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Biomedical subjects

R F Bonner

Publications and source records attributed to R F Bonner.

At least 19 recordsLinked to original sources

Atherosclerotic saphenous vein grafts treated with different interventional procedures assessed by intravascular ultrasound.

Intravascular ultrasound imaging of saphenous vein grafts may enhance the angiographic interpretation of results following transcatheter interventions. We used intravascular ultrasound to study 18 patients with stenotic vein grafts following balloon angioplasty, atherectomy, or stent placement. In real-time imaging the three-layer appearance was rarely seen, calcification was infrequent (11% of patients), and atheroma were usually mildly echogenic ("soft"). Despite excellent angiographic results (reduction in percent diameter stenosis from 90 +/- 8% to 17 +/- 8%) and concordant improvement in lumen area by ultrasound regardless of the intervention, there was usually significant retained atheroma at the treatment site. Following balloon angioplasty, ultrasound showed multiple superficial fissures and fractures without discrete dissections. Atherectomy caused a smooth lumen surface without deep dissections or resections, but significant retained atheroma was observed with each one of the atherectomy procedures. Endovascular stents were concentric in the vein with reflective struts above compressed atheroma and an outer echogenic adventitia. Stent expansion was asymmetric axially and longitudinally and evidence of stent recoil was present. Thus intravascular ultrasound may be an important adjunct to angiography in characterizing postintervention results in saphenous vein grafts.

Aged

Pulsed laser and thermal ablation of atherosclerotic plaque: morphometrically defined surface thrombogenicity in studies using an annular perfusion chamber.

Although clinical trials using laser and thermal angioplasty devices have been underway, the effects of pulsed laser and thermal ablation of atherosclerotic plaque on surface thrombogenicity are poorly understood. This study examined the changes in platelet adherence and thrombus formation on freshly harvested atherosclerotic aorta segments from Watanabe-heritable hyperlipidemic rabbits after ablation by two pulsed laser sources (308-nm xenon chloride excimer and 2,940-nm erbium:yttrium-aluminum-garnet [YAG] lasers) and a prototype catalytic hot-tip catheter. Specimens were placed in a modified Baumgartner annular chamber and perfused with citrated whole human blood, followed by quantitative morphometric analysis to determine the percent surface coverage by adherent platelets and thrombi in the treated and contiguous control areas. Pulsed excimer laser ablation of plaque did not change platelet adherence or thrombus formation in the treated versus control zones. However, photothermal plaque ablation with a pulsed erbium:YAG laser resulted in a 67% reduction in platelet adherence, compared with levels in control areas (from 16.7 +/- 2.2% to 5.5 +/- 1.8%; p less than 0.005). Similarly, after plaque ablation using a catalytic thermal angioplasty device, there was a 74% reduction in platelet adherence (from 29.2 +/- 5.1% to 7.7 +/- 1.6%; p less than 0.005) and a virtual absence of platelet thrombi (from 8.6 +/- 2.3% to 0.03 +/- 0.03%; p less than 0.005). This reduced surface thrombogenicity after plaque ablation with either an erbium:YAG laser or a catalytic hot-tip catheter suggests that thermal modifications in the arterial surface ultrastructure or thermal denaturation of surface proteins, or both, may be responsible for reduced platelet adherence. These in vitro findings indicate that controlled thermal plaque ablation by catheter-based techniques may elicit endovascular responses that can reduce early thrombus formation during angioplasty procedures.

Angioplasty, Laser

In vitro and in vivo intravascular ultrasound imaging.

This paper presents our experience with intravascular ultrasound imaging of animal and human arteries in vitro and in vivo using a high-frequency (20 M Hz) ultrasound transducer. In vitro, 32 human coronary artery segments were imaged with intravascular ultrasound and compared with corresponding histological sections. Ultrasound and histology measurements correlated significantly (P less than 0.0001) for coronary artery cross-sectional area (r = 0.94), lumen cross-sectional area (r = 0.85) and wall thickness (r = 0.92). In vivo, 19 sheep and eight human common femoral arteries were imaged and the angiographic lumen diameter of 14 animal and six human arteries was compared to the diameter of the corresponding ultrasound images. Significant correlations were found for lumen diameter in animals and humans (P less than 0.001, r = 0.91 and P less than 0.0001, r = 0.96, respectively). These studies demonstrate that this technique can provide high resolution images of arterial vessels and may have unique advantages in diagnosing atherosclerotic vascular disease and in catheter based therapies.

Adult

Dose-dependent smooth muscle cell proliferation induced by thermal injury with pulsed infrared lasers.

BACKGROUND: Recently, laser-heated and radio frequency-heated balloon angioplasty techniques have been proposed as a means to treat or minimize dissection and elastic recoil but have been associated with a high rate of clinical restenosis. Similarly, pulsed laser angioplasty techniques proposed to minimize thermal injury while ablating obstructing atheroma have failed to reduce clinical restenosis. Because "hot balloon" and pulsed laser angioplasty create both mechanical and thermal injury, it has been difficult to discern the cause of the smooth muscle cell (SMC) proliferation resulting in restenosis and whether such magnitude of proliferation is predictable and dose related. This study was undertaken to explore these issues. METHODS AND RESULTS: Localized thermal lesions accompanying efficient ablation were created with a pulsed Tm:YAG laser in nine rabbit aortas, which consistently led to a focal proliferation of SMC that filled the ablated region by 4 weeks. Transcutaneous Ho:YAG pulsed laser irradiation at multiple independent sites of 24 central rabbit ear arteries without ablation led to brief approximately 30 degrees C thermal transients and thermal damage to the artery wall resulting in significant neointimal proliferation by 3 weeks and a mean cross-sectional narrowing of 59 +/- 17% at a dose of 390 mJ/mm2. Acute and chronic responses to varying total energy deposition were studied by histology after the rabbits were killed at 2 hours to 4 weeks. Arterial segments midway between laser injuries were unaffected and served as internal controls. Neointimal proliferation at 3 weeks after laser injury exhibited a clear dose dependence. Mean cross-sectional narrowing increased from 34 +/- 10% to 85 +/- 15% as laser fluence increased from 240 mJ/cm2 to 640 mJ/cm2 (r = 0.84). Similarly, cross-sectional narrowing caused by SMC neointimal proliferation increased from 20 +/- 10% to 77 +/- 17% for a fixed surface irradiation as the depth of the most superficial arterial media decreased from 600 microns to 330 microns (r = 0.94). CONCLUSIONS: Thermal injury to the arterial wall is a potent stimulus for SMC proliferation and may necessitate reduction in laser or thermal energy used for angioplasty. Moreover, a dose-response relation exists between the degree of thermal injury and SMC proliferative response. Hence, this technique could be used as a practical model of restenosis suitable for screening therapies for inhibition of SMC proliferation.

Animals

Effects of two viral inactivation methods on platelets: laser-UV radiation and merocyanine 540-mediated photoinactivation.

Two viral inactivation methods suggested for use with cellular blood products have been evaluated as to their effects on platelets. In the first study, it was proposed that pulsed laser-ultraviolet radiation (UVB) at 308 nm could favor photodamage to UVB-sensitive viral nucleic acid with minimal effects on blood platelets. A "window of efficacy" was observed with UVB doses of 10.5-21.5 J/cm2 at which 4-6 log10 poliovirus were inactivated while platelets were relatively tolerant. However, this "window" occurred only with low-intensity UVB radiation (less than or equal to 0.25 MW/cm2). Damage to platelet proteins, evident at high laser intensities, was probably due to multiple photon excitation of amino acids. In the second study, platelets and viruses were treated with the photosensitizer, merocyanine 540 (MC 540) (less than or equal to 24 micrograms/ml), and visible light (450-600 nm) (less than or equal to J/cm2). Activation of washed platelets by dye/light treatment resulted in a spontaneous release of serotonin, spontaneous aggregation, and marked morphological changes. Increasing concentrations of albumin in the suspension medium protected against dye-mediated photodamage to platelets, but also significantly reduced the antiviral activity of MC 540 and light. These results illustrate the relative sensitivities of platelets and viruses to two inactivation methods and the difficulty in optimizing inactivation of viruses and preservation of platelet function in a protein-rich medium.

Blood

In vivo human atherosclerotic plaque recognition by laser-excited fluorescence spectroscopy.

Arterial wall perforation and chronic restenosis represent important factors limiting the clinical application of laser angioplasty. Discrimination of normal and atherosclerotic vessels by laser-excited fluorescence spectroscopy may offer a means of targeting plaque ablation, thereby reducing the frequency of restenosis and transmural perforation. In this study, with use of a 325 nm low power helium-cadmium laser, in vivo endogenous surface fluorescence was excited through a flexible 200 microns optical fiber within a 0.018 in. (0.046 cm) guide wire in contact with the intima of 268 vascular interrogation sites from 48 patients either during open heart surgery or during percutaneous catheterization procedures. Fluorescence spectra could be recorded in all patients in bloodless and blood-filled arteries. Endogenous surface fluorescence was analyzed measuring peak intensity, peak position and shape index of the spectra. Compared with normal wall, noncalcified and calcified coronary atheroma showed a 42% (p less than 0.001) and a 58% (p less than 0.001) decrease of peak intensity, and higher shape index (p less than 0.001 and p less than 0.01, respectively). In addition, peak position was shifted to longer wavelengths for noncalcified coronary atheroma (p less than 0.001). Compared with normal aorta sites, aortic plaques demonstrated a 46% decrease of peak intensity, longer peak position wavelengths (p less than 0.05) and a higher shape index (p less than 0.001). Using an atheroma detection algorithm, prospective analysis of aorta and coronary spectra showed a specificity of 100% for identifying normal sites and a sensitivity of 73% for recognizing atherosclerotic sites.(ABSTRACT TRUNCATED AT 250 WORDS)

Adolescent

Occlusive peripheral vascular disease: a multicenter trial of fluorescence-guided, pulsed dye laser-assisted balloon angioplasty.

Fluorescence-guided, laser-assisted balloon angioplasty was performed in 129 patients with iliac and femoropopliteal artery chronic occlusions (range, 0.5-50.0 cm; mean length, 9.9 cm) after failure of recanalization with standard guide-wire techniques. Laser recanalization and short-term angiographic success were achieved in 101 (72%) and 95 (68%) of 140 occlusions, respectively. Laser and balloon angioplasty failures were encountered in heavily calcified plaques or after perforations and dissections. Complications included perforations (19%), hematomas (5%), thromboses (4%), and distal embolizations (4%). Real-time fluorescence spectroscopy identified thrombus, white fibrous plaque, and media but could not avoid perforations in many cases because laser wire advancement outdistanced fluorescence sensing. Disruption of tissue by means of pressure transients and/or mechanical advancement occurred in at least 36% of lesions where the laser energy was insufficient (less than 0.4 J/cm) to ablate significant tissue. Integration of fluorescence guidance with pulsed dye laser ablation is feasible, but additional refinements are necessary to increase safety and efficacy.

Adult

Rabbit ear model of injury-induced arterial smooth muscle cell proliferation. Kinetics, reproducibility, and implications.

Recently, considerable interest has focused on the vascular smooth muscle cell (SMC) response to injury, particularly as it relates to restenosis after angioplasty. In an effort to find an optimal experimental model of arterial SMC proliferation after injury, we examined the effects of external injury to the central artery of the rabbit ear and assessed the reproducibility, morphological changes, and time course of cellular proliferation after such an injury. With rabbits under general anesthesia, direct pressure was applied at two sites along the central artery of the ears of 19 New Zealand White rabbits. Rabbits were maintained on a diet of 2.4% fat and 0.001% cholesterol throughout the experiment. In seven rabbits examined after 21 days, marked SMC proliferation with neointimal formation was observed at all 28 sites (100%). Mean neointimal area, expressed as a percentage of the area of the tunica media, was 82 +/- 40% (range, 21-203%). Compared with the uninvolved artery displaced 2 mm from the injury site, mechanical crush caused a 38% increase in total vessel area (p less than 0.001), a 40% decrease in luminal area (p less than 0.002), and no change in the area of the media. Serial histological studies were performed 1-42 days after injury, using light and electron microscopy and bromodeoxyuridine immunohistochemistry. Beginning at day 3, activated medial SMCs were noted to migrate through defects in the internal elastic membrane, with a gradual increase in neointimal area between days 5 and 12. Peak DNA synthesis was identified in the media 5 days after injury, with proliferative activity shifting almost exclusively to the neointima thereafter.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals

Microcirculatory adaptations in sickle cell anemia: reactive hyperemia response.

With the technique of laser-Doppler velocimetry, cutaneous blood flows in the forearm of patients with stable sickle cell disease after graded periods of proximal ischemia were compared with normal subjects matched for age, race, and sex, and with patients with anemia caused by beta(+)-thalassemia. In the sickle cell patients the reactive hyperemia was characterized by an increased time interval between the release of the occlusion and the peak amplitude response (time-to-peak) and by a greater period of blood flow above the base-line value (payback ratio) compared with controls. In addition, prolongation of the occlusion period led to an augmentation in the magnitude of the characteristic basal flow oscillations or an induction of this phenomenon at sites not exhibiting it before ischemia. Base-line or ischemia-provoked flow oscillations of either this magnitude or frequency were only observed in normal or thalassemic controls during brief intervals in the rapidly decaying portion of the hyperemic response and in one subject with homozygous hemoglobin C disease. These results would support a model of a local integrative control of microcirculatory blood flow, which appears to become augmented, synchronized, and sustained in sickle cell subjects.

Adaptation, Physiological

Fluorescence-guided laser-assisted balloon angioplasty in patients with femoropopliteal occlusions.

In 12 patients (aged 64 +/- 10 years) with femoropopliteal occlusions (1-27 cm; average, 8.4 cm length) that could not be recanalized by standard guidewire-balloon angioplasty techniques, percutaneous laser-assisted balloon angioplasty was performed by use of a new fluorescence-guided dual-laser system. Plaque detection by 325-nm laser-excited fluorescence spectroscopy provided real-time feedback control to a 480-nm pulsed dye laser (2-microseconds pulses) for atheroma ablation. By means of a common 200-microns optical fiber, after diagnostic fluorescence sensing, computer algorithms directed a fire or no-fire signal (5 Hz) to the treatment laser for selective plaque removal. Laser recanalization (15-50 mJ/pulse) was successful in 10 of 12 patients; this procedure was followed by definitive balloon angioplasty in seven of 12 patients with increased ankle/arm indexes (from 0.60 +/- 0.12 at baseline to 0.84 +/- 0.11 after treatment, p = 0.0043). In laser and balloon angioplasty failures, all femoropopliteal occlusions were heavily calcified, and there were two mechanical guidewire perforations without clinical sequelae. Ablation of calcified lesions required higher pulse energies and greater total energy per centimeter of recanalized tissue (1,837 +/- 1,251 mJ/cm vs. 90 +/- 39 mJ/cm, p = 0.0036). Fluorescence spectroscopy (n = 219 sites) was helpful in flush occlusions and correctly identified plaque, underlying media, and thrombus by changes in fluorescence intensity, shape, and peak position. Thus, when fluorescence-guided laser angioplasty was used in a subgroup of patients refractory to standard angioplasty techniques, primary recanalization and subsequent balloon angioplasty of femoropopliteal occlusions was successful in 83% and 58% of the patients, respectively. Importantly, treatment of heavily calcified lesions accounted for all of the failures and will require modified delivery systems to create larger primary channels and to increase catheter-tip control, which should improve clinical results in the future.

Adult

Posterior vitreous fluorophotometry. I. Description of a new analysis procedure and results in normal subjects.

A new automated analysis procedure was used to evaluate the apparent blood-retinal barrier permeability (mean +/- SD = 1.31 = 0.31 X 10(-7) cm/s at 60 minutes after intravenous dye administration) and the effective diffusivity (mean +/- SD = 0.88 +/- 0.40 X 10(-5) cm2/s) for fluorescein in the vitreous of 21 normal subjects. The analysis improvements include (1) use of an individualized convolution (spread) function for each eye in comparing simulated and experimental scans, (2) separation of vitreous and chorioretinal fluorescence, and (3) precise determination of vitreous position relative to the retina. The average reproducibility in six subjects was 23% for permeability and 22% for diffusivity based on repeated determinations separated in time by at least a week. Diffusivity values, but not permeability values, significantly associated in comparisons of first and second determinations, suggesting permeability may fluctuate in time while diffusivity remains relatively constant. The fluorescence at 3 mm anterior to the retina (commonly employed as a measure of blood-retinal barrier leakiness) was strongly associated with diffusivity. In contrast, the anticipated association between permeability and 3-mm fluorescence was weak or absent.

Adult

Posterior vitreous fluorophotometry. II. Comparison of diabetic patients and controls with the use of a new analysis procedure.

We used a new computerized procedure to analyze posterior vitreous fluorophotometry scans, obtained with a commercial fluorophotometer (Fluorotron Master Coherent, Palo Alto, Calif), in insulin-dependent diabetic patients and controls. Diabetic patients with minimal retinopathy had significantly higher effective fluorescein vitreous diffusivity and 30-minute 3-mm vitreous fluorescence values than either controls or diabetic patients with no retinopathy. However, there was no significant difference between the groups for the apparent permeability of the blood-retinal barrier to fluorescein. These results suggest the possibility that the higher 3-mm fluorescence levels found in the diabetic patients with minimal retinopathy may result in part from enhanced movement of fluorescein through the vitreous.

Adult

Measurement of multiple microcirculatory parameters in human nasal mucosa using laser-Doppler velocimetry.

LDV has been modified to measure four microcirculatory responses in human nasal mucosa. Resting nasal blood flow was measured in 115 observations in 23 nonatopic subjects and 111 observations in 21 atopic subjects with allergic nasal disease. Other parameters measured concurrently were the number density of moving red blood cells (RBC), mean RBC speed, and flow pulsatility. Challenges with aerosolized buffered saline or water had no significant effect on any parameter. By contrast, nasal application of alpha-adrenergic agonists, oxymetazoline and phenylephrine, produced significant dose-dependent reductions in flow without any significant change in RBC number density. These results suggest a selective alpha-agonist effect on resistance vessels but not on capacitance vessels. Topical cholinergic stimulation with methacholine selectively reduced the RBC number density without affecting other parameters. These modifications of LDV may prove useful in analyzing nasal responses to provocation and determining the sites of action of vasoactive agents on the microcirculation.

Adult

Microvascular blood flow, volume, and velocity measured by laser Doppler techniques in IDDM.

A laser Doppler device with the capability to simultaneously measure skin blood flow, microvascular volume, and erythrocyte velocity was used to assess blood flow changes in 35 insulin-dependent diabetes mellitus (IDDM) subjects, mean age 33 +/- 1 yr, with average duration of diabetes 14 +/- 1 yr, and in a nondiabetic control group. Blood flow was determined at 35 and 44 degree C at several sites on the upper and lower extremities with a temperature-regulated probe. Blood flow was highest at both temperatures on the pulps of the index finger and the first toe, regions of high density of arteriovenous anastomoses. There was significantly greater blood flow at most locations for the nondiabetic than the diabetic group at 35 degree C, and the differences between the two groups were substantially larger at 44 degree C. At 44 degree C, blood flow in the control group was approximately 40% greater in the upper extremity and 50% greater in the lower extremity than it was in the diabetic subjects. The differences were attributed to decreases of both microvascular volume and velocity in the diabetic group. In the upper extremity, volumes in the diabetic patients were 10-15% lower and velocities 10-40% lower than in the nondiabetic subjects. In the lower extremity, volumes were 20-25% lower and velocities 40-50% lower. We conclude that laser Doppler techniques can be used to assess microvascular changes in the skin of diabetic patients. This approach may be useful to evaluate and model diabetic microangiopathy.

Adult

The determination of protein, oligonucleotide and peptide molecular weights by ion-spray mass spectrometry.

The mass spectra of several compounds with molecular weights in the 2500-20,000 Da range were obtained with a quadrupole mass spectrometer equipped with an atmospheric pressure ion source. Average molecular weight determinations of mellitin (2846.4 Da), a synthetic oligonucleotide (4262.8 Da), myoglobin (16,950.4 Da) and on the subunits of beta-lactoglobulin (18,277.1 Da) requiring as little as 1 pmol of material were achieved with accuracies and precisions of +/- 1 Da. An ion-spray interface was used to produce ions via the ion evaporation process, producing mass spectra containing a series of multiply-charged molecular species. A simple method for calculating the molecular weight of unknown compounds from the spectra containing multiply-charged ions is described.

Lactoglobulins

Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation.

In vivo plaque recognition may be important for safe and precise intra-arterial atheroma ablation during laser coronary angioplasty. This study examined the feasibility and sensitivity of utilizing quantitative fluorescence spectroscopy and video-enhanced fluorescence imaging for plaque identification in atherosclerotic human necropsy arterial wall before and after laser atheroma ablation. With wide-band (450 to 490 nm) blue light excitation, the 540 nm fluorescence intensity ratio of normal to diseased sites (n = 13) was 2.09 +/- 0.82 (p less than 0.001) and video fluorescence imaging provided enhanced delineation of atheroma surface characteristics. Continuous argon and pulsed excimer (308 nm) laser ablation of atheroma decreased fluorescence intensity ratios by 42 and 20% (p less than 0.001), respectively (that is, from abnormal to nearly normal). Low power 325 nm laser-excited fluorescence spectroscopy from normal (n = 115) and abnormal (n = 146) necropsy sites revealed an average 45% decrease in atheroma fluorescence intensity (p less than 0.0001) and changes in fluorescence spectra appearance that corresponded to plaque morphologic subtypes. Studies using a dual laser system combining 325 nm laser-excited fluorescence plaque recognition and a 480 nm pulsed dye laser for tissue ablation with common optical fibers demonstrated normalization of both fluorescence intensity and spectra appearance after laser atheroma ablation. Thus, in vitro analysis of surface arterial fluorescence by quantitative spectroscopy and video fluorescence imaging reliably differentiate plaque from normal tissue and may provide the feedback signal needed to activate a laser source for selective plaque removal.

Adult

Early and late healing responses of normal canine artery to excimer laser irradiation.

Acute in vitro histologic studies have shown that the pulsed xenon chloride excimer laser causes precise microablation without the surrounding thermal tissue injury associated with frequently used continuous-wave lasers such as the argon, carbon dioxide, and neodymium:yttrium aluminum garnet lasers. However, the in vivo healing response of artery wall to excimer laser injury is not known. Accordingly, a xenon chloride excimer laser (308 nm, 40 nsec pulse width, 39 mJ/mm2/pulse) was transmitted via a 600 micron fused silica fiber to create 420 craters of varying depths (30 to 270 micron) in 21 normal canine femoral and carotid arteries. At 2 hours, 2 days, 10 days, and 42 days after excimer laser ablation, the artery segments were perfusion fixed in situ and analyzed by light, scanning, and transmission electron microscopy. At 2 hours, craters were covered by a carpet of platelets and entrapped red blood cells. Fibrin and exposed collagen fibers were seen at the crater base. There was a sharp demarcation of the crater-artery wall interface without lateral laser tissue injury. At 2 days, adherent platelets persisted with thrombus covering the base of the craters. Early healing responses were present, consisting of polymorphonucleated leukocytes and new endothelial cells, which extended over the crater rims. At 10 days, no thrombi were seen, and healing continued with almost complete reendothelialization. Macrophages, fibroblasts, fibrin, and entrapped red blood cells were present below the reendothelialized surface. At 42 days, healing was complete with obliteration of the craters by fibrointimal ingrowth. The surface was completely covered by a smooth monolayer of axially aligned endothelial cells. There were no aneurysms or surface hyperplastic responses. These favorable healing responses in normal canine arteries suggest that pulsed lasers with high tissue absorption coefficients, such as the xenon chloride excimer laser, may be suitable energy sources for clinical laser angioplasty procedures. However, further studies in atherosclerotic animals are required before human clinical responses can be accurately predicted.

Animals

Model for photon migration in turbid biological media.

Various characteristics of photon diffusion in turbid biological media are examined. Applications include the interpretation of data acquired with laser Doppler blood-flow monitors and the design of protocols for therapeutic excitation of tissue chromophores. Incident radiation is assumed to be applied at an interface between a turbid tissue and a transparent medium, and the reemission of photons from that interface is analyzed. Making use of a discrete lattice model, we derive an expression for the joint probability gamma(n, rho)d2 rho that a photon will be emitted in the infinitesimal area d2 rho centered at surface point rho = (x, y), having made n collisions with the tissue. Mathematical expressions are obtained for the intensity distribution of diffuse surface emission, the probability of photon absorption in the interior as a function of depth, and the mean path length of detected photons as a function of the distance between the site of the incident radiation and the location of the detector. We show that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile. Results of relevant computer simulations are presented, and illustrative experimental data are shown to be in accord with the theory.

Computer Simulation