhD, Università de Firenze, Florence, Italy

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

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