Studies on Mathematical Modeling of Middle Ear Gas Exchange

Middle ear (ME) pressure regulation is a topic of fundamental interest to the pediatric otolaryngology community since a lack of proper regulation is a precursor to middle ear disease. Development of mathematical models of ME gas exchange can improve understanding of the underlying ME physiology. Previous models were limited in their description of gas exchange (based on inputted empirical exchange constants) and in their application (few models posses capacity for clinical relevance in diagnosis). Here, we present investigations which improve and expand on previous models. The first study presents a global description of ME pressure regulation and applies the model to flight-related barotrauma. While a well functioning Eustachian tube has long been known to protect from barotrauma, the simulation results show that a variety of buffering mechanisms can reduce the demand placed on the efficiency of that function. Using these results, subclasses of ears with little risk for barotrauma were identified and an algorithm was developed that makes these assignments based on measurable variables. The second study outlines and analyzes a morphometric approach to describing transmucosal gas exchange within the middle ear. Implementation of the morphometric model requires the measurement of diffusional length (tao) for the ME mucosa which contributes to the mucosal diffusing capacity, a measure of the resistance to gas flow between airspace and capillary. Two methods for measuring tao have been proposed: the linear distance between air-mucosal boundary and capillary as described by Ars and colleagues, and the harmonic mean of all contributing pathway lengths as described by Weibel and colleagues. Here, oxygen diffusing capacity was calculated for different ME mucosal geometries using the two tao measures, and the results were compared to those predicted by a 2-dimensional finite element analysis. Predictive accuracy was improved by incorporating the tao measure described by Weibel which captures important information regarding variations in capillary shape and distribution. However, when compared to the oxygen diffusing capacity derived from the finite element analysis, both measures yielded non-linear, positively biased estimates. The morphometric techniques underestimate diffusion length by failing to account for the curvilinear gas flow pathways predicted by the finite element model

Analysis and Modeling of Noninvasive measurement of Tissue Chromophores by the Optical Pharmacokinetic System

Efficient design of anti-cancer treatments involving radiation- and photo-sensitizing therapeutics requires knowledge of tissue-specific drug concentrations. This dissertation investigates the utility of the Optical Pharmacokinetic System (OPS), a fiber-optic based elastic-scattering spectroscopy device, to noninvasively quantitate concentrations of sensitizing compounds and hemoglobin within tissue in vivo. The OPS was used to quantitate concentrations of motexafin gadolinium (MGd), in mouse tissues in vivo and in situ. An algorithm was developed to quantify MGd absorbance by integration of the MGd peak absorbance area, thereby relaxing the requirement that the extinction coefficient be known a priori. Concentrations measured by OPS were well-correlated with measurements by high-performance liquid chromatography (HPLC). Compartmental pharmacokinetic models were developed from tissue-specific MGd concentrations measured by OPS and HPLC. Models predicted both rapid initial distribution and slow elimination of MGd in plasma, fast transport of MGd out of the skin, and MGd retention at long times in the tumor. In vivo tumor MGd concentrations measured by the OPS were estimated by a linear combination of the plasma, tumor, and skin PK profiles. A theoretical analysis of the OPS measurement of tissue was conducted using a Monte Carlo (MC) model of light transport through tissue that included discrete blood vessels. Simulation results motivated extensions to a previous analysis algorithm, including: (1) a novel analytic functionality between mean photon path length and total absorption coefficient; and (2) incorporation of a vessel correction factor to account for the pigment packaging effect of discrete vessels on the OPS-estimated absorption coefficient. These extensions improved OPS-estimates of both silicon phthalocyanine (Pc4) and hemoglobin concentration in a mouse xenograft in vivo following photodynamic therapy (PDT). Mathematical models were utilized to investigate in silico the sensitivity of the OPS to chronically and acutely hypoxic regions within tumor tissue. PDT-induced acute hypoxia occured via simulation of the photodynamic reaction. Subsequent simulation of the OPS measurement suggested that the OPS may be sensitive to the presence of chronically hypoxic vessels (an OPS-estimated hemoglobin saturation of &ge 57 indicated < 6 of vessels hypoxic), but may have limited application to detection of acute hypoxia following PDT

Spectroscopic Separation of Čerenkov Radiation in High-Resolution Radiation Fiber Dosimeters

We have investigated Čerenkov radiation generated in phosphor-based optical fiber dosimeters irradiated with clinical electron beams. We fabricated two high-spatial resolution fiber-optic probes, with 200 and 400  μm core diameters, composed of terbium-based phosphor tips. A generalizable spectroscopic method was used to separate Čerenkov radiation from the transmitted signal by the fiber based on the assumption that the recorded signal is a linear superposition of two basis spectra: characteristic luminescence of the phosphor medium and Čerenkov radiation. We performed Monte Carlo simulations of the Čerenkov radiation generated in the fiber and found a strong dependence of the recorded Čerenkov radiation on the numerical aperture of the fiber at shallow phantom depths; however, beyond the depth of maximum dose that dependency is minimal. The simulation results agree with the experimental results for Čerenkov radiation generated in fibers. The spectroscopic technique used in this work can be used for development of high-spatial resolution fiber micro dosimeters and for optical characterization of various scintillating materials, such as phosphor nanoparticles, in ionizing radiation fields of high energy

Dual-Channel Red/Blue Fluorescence Dosimetry with Broadband Reflectance Spectroscopic Correction Measures Protoporphyrin IX Production during Photodynamic Therapy of Actinic Keratosis

Dosimetry for aminolevulinic acid (ALA)-induced protoporphyrin IX (PpIX) photodynamic therapy of actinic keratosis was examined with an optimized fluorescence dosimeter to measure PpIX during treatment. While insufficient PpIX generation may be an indicator of incomplete response, there exists no standardized method to quantitate PpIX production at depths in the skin during clinical treatments. In this study, a spectrometer-based point probe dosimeter system was used to sample PpIX fluorescence from superficial (blue wavelength excitation) and deeper (red wavelength excitation) tissue layers. Broadband white light spectroscopy (WLS) was used to monitor aspects of vascular physiology and inform a correction of fluorescence for the background optical properties. Measurements in tissue phantoms showed accurate recovery of blood volume fraction and reduced scattering coefficient from WLS, and a linear response of PpIX fluorescence versus concentration down to 1.95 and 250 nM for blue and red excitations, respectively. A pilot clinical study of 19 patients receiving 1-h ALA incubation before treatment showed high intrinsic variance in PpIX fluorescence with a standard deviation/mean ratio of \u3c0.9 . PpIX fluorescence was significantly higher in patients reporting higher pain levels on a visual analog scale. These pilot data suggest that patient-specific PpIX quantitation may predict outcome response

Analysis and modeling of noninvasive measurement of tissue chromophores by the Optical Pharmacokinetic System

Efficient design of anti-cancer treatments involving radiation- and photo-sensitizing therapeutics requires knowledge of tissue-specific drug concentrations. This dissertation investigates the utility of the Optical Pharmacokinetic System (OPS), a fiber-optic based elastic-scattering spectroscopy device, to noninvasively quantitate concentrations of sensitizing compounds and hemoglobin within tissue in vivo. The OPS was used to quantitate concentrations of motexafin gadolinium (MGd), in mouse tissues in vivo and in situ. An algorithm was developed to quantify MGd absorbance by integration of the MGd peak absorbance area, thereby relaxing the requirement that the extinction coefficient be known a priori. Concentrations measured by OPS were well-correlated with measurements by high-performance liquid chromatography (HPLC). Compartmental pharmacokinetic models were developed from tissue-specific MGd concentrations measured by OPS and HPLC. Models predicted both rapid initial distribution and slow elimination of MGd in plasma, fast transport of MGd out of the skin, and MGd retention at long times in the tumor. In vivo tumor MGd concentrations measured by the OPS were estimated by a linear combination of the plasma, tumor, and skin PK profiles. A theoretical analysis of the OPS measurement of tissue was conducted using a Monte Carlo (MC) model of light transport through tissue that included discrete blood vessels. Simulation results motivated extensions to a previous analysis algorithm, including: (1) a novel analytic functionality between mean photon path length and total absorption coefficient; and (2) incorporation of a vessel correction factor to account for the pigment packaging effect of discrete vessels on the OPS-estimated absorption coefficient. These extensions improved OPS-estimates of both silicon phthalocyanine (Pc4) and hemoglobin concentration in a mouse xenograft in vivo following photodynamic therapy (PDT). Mathematical models were utilized to investigate in silico the sensitivity of the OPS to chronically and acutely hypoxic regions within tumor tissue. PDT-induced acute hypoxia occurred via simulation of the photodynamic reaction. Subsequent simulation of the OPS measurement suggested that the OPS may be sensitive to the presence of chronically hypoxic vessels (an OPS-estimated hemoglobin saturation of ≥57% indicated <6% of vessels hypoxic), but may have limited application to detection of acute hypoxia following PDT

Empirical model of the photon path length for a single fiber reflectance spectroscopy device

A reflectance spectroscopic device that utilizes a single fiber for both light delivery and collection has advantages over classical multi-fiber probes. This study presents a novel empirical relationship between the single fiber path length and the combined effect of both the absorption coefficient, mu(a) (range: 0.1 - 6 mm(-1)), and the reduced scattering coefficient, mu(S)' (range: 0.3 - 10 mm(-1)), for different anisotropy values (0.75 and 0.92), and is applicable to probes containing a wide range of fiber diameters (range: 200 - 2000 mu m). The results indicate that the model is capable of accurately predicting the single fiber path length over a wide range (r = 0.995; range: 180 - 3940 mu m) and predictions do not show bias as a function of either mu(a) or mu(S)'

Extraction of intrinsic fluorescence from single fiber fluorescence measurements on a turbid medium

This study utilizes Monte Carlo simulations of single fiber fluorescence to develop an empirical model that corrects for the influence of scattering and absorption on fluorescence intensity (F-SF). The model expresses F-SF in terms of the reduced scattering coefficient (mu(s)') and absorption coefficient (mu(a)), each determined independently at excitation and emission wavelengths (lambda(x) and lambda(m)), and the fiber diameter (d(f)). This model returns accurate descriptions (mean residual <6%) of F-SF across a biologically relevant range of mu(s)' and mu(a) values and is insensitive to the form of the scattering phase function. (C) 2012 Optical Society of Americ

Method to quantitate absorption coefficients from single fiber reflectance spectra without knowledge of the scattering properties

This study presents a methodology to accurately extract the absorption coefficient from single fiber reflectance spectra measured in turbid media without a priori knowledge of either the reduced scattering coefficient or the phase function. This novel approach accounts for the interrelated effects these properties have on the photon path length, yielding estimates of an absorption coefficient on average within <7.5% of true values over a wide range of biologically relevant optical properties. (C) 2011 Optical Society of Americ