caption for
1Robert J. Dempsey (1), Daron G. Davis (2), Robert G. Buice, Jr. (3) and Robert A. Lodder (3)
1. Department of Neurosurgery, University of Wisconsin Clinical Science Center, 600 Highland Ave., H4/338, Madison, WI 53792-3232.
2. Department of Pathology, University of Kentucky Medical Center, Lexington, KY 40536-0093.
3. College of Pharmacy, University of Kentucky Medical Center, Lexington, KY 40536-0082, Telephone: 606-257-9232, Email: Lodder@pop.uky.edu
Near-IR spectrometry is being applied to the solution of problems in many areas of biomedical and pharmaceutical research including cardiovascular radiology, brain imaging, formulation, quality/process control, and even clinical trials. The technique can also play a role in the biotechnology industry in the nondestructive analysis of small quantities of expensive materials. This report first defines near-IR spectrometry and imaging, then describes its application to atherosclerosis and stroke research. New developments in near-IR optics and instrumentation that make effective biomedical near-IR spectrometry possible are related, and finally, new computational research results in parallel supercomputing for near-IR imaging are described. Together, instrumentation, optics, and computing combine to poise biomedical near- IR spectrometry for great advances as it enters the next century.
Near-IR spectrometry is characterized by low molar absorptivities and scattering, which permit nearly effortless evaluation of pure materials, and broad overlapping bands, which diminish the demand for a large number of wavelengths in calibration and analysis. The near-IR region of the electromagnetic spectrum, once regarded as having little potential for analytical work, has become one of the most promising for molecular spectrometry. The advent of inexpensive and powerful computers has contributed to the surge of near-IR spectrometric applications. The near-IR region is usually estimated to include wavelengths between 700 nm (near the red end of the visible spectrum) and 3000 nm (near the beginning of infrared stretches of organic compounds). Absorbance peaks in the near-IR region originate from overtones and combinations of the fundamental (mid-IR) bands and from electronic transitions in the heaviest atoms. For example, C-H, N-H, and O-H bonds are responsible for most major absorbances observed in the near-IR, and near-IR spectrometry is used chiefly for identifying or quantifying molecules including unique hydrogen atoms. Near-IR spectrometry is thus in routine service for quantitative analyses of water, alcohols, amines, and any compounds comprising C-H, N-H, and/or O-H groups. Numerous other elementary bond combinations are also likely to generate near-IR absorbance peaks (1).
Near-IR spectrometry conserves time and materials in comparison to many more conventional analytical methods because:
1. Analysis times under 1 second are possible
2. Simultaneous multicomponent analysis is the norm
3. No sample preparation is usually required for liquids, solids, or gases.
4. Noninvasive and nondestructive analysis is possible
5. Cost per analysis is very low (no reagents are used)
6. Physical properties and biological effects can be calculated from spectra
of samples.
7. Automated correction of background and interferences is performed in
instruments using computer algorithms
8. Detection limits can be very low
9. Samples sizes ranging "from picograms to planets" can be analyzed.
10. Molecular structural information can be derived from spectra.
Near-IR spectrometers and techniques have undergone significant evolutionary transformations since their inception. The earliest near-IR quantitative investigations were executed in much the same manner as familiar UV-vis (visible light) experiments. In fact, the original near-IR instruments were usually UV-vis spectrometers that reached into the near-IR region. Compounds being analyzed were routinely separated from their matrix (solid or liquid) by extraction for scanning in these old spectrometers, and transmission readings were recorded. The usual solvents were carbon tetrachloride and carbon disulfide (both are considered transparent in the near-IR region). When samples were not soluble in these solvents, other solvents with bands of transparency where the analyte has absorbance peaks were used.
Modern near-IR spectrometers and sampling techniques have improved to the point where it is now possible to analyze intact finished pharmaceutical products and even living human patients. In vivo near-IR spectrometry has been plagued historically by problems with high water absorbance in tissue, light scattering, peak overlap, and peak shifting with temperature and sample-matrix composition. Driving near-IR spectrometry into increasingly complex biological and medical problems are more intense and more stable light sources as well as more efficient detectors (and in many cases, more efficient imaging detectors), and improved methods of obtaining rapid wavelength selectivity. The importance of these instrumental advances is evident in the application of near-IR spectrometry to atherosclerosis and stroke research.
Arterial disease contributes to most of the deaths in the United States. The U.S. Public Health Service Agency for Health Care Policy and Research estimates that caring for victims of stroke alone currently costs $30 billion per year. Epidemiological studies performed over a period of years have indicated that reduction of blood lipoprotein cholesterol levels significantly reduces the risk of atherosclerosis, ischemia, and death. For some time these data have been cited in experimental attempts to prevent arterial disease.
The variety of lipoproteins and apolipoproteins can pose an analytical problem. About 2/3 of the total cholesterol in plasma is carried in low-density lipoprotein (LDL) and intermediate- density lipoprotein (IDL) particles from 21-35 nm in diameter. The LDL particles have a surface layer that is about 8% cholesterol while the core is about 42% cholesterol esters. The remainder of the LDL particles is 6% triglycerides (found in the core), 22% phospholipids (found at the surface), and 22% protein (also found at the surface). The principal LDL apolipoprotein is apoB (95% of apolipoprotein content, and 90% of apoB in plasma is carried in LDL), but traces of at least 7 other apoproteins can be found. The effect of in vivo oxidative processes on all of these apoproteins remains uncertain (2).
Serum LDL is known to be a heterogenous substance by ultracentrifugation and by nondenaturing gel electrophoresis. There are as many as 7 LDL subclasses with particles ranging in size from 20-40 nm, and molecular weights from 2 million to 3.5 million daltons (3). Genetics influences the distribution of serum LDL across these classes, and it has been proposed that two distinct LDL subclass phenotypes exist, A and B. In one phenotype, a predominance of large, low density LDL particles exists, while in the other, small dense LDL particles are present in greater numbers (4). A number of studies in the literature suggest that the small, dense LDL phenotype is correlated to progression of atherosclerosis. A detailed analysis of the apoprotein composition of the LDL subclasses has not been made. Environmental influences such as drug treatments and oxidation have also been shown to affect the distribution of serum LDL across the subclasses (5,6). Elevated levels of serum LDL have been shown to increase the risk of cardiovascular disease (7). Oxidation of serum LDL (forming oxLDL) has also been shown to promote lesion formation and growth in animal models of atherosclerosis (8). Much less research has been done on the lipoprotein content of the arterial wall and atheromatous lesions.
There is currently no accurate nondestructive in vivo reference assay for HDL, LDL, or apolipoproteins immobilized in the walls of living arteries in humans. The true life cycle of atherosclerotic plaques remains a mystery from a chemical standpoint because chemical assays currently require interrupting the life cycle. Fiber-optic catheters have been used to locate atherosclerotic lesions, but current techniques can do no more than distinguish lesions from healthy arterial tissue (a detailed breakdown of constituent proteins is not possible). Research currently underway in this laboratory employs InSb FPA and PtSi CCD near-IR video cameras and tunable light sources to identify lesions in living arteries of human patients and map their chemical constituents in 3 spatial dimensions. Results show significant (p<0.05) correlations between certain lipoprotein combinations in carotid plaques and diseases reported in the medical histories of patients, as well as correlations to plaque constitution as determined postoperatively by a pathologist. Furthermore, near-IR spectra of the plaques show similar significant correlations (p<0.05) to medical history and pathology, indicating a likelihood that the analytes being monitored play important (but as yet undefined) roles in the disease process. Tunable light sources based on blackbody emission and tunable filters, as well as a Nd:YAG-pumped KTP/OPO tunable near-IR laser system, are used for different imaging experiments depending upon the light intensity required. Chemical analysis of lesions in vivo permits the kinetic study of atherogenesis and contributes to the understanding of lesion formation and growth. As new processes (e.g., oxidation of LDL) are identified as playing key roles in the initiation and progression of lesions, better treatment programs will be designed that focus on these mechanisms.
Our laboratory has published successful spectroscopic identification and determination of high-density and low-density lipoproteins, apolipoproteins A-I, A-II, and B as well as total cholesterol in human samples. To summarize a few of the more relevant results, the correlation between total serum cholesterol concentration and the serum cholesterol concentration calculated by the near-IR assimilation method is excellent (r2=0.99) [assimilation refers to the complete iterative process of calibration, cross validation, routine sample testing for class membership, recalibration and validation]. The standard error of prediction (SEP) for this calibration is only 12.6 mg/dl. The standard error of estimate (SEE) for apoA-I was 1.8 mg/dl (r2=0.98), and the SEP calculated from cross validation samples (not used to develop the calibration) was 1.9 mg/dl. The SEE=2.0 mg/dl and the SEP=2.1 mg/dl for apoB (r2=0.98).
Research into spectrometry of lipoproteins in solution alone is nearing a logical end point. It will be difficult to gain much additional insight into the role of lipoproteins in atherosclerosis without investigating the role lipoproteins play in the blood vessel wall. We have begun to use the information obtained in serum studies to examine LDL and oxidized LDL (oxLDL) in atherosclerotic plaque in the carotid arteries of endarterectomy patients. One important motivation for near-IR scanning of carotid plaque is that it can potentially be performed transcutaneously on patients presenting with stroke symptoms, in conjunction with sonography, to test the hypothesis that chemical composition is useful in assigning patients with transient ischemic attacks (TIAs) to surgical or drug interventions. The lipoprotein content of carotid plaque is exhibited in near-IR spectra of the plaque. For comparison purposes, ultracentrifugation and SDS-PAGE are also used to measure LDL and oxLDL extracted from the plaque.
In the operating room, two digital cameras (one for near-IR light
and one for visible) are utilized side-by-side on a tripod. The cameras
are located outside the sterile field, about 1 meter from the patient. During
a typical carotid endarterectomy, the carotid bifurcation is surgically
exposed and a venous bypass is installed around the region of stenosis (blockage
of the artery). Near-IR and visible images are obtained from the carotid
prior to installation of the bypass. The carotid is then opened and the
plaque is removed microsurgically. The plaque is dissected away down to
the smooth muscle cell layer of the blood vessel wall. The excised plaque
is examined by a pathologist and frozen in liquid nitrogen for in vitro
near-IR scanning and validation of lipoprotein composition by extraction,
ultracentrifugation, and gel electrophoresis. Near-IR images can be obtained
after removal of the plaque to identify the spectral signature of the plaque.
The vessel is closed and the bypass removed before the incision is sutured.
The visible image obtained during one surgery appears in Fig.
1.caption for
1
The visible image shows the carotid bifurcation (where the common carotid artery branches into the internal and external carotids) as well as surgical instruments and two calibrated, sterile spherical reflectance standards for the near-IR images. The standards are used to correct for variations in positioning of light sources and in light intensity at each wavelength. Before a series of patient images are analyzed, the offset and gain at each wavelength in the image are adjusted computationally by multiplicative scatter correction of image planes to make the two standards appear identical in all patients at each wavelength. Optical ray tracing enables the positions of light sources to be calculated from specular reflections on the surface of the standards. The surface of the standards provides both specular and diffuse reflections to use in standardizing sample spectra, which can also exhibit both specular and diffuse reflections. The use of spherical standards enables irregular sample surfaces at different angles to be referenced to the reflectance at similar angles on the standards if necessary.
Fig. 2 
caption for 2 shows six
near-IR images of the same blood vessel depicted in the previous visible
image. The near-IR images shown are those at 1678, 1944, 2098, 2180, 2230,
and 2312 nm. In this figure, the colors represent the intensity of absorbance
(from low to high absorbance; white, violet, blue, green, yellow, orange,
red, and black). White and black areas represent signals off the depicted
absorbance scale (low and high, respectively). The fact that the areas of
most intense absorbance change between images indicates that even simple
wavelength images contain useful structural information. The image at 1944
nm, for example, shows high absorbance in the lower portion of the frame
that is caused by a fold of skin and pooling of aqueous solution at the
bottom of the incision. In Fig.
3
caption
for 3, the high spatial resolution of the
InSb camera is observable in the specular reflections of the two light sources
seen in the visible image of the black spherical reflectance standard.
Spectral image information at a large number of wavelengths can be
condensed into either (a) a plot that depicts selected chemical concentrations
at each point in the image, or (b) a plot that expresses the probability
that certain states or constituents exist at each point in the image. Determination
of chemical constituents requires calibration (by Beer's Law, for example)
using samples containing a known range of the chemical constituents under
analysis. Plotting probabilities as distances in SD's does not require calibration
with a complete range of characterized standards, only a calibration set
that defines spectra considered normal (or abnormal). In Fig.
4
caption
for 4 probabilities are plotted as distances
of image spectra in SDs from the center of a calibration set of atherosclerotic
plaque (abnormal tissue because in vivo spectra of normal carotid
wall are difficult to obtain - such patients do not elect to have carotid
surgery). Regions of tissue with lipoprotein spectra that resemble atherosclerotic
plaque are shown in shades of blue (less than 3 SD's from the center of
the spectra of atherosclerotic plaque). Normal human tissue spectra (which
are found 3 to 6 SD's from the center of atherosclerotic plaque spectra)
are shown in shades of green. Red represents spectra in the image that are
human skin or not human in origin at all (6 to 80 SDs from the center of
atherosclerotic plaque spectra). The software enables the user to place
crosshairs on any location in the image to obtain either concentrations
or distances in SDs, depending on the calibration samples. In Fig.
4, the distance of the point under the crosshairs from the center of
the spectra of atherosclerotic plaque is 4.3 SDs.
The statistical significance of the correlation in each of the following
6 histograms is established at p<0.05 each of two separate tests: H:r2=0,
A:r2 0 and H:åv2/åc2=1, A:åv2/åc2>1. Proteins
are monitored on the gels from 8 to 200 kD in 2 kD increments by capturing
images of the gels on a CCD camera. Fig. 5
caption for 5 shows the strongest significant correlations between
the gel data and the medical histories of the patients (nc=29, nv=29). The
white bars show the value of the Pearson correlation coefficient and the
black bars show the percentage of the total spectral variation accounted
for by the principal components showing the correlation (an indication of
the relative size of the near-IR signal). The linear combination of proteins
responsible for each correlation is readily calculated. For instance, the
proteins that correlate to the presence of coronary artery bypass grafts
are shown in Fig. 6
caption for 6.
Coronary artery disease (CAD) and bypass grafts (CABG) have similar correlations
and contributions to variation. While the CAD and CABG patients overall
had less protein than average in the 8-200 kD range in their plaques, the
plaques were relatively enhanced in their content of the proteins at 16,
28-38, and 66 kD. A smaller relative enrichment of the proteins at 84, 96,
and 125-140 kD was also observed. The gels of patients experiencing speech
problems show a similar overall pattern, with a slightly different band
region from 30-40 kD.
The SDS-PAGE of LDL (solid line) and oxLDL (dashed line) in Fig. 7
caption for 7 show that oxidation
of commercial LDL standards (pooled from multiple donors, so LDL subclass
phenotypes are obscured) reduced the number of peaks present in the gel,
and appears to shift the molecular weight to slightly lower values. A medical
history of previous major surgery also appears to reduce the amount of larger
proteins in the targeted mass range, but increase the amount of smaller
proteins. The crossover point is about 45 kD, and the peak features at 66
and 130 kD are particularly reminiscent of those in the LDL standard samples.
There are also strong correlations between the proteins in the plaque
and examination of the plaque by pathologists (see Fig.
8
)caption
for 8. Microhemorrhage and microulceration
produce the strongest correlations to protein content, and these correlations
account for major fractions of the total variation in the gels. The most
visible protein feature of microhemorrhage involves the proteins at 130
kD. Overall, the loss the proteins in the patient plaques is similar to
that seen in the cases of medical histories of CAD, CABG, and major surgery.
Microulceration is associated with more proteins with mass around 82 kD,
a minor peak in the CAD and CABG cases. These peaks are present in LDL,
and to a lesser extent, fully oxidized LDL. Microulceration is associated
with a loss of proteins with a mass near 170 kD, as is microhemorrhage and
CAD, CABG, and major surgery.
Other interesting associations appeared in the gel electrophoresis reference measurements. The presence of fibrous cap in the pathologists examinations and bruit in the medical history both correlate significantly to the proteins observed. Moreover, the proteins associated with fibrous cap appear to be the same proteins associated with bruit. The major features in both fibrous cap and bruit are a relative increase in the amount of proteins at 30 and 105 kD, and a relative loss in the amount of proteins at 70 kD and in the high molecular weight region from 150 to 200 kD.
The presence of necrosis in the plaque in the report of the pathologists' microscopic examination of the plaque is significantly correlated to certain proteins in the plaque. A major protein feature in necrosis is an increase in the amount of proteins with masses 38 kD and from 125-130 kD. These proteins are also easily identifiable features in patients with medical histories of CAD, CABG, and major surgery. The severity of disease seems to be correlated to the concentration of these proteins in the plaque. The peaks are present in the plaques of CAD patients. The peaks are larger in size, however, in the patients in which CAD has progressed to the point that a bypass graft is necessary. The 130 kD peak is even more pronounced in patients that have developed speech problems, and by the time major surgery is necessary (such as CABG or endarterectomy on the other side) the peak is very large indeed relative to the others in the plaque.
Near-IR spectra correlate significantly (f test and test of H:r2=0, p=0.05, nc=23, nv=21) to the concentration of nearly all of the 93 protein molecular weights monitored by gel electrophoresis (protein peaks at 20, 162, and 180 kD are the exceptions). The correlation is strongest in the proteins that produce the largest peaks in the electrophoresis, which is not surprising because the absorbance values at these molecular weights are likely to be the least noisy. Near-IR spectra are generally far less noisy and have a much larger linear dynamic range than gel electrophoresis (up to 6 orders of magnitude for near-IR spectrometry, compared to at most 2 for gel electrophoresis). In fact, gel electrophoresis is used as a calibration method for near-IR spectrometry only because it is widely employed, fairly well understood, and permits quantification of a large number of proteins in a sample simultaneously. The eventual replacement of gel techniques with near-IR ones will not only speed the process of plaque analysis but may make it more precise as well.
Quantification of proteins in plaque by near-IR spectrometry compares
favorably to values obtained by ultracentrifugation and gel electrophoresis
when these separation methods are used for calibration and validation. In
Fig. 9
caption for 9, a single
near-IR spectrum of each plaque (nc=23 calibration plaques, nv=21 validation
plaques for RSD calculation) was run through 10 calibration models simultaneously
to predict the concentration of each of the 10 protein peaks selected from
the gels. The calibration model selected made bias=0. The results are about
as accurate as quantification by gel electrophoresis itself (less than 20%
RSD across most of the middle of the gel). The precision is for the most
part independent of the amount of variation accounted for by each protein,
again suggesting that the gel measurements are the source of the 20% RSD,
and not the near-IR measurement, because in near-IR spectrometry increasing
the amount of spectral variation generally increases precision (reduces
RSD).
Inverse principal axis transformation of near-IR spectra permits calculation of the approximate spectrum of each protein in its natural plaque matrix. For example, the spectrum of the 128 kD protein shows increasing absorbance with increasing concentration at the characteristic 1750 and 2310 nm, indicating that the proteins are lipoproteins or have substantial lipophilic character. A similar spectral pattern was noted for the other proteins, with the exception of the 40 kD protein, which does not appear to possess much lipophilic character.
Principal component analysis indicates 15 different orthogonal factors
above the noise level in the near-IR spectra of the human carotid plaques
scanned. Analyses of near-IR principal components reveal significant correlations
to age, smoking history, previous stroke, diabetes, hypertension, and sex
(see Fig. 10
)caption for 10. Near-IR
spectrometry provides a rapid and nondestructive new means of assessing
the lipid oxidation status of plaque, and near-IR data suggest that oxidative
processes are related to the progressive increase in carotid atherosclerotic
plaque with age and smoking. Significant near-IR correlations (p<0.05)
to pathology reports of gross plaque hemorrhage, gross plaque thrombosis,
microscopic hemorrhage (recent and past), microscopic necrosis, microscopic
ulceration, microscopic surface thrombosis, and the presence of a fibrous
cap on the plaque have been observed. The near-IR spectrometric technique
permits enormous quantities of data on the protein and lipid composition
of carotid plaque to be quickly obtained with high S/N, and makes the testing
of hypotheses about atherogenesis and the progression of disease easy to
investigate in a nondestructive fashion. The eventual extension of this
technology to noninvasive transcutaneous laser measurements in patients
should increase greatly our understanding of the disease process, and may
even make a rational assignment of symptomatic patients to drug and/or surgical
interventions possible.
The long term goal of these studies is to rank proteins in the LDL fraction by importance in reactions suggested by supercomputer simulations and by correlation to characteristics that increase the likelihood of the proteins being important in initiation or progression of disease. The stoichiometry of the reactions suggested by simulations should be observed and measured experimentally. At that time, rate laws will be calculated for the proposed mechanisms, and measurements of products and reactants made by near-IR imaging (or other methods as needed). Once a reasonable order of investigation is established, the first protein in the list will be sequenced and the secondary and tertiary structure determined by x-ray crystallography, near-IR spectroscopy and VCD, and NMR. By assuming LDL and apoB are among the reactants forming the species in the oxLDL layer in the plaque extract, and that the proteins on the list are among the products, reaction stoichiometries and mechanisms can begin to be tested with the help of molecular mechanics, ab initio or semiempirical modeling methods and calculation of Moller-Plesset electron correlation energies. (Propitiously, the latest version of Gaussian 94 has just been parallelized by HP-Convex for our Exemplar supercomputer.) Given time, and using vibrational overtone and combination bands calculated by computer and a constrained optimization linear-programming assignment algorithm, near-IR peak assignments may be made for every motion in a molecule with an error constrained to less than 20 nm for all peaks. The final mechanisms can be tested kinetically by noninvasive near-IR laser imaging of the carotid and by isolation of any intermediates. Once mechanisms have been established, drug interventions can be proposed and tested in vitro.
In most cases, technology derived from other fields has been advancing near-IR research. For example, in the past few years, many new methods of fabricating diamond components have been developed, in part because the wide band gap in diamond has attracted the interest of researchers and engineers in a number of fields. Diamond films are likely to be used more in biomedical near-IR imaging and change the way some spectra are collected. Chemical vapor de- posited (CVD) diamond can be used to produce ideal sample cells that are transparent and easy to control thermally. In addition, a new procedure developed by GE Superabrasives that attaches optical windows made of diamond film to metal flanges provides imaging components with immunity to extreme heat, harsh chemicals and abrasion (9).
Applications for which diamond optics are particularly well suited
include use as optical windows in cameras for near-IR spectrometry, cold
filter substrates (where diamond lets cameras cool very rapidly in preparation
for emergency procedures in patients), and pressure relamination of InSb
wafers to Si CMOS multiplexers in near-IR cameras with malfunctioning pixels
(see Fig. 11
)caption for 11. Although
diamond is more expensive than optical materials such as zinc selenide and
sapphire, diamond film has exceptional thermal conductivity (typically better
even than copper), resists chemicals and even heat up to 700 degrees C without
hazing (a useful characteristic for parts that may have to be sterilized).
In the past it has been difficult to bond diamond film to metal because of the differential between the coefficients of thermal expansion of the materials. Thermal expansion coefficients of metal are two to eight times higher than that of diamond. This difference in expansion can cause the diamond to crack at extreme temperatures. GE's method overcomes that problem by compensating for the differences in expansion within the film they produce. The diamond film is pure diamond but possesses a unique structure that is polycrystalline in nature with some defined orientation. Consequently, it is strong and maintains full-spectral (UV-visible through infrared) transmission characteristics. Free-standing diamond plates are available in diameters up to 70 mm and thicknesses from 0.2 to 1.2 mm, suitable for detector array repairs, cold filters, and windows.
The optical effects typically observed in near-IR spectrometry are linear effects. In other words, when near-IR light interacts with matter, matter usually responds proportionately, and it is this proportionate response that produces the well-known optical characteristics of reflection, refraction, scatter, and absorption (10).
The linear optical responses of matter modulate near-IR light in many analytically useful ways, but they do not alter the wavelength of the light. For example, after a beam of light at 2310 nm reflects from adipose tissue the wavelength is still 2310 nm. The beam might not be headed in the same direction because of reflection, and it might not have the same intensity because of absorption, but at least it leaves the adipose tissue with the same wavelength.
However, virtually all electrooptical technologies of consequence now rely on at least one nonlinear optical effect. Research into nonlinear methods and materials has become among the most vital and influential research in contemporary optics. In addition to well-known effects like second-harmonic generation (SHG), the list of nonlinear optical effects includes optical rectification, the Pockels electrooptical effect, sum- and difference-frequency mixing, the Kerr electrooptical effect, third-harmonic generation, general four-wave mixing, the optical Kerr effect, stimulated Raman scattering, stimulated Brillouin scattering, phase conjugation, self- focusing, self-phase modulation, and two-photon absorption, ionization, and emission. Some nonlinear phenomena (such as the Raman, Pockels, and Kerr effects) were discovered long ago, but it wasn't until the arrival of lasers that new nonlinear results were obtained for the first time. The tools created using these results are now poised to initiate a renaissance in biomedical near- IR spectrometry. In particular, tunable solid-state near-IR lasers using optical parametric oscillation provide high power (3 megawatts or more effective power in pulsed mode), narrow wavelength (500 mhz SLM in the near-IR is attainable), pulse uniformity (<3% pulse-to-pulse variation), and rapid tuning for near-IR spectrometry of tissue.
Lasers have had a profound impact on nonlinear optics because nonlinear effects normally appear only in the presence of large electric or magnetic fields. The Lorentzian dipole model can be used to explain why these effects appear in large fields. When light passes through dielectric matter like glass, the dipole model describes the interaction in terms of an oscillating electric field (the light wave) and a collection of harmonically driven dipoles (the atoms). At conventional irradiance levels (several W/m2), the atomic dipoles respond linearly to the driving energy of the light wave (there is a one-for-one correspondence between the frequency of the light wave and the vibration frequency of the dipoles). However, at very high levels of irradiance (several MW/m2), the dipoles no longer respond linearly and begin to oscillate anharmonically. Anharmonicity arises because the electric-field strength of the light wave (the driving energy) is comparable to the binding force (restoring force) of each atom in large fields.
Every linear optical effect seems to have a nonlinear, frequency-shifting, intensity-dependent counterpart. For example, Brillouin and Raman scattering can each shift pump light frequencies both higher (anti-Stokes shift) and lower (Stokes shift). As a result, stimulated Raman scattering and stimulated Brillouin scattering are used to convert laser pump beams into tunable near-IR light. Research and development efforts continue to yield novel nonlinear materials for bulk, wave-guide, and nanostructure devices, including an organic "squaraine" compound that yields nonlinear effects like second harmonic generation when placed in a Langmuir-Blodgett monolayer, in spite of the fact that it is definitely centrosymmetric (11).
The difference between harmonic dipole oscillators and anharmonic
dipole oscillators (and between linear and nonlinear effects) becomes obvious
when their potential energy is plotted as a function of the displacement
between the poles. When the interaction of light and matter is purely linear,
the dipole oscillator obeys Hooke's law and the potential-energy curve is
parabolic. However, at sufficiently high field the dipole-restoring force
no longer increases linearly with displacement. Hooke's law is violated,
and the potential-energy curve deviates from a parabola. The manner in which
the energy curve deviates from a perfect parabola depends on the dipole,
which in turn depends on the molecular structure of the material itself.
Molecular structures can be classified into two general categories: those
with a center of symmetry (centrosymmetric) and those without (noncentrosymmetric).
Fig. 12
caption for 12 plots potential
energies for dipole oscillators in both categories of matter. The asymmetry
of the anharmonic dipole is most noticeable in a noncentrosymmetric medium.
The skewed response of this dipole reveals the eccentric influence of adjacent
dipoles. Dipoles in condensed matter are not sequestered, and each dipole
is influenced by the local fields of its neighbors as well as by the external
field of the light wave.
Dipole susceptibility is defined in tensor form in condensed dielectric matter to account for the combined effect of all the local force fields. Once the dipole susceptibility is characterized for a material, then the response to an applied electric field can be expressed as equation 1.
The variable n can assume any positive integer value, and it's value determines the optical interaction under study (if n=1, then the polarization P induced by the electric field E is linear and the material displays regular optical properties. If n=2 or more, then the induced polarization is nonlinear. The recurrent nature of the light wave is duplicated in the material polarization. The polarization wave created by oscillating dipoles in the material is what creates secondary light waves inside the medium. In linear optical behavior, the polarization wave is highly correlated to the light wave, but under nonlinear conditions the two waves differ. Fourier analysis of the polarization waveforms is sometimes used to explain the optical properties of materials. In the nonlinear response of noncentrosymmetric media, the asymmetry of the anharmonic dipole is reflected in the generated polarization wave, leveling its peaks. Fourier analysis of this waveform shows three superimposed waveforms: a sine wave with the same frequency as the fundamental light wave (v1), a sine wave with twice the frequency of the fundamental (2 v1), and a negative offset (v=0). A single polarization wave can be considered the source of normal refraction, SHG (second harmonic generation or frequency doubling), and optical rectification.
In a vacuum simple superposition of electromagnetic waves is the rule, and light wave mixing does not occur. Only the nonlinear interaction of light with matter makes such energy transfer possible. The nonlinear polarization wave itself joins the energy from one light wave to another, acting as a intermediary between the two. This coupling is the optical parametric interaction.
If two monochromatic light waves with different wavelengths pass together through the same noncentrosymmetric medium, the complex polarization wave they induce in the material contains components at the two fundamental frequencies (v1, v2), the sum and difference frequencies of the two fundamentals (v1ñv2), the second harmonics of both fundamentals (2 v1, 2 v2), and a dc offset (v=0). The polarization wave includes all the linear and second-order nonlinear optical effects (n = 1 and 2 in the equation given earlier). The second-order nonlinear effect comprises wave-mixing mechanisms in which waves of differing frequencies mix to generate other frequencies. Second-harmonic generation can be thought of simply as a unique instance of wave mixing in which the two fundamental frequencies are equal, yielding the second harmonic. The Pockels electrooptical effect can be considered the mixture of a fundamental frequency with v=0, which modifies the material polarization to create a situation in which the refractive index of the material is proportional to the DC field. In three-wave mixing, the second-order nonlinear effect creates sum or difference frequencies (v3=v1ñv2).
The efficiency of energy exchange in mixing depends upon the relationship between the phase velocities of the polarization wave and the light waves traveling through the material. In SHG, for example, the nonlinear polarization wave propagates through the material with a phase velocity that equals that of the primary refracted wave. This is because the refracted wave provokes the material polarization. But the second-harmonic light wave (which is generated by the nonlinear polarization wave) propagates more slowly through the material due to dispersion. As a result, the polarization wave and its resulting second-harmonic light wave pass in and out of phase as they propagate through the material. The energy exchange between the waves is limited because the waves cannot add constructively. When the phase velocities of the two waves are equal a continuous increase of the second-harmonic wave in the forward direction occurs. Birefringent crystals (crystals whose refractive indices depend on the direction and polarization of the propagating light) provide a handy way to control phase velocities. When a polarized light wave traverses a birefringent crystal at precisely the right angle, the phase velocities of the induced polarization wave and second-harmonic wave are identical. In lithium niobate, which is used in the near-IR, angle phase matching converts the fundamental frequency to its second harmonic with high efficiency.
For many nonlinear phenomena phase matching determines the nonlinear
effect that arises. In difference-frequency mixing, when a noncentrosymmetric
crystal is exposed to a high-power (pump) beam with frequency v3 and a weak
(signal) beam with frequency v2, the material reacts by creating a nonlinear
polarization wave component at the beat frequency of v1, which generates
the idler beam. The idler beam can also beat with the pump beam to create
another polarization component at the signal-beam frequency v2. The effect
amplifies the signal wave in a frequency-mixing strategy termed optical
parametric amplification. If all three waves are properly phase matched
with their corresponding polarization waves, optical parametric amplification
can be considerable. In our laboratory, this effect is exploited in dual
antirotated KTP crystals to amplify near-IR light to an intensity where
it can be used effectively to probe arterial walls through blood or surrounding
tissue (see Fig. 13
)caption for 13.
The KTP crystals in the OPA are pumped by a Nd:YAG laser, and the signal
beam is provided by an optical parametric oscillator (OPO).
The OPO is also two antirotated KTP crystals, only these crystals
are placed inside a reflective cavity. The OPO needs only a single pump
beam (provided by the doubled Nd:YAG, at 532 nm) to generate both signal
and idler waves because the signal frequency derives from the naturally
occurring optical noise within the crystal. In an OPO, phase matching conditions
prescribe the signal and idler frequencies; therefore, altering the phase
matching conditions tunes the output frequencies (12). Efficient frequency
conversion of CW lasers needs an enhanced electric field that can be obtained
by placing the nonlinear crystal within the laser cavity. An alternative
approach is to place the nonlinear crystal in an external resonator for
field build-up. Changing the angle or temperature of the crystals are commonly
used for tuning OPOs. The use of dual antirotated KTP crystals in our near-IR
system enables angle tuning the OPO without deflecting the output beams.
The OPO/OPA system using four KTP crystals and a Nd:YAG pump produces near-IR
and IR light with a tunable output wavelength between 1.4 æm and 4.1
æm (see Fig. 14
)caption for 14.
Three factors account for the recent success of the OPO: an improved pump
laser source, better nonlinear optical materials; and effective wavelength
conversion via nonlinear devices.
Applications of nonlinear optics in routine near-IR spectrometers will require the cost of the nonlinear crystal to fall from thousands of dollars to less than $100. Lithography-based materials-processing methods like those used in the semiconductor industry are reducing the cost of nonlinear crystal production. In addition to lowering cost, planar processing enables the nonlinear material to be engineered for maximum conversion at selected wavelengths. Planar processing spatially modulates the nonlinear optical coefficients of materials such as lithium niobate, lithium tantalate and KTP. Such crystals are referred to as quasi-phase-matched (QPM).
The progression from bulk polished and coated large crystals to planar-processed crystal "chips" has already begun in research laboratories. For example, thousands of nonlinear QPM crystal chips have been produced at Stanford University. Planar construction appears to be the best way to create low-cost OPAs and OPOs engineered to meet specific performance requirements.
A QPM guided-wave OPO in lithium niobate pumped at 790 nm has been used to create signals in the 1300 and 1500 nm communication bands (13). The sign of the nonlinear coefficient of lithium niobate has also been adjusted successfully by QPM. A comparable chip was assembled to produce IR light by mixing the output of two diode lasers. The QPM OPO will extend the wavelength range of diode-pumped solid-state lasers for applications that require tunable near-IR and IR light.
Usually, none of the second-order nonlinear effects described above are observed in centrosymmetric optical materials (including amorphous substances such as glass, liquids, and gases). Only odd harmonics of the fundamental frequency occur in centrosymmetric media because of the symmetrical nonlinear response of the dipoles. In noncentrosymmetric crystals, both odd and even harmonics are observed. Of the 32 molecular symmetry point groups used to classify crystal symmetry, 11 point groups are centrosymmetric and cannot support second-order optical effects. For these 11 crystal groups, third-order (n=3) nonlinear effects are the first nonlinearities observed.
The third-order material polarization exhibits some analogous behaviors to the second- order, such as frequency tripling (v2 = 3 v1) and four-wave mixing (for example, v4= v1 + v2 + v3). What differentiates third-order nonlinear polarization from the second-order kind is the linkage of the refractive index to the light intensity. This third-order effect, called the optical Kerr effect, enables high-power light beams to actually alter the refractive index of the materials they traverse. Optical phase conjugation (OPC) is probably the most well known application of the optical Kerr effect. OPC can compensate for any distortions between the light source and the phase conjugate mirror through phase reversal, making it an interesting technique but one that has not been exploited in traditional near-IR spectrometry.
The optical Kerr effect can be employed to self-focus a laser beam using the Gaussian intensity profile of the beam. This effect is often used in solid state near-IR lasers to compensate for thermally-induced changes in the components. The index gradient induced by the beam in the material creates a positive lens that can bring the light to a focus or restore its collimation. If the power of the generated lens compensates precisely for the normal divergence of the beam, the light becomes caught inside a self-induced index waveguide as it travels through the material, in effect constituting a spatial soliton. The optical Kerr effect also gives rise to self- phase modulation, which can be used to counteract the normal dispersion-broadening of near-IR light pulses in fiber-optic waveguides. Using self-phase modulation, short near-IR light pulses are transformed into solitons that maintain their temporal shape for thousands of kilometers through a nonlinear dispersive waveguide.
Near-IR cameras have been fabricated from detector arrays made of indium antimonide (InSb), lead sulfide (PbS), indium gallium arsenide (InGaAs), platinum silicide (PtSi), and even mercury cadmium telluride (MCT or HgCdTe). InSb and InGaAs are the current materials of choice for near-IR cameras. InSb detectors respond to near-IR light from 1000-5500 nm while InGaAs detectors respond to near-IR light from 900-1700 nm. The wavelength range of InGaAs can be extended to 2500 nm by increasing the indium content of the alloy. InSb detectors cover a wider wavelength range with less overall noise but require cryogenic cooling. Both InSb and InGaAs cameras are available with array sizes in the 128x128 range and the two are comparably priced. Larger formats of 256x256 and even 512x512 are also either available now or will be available very soon. The most successful imaging detectors have high quantum efficiency (70% or more) and D* (1012 or more) and fast frame rates (50 frames/sec or more).
InSb cameras are typically refrigerated with either Sterling cycle coolers or liquid nitrogen. In InSb cameras a cold filter is located inside the dewar behind a transparent window to eliminate blackbody radiation that would otherwise saturate the detector. The details of construction of these cameras have been published elsewhere and will not be repeated here (14).
Most InSb near-IR cameras are really IR cameras designed for thermal imaging but converted to near-IR use. Conversion generally requires (a) changing the cold filter from one that passes mid-IR light to one that passes near-IR light, (b) changing the stare time of the array to one optimal for the new signal level caused by changing the cold filter, and (c) adjusting the gain and offset of each pixel in the array to provide a uniform response with the new optics. While InSb FPA manufacturers have made this conversion process easier than it was in 1990, it is still a process that is usually performed by the end user.
One might ask, "Why use supercomputers at all in near-IR spectrometric research?" Certainly, the computational power now available on the desktop is more than adequate for routine near-IR analyses. However, five years from now, the power of today's supercomputers will be sitting on the desktop, and today's researchers are responsible for preparing for what can be done at such a future time.
In our laboratory, supercomputing resources are used primarily for preparing video, for simulation of complex systems, and for exploring the theoretical limits of data-analysis procedures. Video is calculated from near-IR spectra obtained by nonimaging intra-arterial catheters and by near-IR cameras imaging living targets. Full-motion video from catheters shows the lipoprotein composition of the arterial wall as the catheter passes along the length of the artery. Near-IR video is also useful for in vivo human lipoprotein measurements in arteries dissected away from their surrounding tissues. Under these circumstances, the artery moves with each heart beat, and computerized composition analysis of images requires the target in each video frame to be translated to common coordinates for all frames in a given signal integration. The complex system being simulated on a supercomputer is a scanning near-field near-infrared microscope that can produce spectrometric images on a nanometric level. For this microscope, an optical fiber is pulled to a subwavelength tip. The fiber is then coated with gold in order to contain the evanescent near-IR light. This small aperture light source by itself is not enough to achieve the desired resolution. The sample must also be within the near-field ( /2) of the source. Both reflection and transmission images can be obtained point by point by scanning the probe across the sample. The transmission near-field microscope has been numerically modeled using the moment method on a 32-node parallel supercomputer. The probe is modeled as an infinite perfectly conducting plane with a subwavelength aperture. The sample for this model is a varying number of thin perfectly conducting wires with a finite length. Work is now underway to expand the model to include dielectric sample materials, such as cell membrane receptors. With this model, the capabilities and behavior of the microscope can be studied as well as compared to real NSOM image data.
One theoretical study of an image analysis procedure being undertaken
on our supercomputer is the study of the BEST (Bootstrap Error-adjusted
Single-sample Technique) algorithm used to generate the atherosclerotic
plaque image in Fig. 4 (15). The BEST calculates distances in multidimensional
asymmetric nonparametric central 68% confidence intervals in spectral hyperspace
(roughly equivalent to standard deviations, see Fig.
15
)caption
for 15. The BEST metric can be thought of
as a "rubber yardstick" with a nail at the center (the mean).
The stretch of the yardstick in one direction is therefore independent of
the stretch in the other direction. This independence enables the BEST metric
to describe odd shapes in spectral hyperspace (spectral- point clusters
that are not multivariate normal, like the calibration spectra of many biological
systems). BEST distances can be correlated to sample composition to produce
a quantitative calibration, or simply used to identify similar regions in
a spectral image. The BEST automatically detects samples and situations
unlike any encountered in the original calibration, making it more accurate
in biomedical analysis than typical regression approaches to near-IR analysis.
The BEST produces accurate distances even when the number of calibration
samples is less than the number of wavelengths used in calibration, in contrast
to other metrics that require matrix factorization. Unlike its predecessor,
the BEAST, the BEST retains the direction vector of a standard deviation
in hyperspace throughout all calculations, an essential characteristic for
multicomponent quantification of sample composition.
The supercomputer used to run the BEST is a 4 hypernode (32 processor) Convex Exemplar SPP-1200 system with 7 Gigabytes of memory and 80 Gigabytes of disk storage. The unit processor in the Exemplar SPP1200/XA is Hewlett-Packard's PA-RISC 7200 processor with 240 MFLOPS peak performance. The SPP1200/XA can have up to 16 hypernodes, for a total of 128 processors, with a peak performance of 30.7 GFLOPS.
The theoretical studies of the BEST involve parallelizing the code
to speed its performance in data analysis to match the speed of the near-IR
cameras in data collection. The ability to process large amounts of data
rapidly is also important in hyphenated near-IR techniques like MAReNIR
(magnetohydrodynamic acoustic-resonance near-IR spectrometry) (16). In the
studies described here, the time required to create a calibration for n
samples at d wavelengths, and validate this calibration by n cycles of leave-one-out
cross validation, is shown. Using a single processor, calibration with n=100
samples scanned at d=100 wavelengths and validated with n=100 cycles requires
22 seconds of "wall-clock" time. "Hot spot" analysis
of the code reveals that about 21 of these seconds are spent in bootstrap
replications of the calibration samples. In routine near-IR analyses, the
replications are needed only once, when the calibration equations are first
calculated. Efficient distribution of the code across 8 processor threads
speeds the execution time for calibration and cross validation to about
1.6 seconds (see Fig. 16
)caption for 16.
For an IRC 64 (64x64) InSb camera in which the full spectra for each pixel
are analyzed, this still corresponds to a worst-case calibration and cross
validation time of 1.8 hrs. Fig. 17
caption for 17
shows the relationship between calibration and cross validation time and
the number of CPUs for a large problem (n=1000 samples and d=1000 wavelengths
with 10000 replicates). When 8 processors are employed the time required
is fairly manageable 16 minutes. (Experiments with 16 or more processors
were not successful because of a bug in the Convex operating system, which
should be corrected soon.) Fig. 18
caption for 18
shows the relationship between calibration and cross validation time and
the size of some typical problems. Typically, the full spectra of every
pixel in the image are not analyzed during an endarterectomy, and operator
intervention in the form of pixel selection with a mouse is used to identify
the likely position of the atherosclerotic plaque. However, in the future,
completely automated near-IR spectrometric imaging and analysis systems
are likely to need the ability to execute full spectral analyses of every
pixel in an image to identify regions of interesting pathology, for example.
Such computational demands ensure a place for supercomputing in biomedical
near-IR spectrometric imaging for at least the next decade.
More biomedical applications of near-IR spectrometry are described on the WWW on http://kerouac.pharm.uky.edu/. Other contemporary research in biomedical near-IR spectrometry and presented in this issue includes the work of Dr. Patrick Treado at the University of Pittsburgh, who is working with acousto-optic tunable filters (AOTF) that can be used to create solid-state spectrometers for high frequency optical switching and wavelength selection. By introducing a combination of RF frequency signals into its transducer, the AOTF acts as an electronically controllable, multiplexing spectrometer. Treado has demonstrated signal to noise enhancement with a Hadamard Transform AOTF spectrometer.
Dr. Mark Arnold at the University of Iowa uses near-IR spectrometry with Fourier filtering and partial least squares regression to determine simultaneously biological components of interest such as glucose, glutamine, ammonia, lactate, and glutamate in solution. The accuracy for individual analytes in these mixtures ranges from 4-8%.
Dr. Neil Lewis in the NIDDK at the National Institutes of Health has used InSb camera technology in conjunction with a step-scan interferometer to produce high-fidelity images of primate brain tissue from 1-5.5 æm. Spectral images of the brain tissue can be related to specific lipid and protein fractions.
Dr. Jim Drennen at Duquesne University in Pittsburgh uses near-IR spectrometry to monitor drug penetration from pharmaceutical transdermal patches. Principal component regression estimates the depth resolution of the near-IR method to be about 31 æm. Depth-resolved NIRS conducted in a practical in vitro system (salicylic acid in a hydrogel matrix) with an artificial neural network based calibration model predicted salicylic acid concentrations with an error of only 123 æg/ml.
If present trends in optics, instrumentation, computation, and pursuit of applications using near-IR spectrometry continue, these researchers and many others will make the turn of the century a time of major advances in biomedical near-IR spectrometry. It seems likely that near- IR methods will play a role in the prevention, treatment, and management of some of the major diseases of our time: atherosclerosis, cancer, and diabetes.
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Fig. 1. A visible-light image of a human carotid bifurcation exposed at the beginning of endarterectomy. The targeted artery is located at about 8 o'clock relative to the black and white sterile reflectance standards. The top two reflections in the black reflectance standard are the surgical lights, which are equipped with cold filters and emit little near-IR light. The two smaller reflections beneath the surgical light reflections are the tungsten sources for the near-IR camera. Images are collected at each wavelength with the near-IR sources on and off to enable correction for sample blackbody emission in the near-IR and for other light sources in the room. Go back to text
Fig. 2. Near-IR images at 6 selected wavelengths (from top to bottom and left to right, 1678, 1944, 2098, 2180, 2230, and 2312 nm) of the carotid in Fig. 1. The images are contour maps in which the contours connect areas of equal absorbance [as log(1/reflectance)]. The colors denote absorbance, which typically ranges from 0.9-1.6 if specular reflectance from surgical instruments is neglected. The color code, from lowest to highest absorbance, is white, violet, blue, green, yellow, orange, red, and black. White and black areas represent signals off the depicted absorbance scale (low and high, respectively). The axis labels denote coordinates in the pixel map of the InSb array. Go back to text
Fig. 3. A digital "zoom in" on the white reflectance standard in a near-IR image. The colors were selected to cover just the range of reflectances observed on this particular standard, forcing the rest of the image off-scale black (with the exception of a reflection of a near-IR source from the black reflectance standard located behind and to the right of the white reflectance standard). This image shows the high spatial resolution of the camera as well as the low noise and high absorbance-unit resolution of the A/D module. Note the lack of "speckling" in the image that would occur if substantial noise were present. Go back to text
Fig. 4. A probability-density contour map of the near-IR spectral data in Fig. 3. A crosshair can be positioned anywhere on a contour map and used to select full spectra for analysis, to calculate a chemical composition at the selected location, or to give a distance from the calibration samples in multidimensional BEST SDs. In this case, the distance for the point under the crosshair is 4.3 SD s. Regions of tissue with lipoprotein spectra that resemble atherosclerotic plaque are shown in shades of blue (< 3 SD's from the center of the spectra of atherosclerotic plaque). Normal human tissue spectra (which are found 3-6 SD's from the center of atherosclerotic plaque spectra) are shown in shades of green. Red represents spectra in the image that are human skin or not human in origin at all (6-80 SDs from the center of atherosclerotic plaque spectra). Go back to text
Fig. 5. The significant correlations (p<0.05) between linear combinations of lipoproteins in carotid plaques and patient medical histories is shown in the white bars. The lipoproteins were determined by extraction, ultracentrifugation, and denaturing gel electrophoresis. The variation shown in the black bars is calculated from principal component analysis of sample lanes in gel images. Go back to text
Fig. 6. Inverse principal axis transformation reveals the linear combination of lipoproteins that correlate to each record in the medical histories. The data were mean-centered, and the majority of the patients had no coronary artery bypass graft (no CABG, dashed line), so the dashed line appears nearly flat at 0 SD. Patients with CABG, on average, have fewer lipoproteins over 25 kD in their carotid plaques than those without CABG. Lipoprotein oxidation, smooth muscle cell proliferation, calcification, and other mechanisms could be responsible for the depletion of these lipoproteins. Go back to text
Fig. 7. The protein distribution in serum LDL (a commercial standard shown as the solid line) and oxLDL (prepared by in vitro oxidation with CuSO4 from commercial standard and shown as the dashed line). The average lipoprotein distribution in carotid plaque resembles the average of the distribution of lipoproteins in serum LDL and oxLDL. Go back to text
Fig. 8. The significant correlations (p<0.05) between linear combinations of lipoproteins in carotid plaque and examination of the plaques by a pathologist is shown in the white bars. The lipoproteins were determined by extraction, ultracentrifugation, and denaturing gel electrophoresis. The variation shown in the black bars is calculated from principal component analysis of sample lanes in gel images. Go back to text
Fig. 9. The measurement precision for 10 lipoproteins determined simultaneously in carotid plaque by near-IR spectrometry (nc=23 calibration plaques, nv=21 validation plaques). The precision of near-IR spectrometry appears to be limited by the extraction /ultracentrifugation/gel electrophoresis reference method. Go back to text
Fig. 10. The significant correlations (p<0.05) between near-IR spectra of carotid plaque and medical history is shown in the white bars. The lipoproteins were determined by extraction, ultracentrifugation, and denaturing gel electrophoresis. The variation shown in the black bars is calculated from principal component analysis of the near-IR spectra. Go back to text
Fig. 11. An InSb camera with Ge/Si lens, iris, optical window for retaining dewar vacuum, and baffles removed to expose the detector array. A modified baffle system that puts direct pressure on the InSb wafer, forcing it back into the Si CMOS multiplexer, can restore response from dead pixels. Go back to text
Fig. 12. The response of different optical materials to an applied electric field varies with field strength and molecular structure. Go back to text
Fig. 13. Two antirotating potassium titanyl phosphate (KTP) crystals comprise an optical parametric amplifier (OPA) when pumped by a Nd:YAG fundamental at 1064 nm and injected collinearly with an idler beam from an optical parametric oscillator (OPO) with output from 1450-2120 nm. Go back to text
Fig. 14. The output of the solid state laser contains both signal (1450-2120 nm) and idler (2120- 4000 nm) photons that can be separated with a prism. The beams in the picture, from left to right, are the 532 nm pump for the OPO, the 1064 nm pump for the OPA, and the combined signal and idler from the OPA. Go back to text
Fig. 15. The BEST metric makes no assumptions about the shape or skew of spectral point clusters in d-dimensional hyperspace, and thus can be used to accurately describe the spectral point distributions of biological samples (d = the number of wavlengths recorded in the spectrum). One BEST standard deviation is defined as a central 68% confidence interval, much like a parametric multidimensional standard deviation, but a BEST SD can be asymmetric. The hyperline along which the SD is calculated connects the test sample spectral point and the center of the calibration spectral points. Go back to text
Fig. 16. Time in seconds to complete the individual routines of the BEST algorithm after parallelization across 8 processors. The assimilation problem was calibration and complete leave-one-out cross validation of n=100 samples with spectra at d=100 wavelengths. Note that the bootstrapping procedure (REPLICA) consumes the vast majority of processing time and so became the focus of parallelization efforts. The execution time of the REPLICA routine dropped from nearly 21 seconds on a single CPU to less than 1.6 seconds on 8 CPUs. Go back to text
Fig. 17. The execution time of a fairly large assimilation problem (1000 samples scanned at 1000 wavelengths with 10,000 bootstrap replications, executed 1000 times during leave-one-out cross validation) improves almost linearly with increasing numbers of processors. Go back to text
Fig. 18. A demonstration of the effect of the assimilation problem size (number of calibration samples and number of replicates) on execution time. A calibration set of 100 samples and 100 wavelengths and 1000 replicates was used as data set A and represents an execution time of 1.0. Data set B is the same with the number of samples increased by an order of magnitude. Data set C has the number of wavelengths increased by an order of magnitude. Data set D has the number of replicates increased by an order of magnitude. Go back to text Return to Cover
