There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We develop sensitivity relations in both the continuous and discrete case with special concentration on the use of the finite element method. A classification of algorithms is presented, and some suggestions for open problems to be addressed in future research are made.

https://iopscience.iop.org/article/10.1088/0266-5611/15/2/022/pdf

Optical tomography in medical imaging

1.1 Photodynamic Therapy and Imaging
The purpose of this review is to present the current state of the role of imaging in photodynamic therapy (PDT). In order for the reader to fully appreciate the context of the discussions embodied in this article we begin with an overview of the PDT process, starting with a brief historical perspective followed by detailed discussions of specific applications of imaging in PDT. Each section starts with an overview of the specific topic and, where appropriate, ends with summary and future directions. The review closes with the authors’ perspective of the areas of future emphasis and promise. The basic premise of this review is that a combination of imaging and PDT will provide improved research and therapeutic strategies.

PDT is a photochemistry-based approach that uses a light-activatable chemical, termed a photosensitizer (PS), and light of an appropriate wavelength, to impart cytotoxicity via the generation of reactive molecular species (Figure 1a). In clinical settings, the PS is typically administered intravenously or topically, followed by illumination using a light delivery system suitable for the anatomical site being treated (Figure 1b). The time delay, often referred to as drug-light interval, between PS administration and the start of illumination with currently used PSs varies from 5 minutes to 24 hours or more depending on the specific PS and the target disease. Strictly speaking, this should be referred to as the PS-light interval, as at the concentrations typically used the PS is not a drug, but the drug-light interval terminology seems to be used fairly frequently. Typically, the useful range of wavelengths for therapeutic activation of the PS is 600 to 800 nm, to avoid interference by endogenous chromophores within the body, and yet maintain the energetics necessary for the generation of cytotoxic species (as discussed below) such as singlet oxygen (1O2). However, it is important to note that photosensitizers can also serve as fluorescence imaging agents for which activation with light in the 400nm range is often used and has been extremely useful in diagnostic imaging applications as described extensively in Section 2 of this review. The obvious limitation of short wavelength excitation is the lack of tissue penetration so that the volumes that are probed under these conditions are relatively shallow.






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Figure 1


(A) A schematic representation of PDT where PS is a photoactivatable multifunctional agent, which, upon light activation can serve as both an imaging agent and a therapeutic agent. (B) A schematic representation of the sequence of administration, localization and light activation of the PS for PDT or fluorescence imaging. Typically the PS is delivered systemically and allowed to circulate for an appropriate time interval (the “drug-light interval”), during which the PS accumulates preferentially in the target lesion(s) prior to light activation. In the idealized depiction here the PS is accumulation is shown to be entirely in the target tissue, however, even if this is not the case, light delivery confers a second layer of selectivity so that the cytotoxic effect will be generated only in regions where both drug and light are present. Upon localization of the PS, light activation will result in fluorescence emission which can be implemented for imaging applications, as well as generation cytotoxic species for therapy. In the former case light activation is achieved with a low fluence rate to generate fluorescence emission with little or no cytotoxic effect, while in the latter case a high fluence rate is used to generate a sufficient concentration of cytotoxic species to achieve biological effects.

/pdf/imaging-and-photodynamic-therapy-mechanisms-monitoring-and-76rc7acuq5.pdf

Imaging and photodynamic therapy: mechanisms, monitoring, and optimization.

There have been three basic approaches to optical tomography since the early 1980s: diffraction tomography, diffuse optical tomography and optical coherence tomography (OCT). Optical techniques are of particular importance in the medical field, because these techniques promise to be safe and cheap and, in addition, offer a therapeutic potential. Advances in OCT technology have made it possible to apply OCT in a wide variety of applications but medical applications are still dominating. Specific advantages of OCT are its high depth and transversal resolution, the fact, that its depth resolution is decoupled from transverse resolution, high probing depth in scattering media, contact-free and non-invasive operation, and the possibility to create various function dependent image contrasting methods. This report presents the principles of OCT and the state of important OCT applications. OCT synthesises cross-sectional images from a series of laterally adjacent depth-scans. At present OCT is used in three different fields of optical imaging, in macroscopic imaging of structures which can be seen by the naked eye or using weak magnifications, in microscopic imaging using magnifications up to the classical limit of microscopic resolution and in endoscopic imaging, using low and medium magnification. First, OCT techniques, like the reflectometry technique and the dual beam technique were based on time-domain low coherence interferometry depth-scans. Later, Fourier-domain techniques have been developed and led to new imaging schemes. Recently developed parallel OCT schemes eliminate the need for lateral scanning and, therefore, dramatically increase the imaging rate. These schemes use CCD cameras and CMOS detector arrays as photodetectors. Video-rate three-dimensional OCT pictures have been obtained. Modifying interference microscopy techniques has led to high-resolution optical coherence microscopy that achieved sub-micrometre resolution. This report is concluded with a short presentation of important OCT applications. Ophthalmology is, due to the transparent ocular structures, still the main field of OCT application. The first commercial instrument too has been introduced for ophthalmic diagnostics (Carl Zeiss Meditec AG). Advances in using near-infrared light, however, opened the path for OCT imaging in strongly scattering tissues. Today, optical in vivo biopsy is one of the most challenging fields of OCT application. High resolution, high penetration depth, and its potential for functional imaging attribute to OCT an optical biopsy quality, which can be used to assess tissue and cell function and morphology in situ. OCT can already clarify the relevant architectural tissue morphology. For many diseases, however, including cancer in its early stages, higher resolution is necessary. New broad-bandwidth light sources, like photonic crystal fibres and superfluorescent fibre sources, and new contrasting techniques, give access to new sample properties and unmatched sensitivity and resolution.

/pdf/optical-coherence-tomography-principles-and-applications-17y32cabbm.pdf

Optical coherence tomography - principles and applications

In vivo medical imaging has made great progress due to advances in the engineering of imaging devices and developments in the chemistry of imaging probes Several modalities have been utilized for medical imaging, including X-ray radiography and computed tomography (x-ray CT), radionuclide imaging using single photons and positrons, magnetic resonance imaging (MRI), ultrasonography (US), and optical imaging In order to extract more information from imaging, “contrast agents” have been employed For example, organic iodine compounds have been used in X-ray radiography and computed tomography, superparamagnetic or paramagnetic metals have been used in MRI, and microbubbles have been used in ultrasonography Most of these, however, are non-targeted reagents

Molecular imaging is widely considered the future for medical imaging Molecular imaging has been defined as the in vivo characterization and measurement of biologic process at the cellular and molecular level1, or more broadly as a technique to directly or indirectly monitor and record the spatio-temporal distribution of molecular or cellular processes for biochemical, biologic, diagnostic, or therapeutic application2 Molecular imaging is the logical next step in the evolution of medical imaging after anatomic imaging (eg x-rays) and functional imaging (eg MRI) In order to attain truly targeted imaging of specific molecules which exist in relatively low concentrations in living tissues, the imaging techniques must be highly sensitive Although MRI, US, and x-ray CT are often listed as molecular imaging modalities, in truth, radionuclide and optical imaging are the most practical modalities, for molecular imaging, because of their sensitivity and the specificity for target detection

Radionuclide imaging, including gamma scintigraphy and positron emission tomography (PET), are highly sensitive, quantitative, and offer the potential for whole body scanning However, radionuclide imaging methods have the disadvantages of poor spatial and temporal resolution3 Additionally, they require radioactive compounds which have an intrinsically limited half life, and which expose the patient and practitioner to ionizing radiation and are therefore subject to a variety of stringent safety regulations which limit their repeated use4

Optical imaging, on the other hand, has comparable sensitivity to radionuclide imaging, and can be “targeted” if the emitting fluorophore is conjugated to a targeting ligand3 Optical imaging, by virtue of being “switchable”, can result in very high target to background ratios “Switchable” or activatable optical probes are unique in the field of molecular imaging since these agents can be turned on in specific environments but otherwise remain undetectable This improves the achievable target to background ratios, enabling the detection of small tumors against a dark background5,6 This advantage must be balanced against the lack of quantitation with optical imaging due to unpredictable light scattering and absorption, especially when the object of interest is deep within the tissue Visualization through the skin is limited to superficial tissues such as the breast7-9 or lymph nodes10,11 The fluorescence signal from the bright GFP-expressing tumors can be seen in the deep organ only in the nude mice 12,13 However, optical molecular imaging can also be employed during endoscopy14 or surgery 15,16

/pdf/new-strategies-for-fluorescent-probe-design-in-medical-1mcbc28raf.pdf

New Strategies for Fluorescent Probe Design in Medical Diagnostic Imaging

The use of optical radiation in medical physics is important in several fields for both treatment and diagnosis. In all cases an analytic and computable model of the propagation of radiation in tissue is essential for a meaningful interpretation of the procedures. A finite element method (FEM) for deriving photon density inside an object, and photon flux at its boundary, assuming that the photon transport model is the diffusion approximation to the radiative transfer equation, is introduced herein. Results from the model for a particular case are given: the calculation of the boundary flux as a function of time resulting from a delta-function input to a two-dimensional circle (equivalent to a line source in an infinite cylinder) with homogeneous scattering and absorption properties. This models the temporal point spread function of interest in near infrared spectroscopy and imaging. The convergence of the FEM results are demonstrated, as the resolution of the mesh is increased, to the analytical expression for the Green's function for this system. The diffusion approximation is very commonly adopted as appropriate for cases which are scattering dominated, i.e., where mu(s) much greater than mu(a), and results from other workers have compared it to alternative models. In this article a high degree of agreement with a Monte Carlo method is demonstrated. The principle advantage of the FE method is its speed. It is in all ways as flexible as Monte Carlo methods and in addition can produce photon density everywhere, as well as flux on the boundary. One disadvantage is that there is no means of deriving individual photon histories.

A finite element approach for modeling photon transport in tissue.

This paper extends our work on applying the Finite Element Method (FEM) to the propagation of light in tissue. We address herein the topics of boundary conditions and source specification for this method. We demonstrate that a variety of boundary conditions stipulated on the Radiative Transfer Equation can be implemented in a FEM approach, as well as the specification of a light source by a Neumann condition rather than an isotropic point source. We compare results for a number of different combinations of boundary and source conditions under FEM, as well as the corresponding cases in a Monte Carlo model.

The finite-element method for the propagation of light in scattering media - boundary and source conditions

Near-infrared light propagation in various models of the adult head is analyzed by both time-of-flight measurements and mathematical prediction. The models consist of three- or four-layered slabs, the latter incorporating a clear cerebrospinal fluid (CSF) layer. The most sophisticated model also incorporates slots that imitate sulci on the brain surface. For each model, the experimentally measured mean optical path length as a function of source-detector spacing agrees well with predictions from either a Monte Carlo model or a finite-element method based on diffusion theory or a hybrid radiosity-diffusion theory. Light propagation in the adult head is shown to be highly affected by the presence of the clear CSF layer, and both the optical path length and the spatial sensitivity profile of the models with a CSF layer are quite different from those without the CSF layer. However, the geometry of the sulci and the boundary between the gray and the white matter have little effect on the detected light distribution.

https://www.uta.edu/rfmems/N_041101/Reference/29.pdf

Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head

We present three-dimensional (3D) in vivo images of human breast cancer based on fluorescence diffuse optical tomography (FDOT). To our knowledge, this work represents the first reported 3D fluorescence tomography of human breast cancer in vivo. In our protocol, the fluorophore Indocyanine Green (ICG) is injected intravenously. Fluorescence excitation and detection are accomplished in the soft-compression, parallel-plane, transmission geometry using laser sources at 786 nm and spectrally filtered CCD detection. Phantom and in vivo studies confirm the signals are due to ICG fluorescence, rather than tissue autofluorescence and excitation light leakage. Fluorescence images of breast tumors were in good agreement with those of MRI, and with DOT based on endogenous contrast. Tumor-to-normal tissue contrast based on ICG fluorescence was two-to-four-fold higher than contrast based on hemoglobin and scattering parameters. In total the measurements demonstrate that FDOT of breast cancer is feasible and promising.

Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans.

This paper presents a method to calculate photon-measurement density functions (PMDF's), which were introduced in Part 1 [Appl. Opt. 34, 7395-7409 (1995), for near-infrared imaging and spectroscopy in complex and inhomogeneous objects through the use of a finite-element model. PMDF's map the sensitivity of a measurement on the surface of an object to the perturbations of the optical parameters within the object. Data are presented for homogeneous and layered circular objects and for a complex two-dimensional model of a head. In particular the influence of the optical parameters on the shape of the PMDF and the distortions caused by boundary layers and complex inhomogeneties are investigated.

Martin Schweiger

Papers

A finite element approach for modeling photon transport in tissue.

The finite-element method for the propagation of light in scattering media - boundary and source conditions

Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head

Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans.

Photon-measurement density functions. Part 2: Finite-element-method calculations