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Density Measurement

Contents

The Nature of Density

Transmittance, Opacity and Density

Diffuse, Specular, and Optical Density

Gray Levels and RODs

Valid Density Measurements

Calibrating Optical Density Values

Semiquantitative Densitometry

Strategies for Semiquantitative Densitometry

Issues in Normalization

Quantitative Densitometry

Density Standards

Interpolation or Approximation

Calculating the Density Value

Limitations in Densitometric Imaging

The Clipping Problem

Extrapolation

Appendix: Densitometric Applications

Receptor Analysis

Total, Nonspecific, and Specific Binding

Autoradiographic Measurement of Rates of CGU, CPS, and CBF

Cerebral Glucose Utilization

Cerebral Protein Synthesis

Blood Flow

References

 


The Nature of Density

Transmittance, Opacity and Density

Incident illumination is light falling on a specimen. Transmittance (light passed through) and reflectance (light reflected) are measurements of the proportion of incident illumination which is obtained from the specimen (equations 1 and 1b).

 

 

Reflectance can be useful in making targets visible. For example, it is reflectance that makes silver grains stand out in dark field illumination. Reflectance can also be used in quantifying opaque specimens, such as some electrophoregrams. However, transmittance measurements are far more common in life science densitometry.

Transmittance decreases as the specimen absorbs more of the incident illumination. For example, our illumination level is 200 units, and a specimen placed between the light source and the sensor reads at 100 units. The transmittance is 0.5. A darker specimen might read 50 units, yielding a transmittance of 0.25. When darker specimens are more heavily labeled (e.g. autoradiography, immunocytochemistry), we could transform transmittance (or reflectance) to opacity (equation 2). As the absorption of the specimen increases (and the amount of label increases), opacity rises.

 

 

Density (equation 3, the common logarithm of opacity) is often preferred to transmittance, reflectance or opacity. Like opacity, density increases as the specimen darkens. Density has the additional advantage that it accords with our perceptual judgments of how dark a specimen is. In making a visual judgment, you would tend to describe a density of 1.0 as being about twice as dark as a density of 0.5.

 

 

Density values (Table 1) found in typical film autoradiographs of brain sections vary from close to 0 (100% transmission) to about 1.2D (6% transmission). Imaging plates, stained gels, and any opaque specimens (e.g. membranes) can exhibit a much broader range of densities, with some specimens going beyond 2D (1% transmission).

Table 1: Optical density and transmission values across a range spanning most biological specimens. By about 1.2 density units, film becomes saturated. Stained or opaque specimens can exhibit a much broader range of densities.

Density

% Transmission

 

Density

%Transmission

0.00

100.00

 

1.00

10.00

0.01

97.72

 

1.20

6.31

0.05

89.13

 

1.40

3.98

0.10

79.43

 

1.60

2.51

0.15

70.79

 

1.80

1.58

0.20

63.10

 

2.00

1.00

0.30

50.12

 

2.20

0.63

0.40

39.81

 

2.40

0.40

0.50

31.62

 

2.60

0.25

0.60

25.12

 

2.80

0.16

0.80

15.85

 

3.00

0.10

 

Diffuse, Specular, and Optical Density

From our definitions, above, density is a proportion of incident to transmitted (or reflected) illumination. Theoretically, a given specimen should always yield the same proportion of incident to transmitted illumination. Unfortunately, the situation is not as simple as this. For a given specimen, a density value is only replicable under tightly controlled measurement conditions. Different density values are observed as the conditions of illumination or the densitometer characteristics are changed. The problem of variable density arises from the many factors that affect the way in which light passes from the light source, through the specimen, and into the densitometer. In the real world, these factors are not easily controlled.

To illustrate the difficulty in making real world measurements, consider the way in which a density reference standard (used for the calibration of densitometers) is made. Density reference standards are composed of a transparent matrix (e.g. celluloid, glass) containing various amounts of light-absorbing materials. The light-absorbing materials (e.g. carbon granules) are selected to maintain constant properties of absorption and reflectance across a broad range of illumination intensities. During calibration, the standard is evenly illuminated over an angle of 180 degrees. Both the amount of incident illumination and the illumination passing through the standard are measured, each over a collection angle of 180 degrees. The sensing element is a simple photometer, that responds linearly to a very wide range of illumination intensities. When a ratio of transmitted to incident illumination is taken under these conditions, the result is a parameter termed diffuse density. A diffuse density value will be constant across a range of illumination intensities, and from densitometer to densitometer -- as long as the measurement conditions are appropriate (180 degree illumination and collection, etc.).

With most biological specimens, it is impossible to control diffusion properties. Also, an image-forming optical system contains lenses which collect light over some angle, and not all of the light passing through the specimen lies within that angle. Light transmitted directly through the specimen reaches the sensor, while scattered light lies beyond the collection angle of the lens and does not contribute to the density measurement. This is quite a different situation from the hemispherical collection required for diffuse density measurements.

The measurement of light from an angle of collection yields a parameter termed specular density. The specular density of a specimen will depend upon the lens formulation, f-stop, and distance from the specimen, and will always differ somewhat from a diffuse density.

Density is also affected by components of the optical chain (e.g. the surface of a glass slide) that reflect or scatter the incident light, and by the response properties (deviations from linear response) of our density sensor. For all of these reasons, the measurement of diffuse density is usually impossible. Instead, we can read optical density (OD). An OD measurement is specular (does not require 180 degree illumination and collection angles), and does not assume diffuse specimens. Rather, OD is just the log of the ratio of transmitted to incident illumination. Under perfect measurement conditions OD will correspond to diffuse density. More often, the OD will vary somewhat from the value that would be read under perfect conditions. Therefore, the OD of a given specimen can vary from densitometer to densitometer, as the measurement conditions (e.g. the angle of collection) vary.

Consider OD as a somewhat relaxed form of density measurement. The measured OD of a given specimen can vary somewhat between instruments, but should remain constant for any one instrument. To achieve internal measurement consistency, most scanning densitometers contain an internal density standard. During the scan, this internal standard is used as a reference and to ensure linear response. That is why you can use a scanning densitometer without having to perform a calibration to external density standards. The calibration is performed within the instrument.

In contrast, cameras cannot be calibrated internally, because there is no practical way to measure both incident and transmitted illumination (though attempts have been made). To obtain replicable camera density measurements, we must calibrate to an external standard. The external calibration step makes the use of cameras slightly more complicated than the use of internally calibrated devices. However, the end result is that consistent OD measurements are available from cameras.

Gray Levels and RODs

Incident light induces a voltage in the density sensor. Light that is below the sensitivity threshold of the sensor induces a voltage that cannot be discriminated from internally generated noise. Light that is too bright will saturate the sensor. Between these extremes is a range of incident illumination that will affect the voltage output of the sensor in a usable fashion. This is the dynamic range of the sensor.

In an analog system, the dynamic range is displayed on a voltage meter. Higher levels of incident illumination cause greater deflections of the indicator. In a digital system, illumination-induced voltage is displayed numerically. Before this can be done, the dynamic range must be broken (digitized) into discrete steps. Imaging systems contain a digitizer, which digitizes the sensor's voltage output range into discrete steps or levels. Each of these levels corresponds to a shade of gray in the image. Therefore, the steps are termed gray levels.

Although 8-bit (256 gray level) density resolution is by far the most common, some imaging systems (MCIDTM and AISTM included) can work with data at greater bit densities. High bit densities are critical when using scanning imagers, imaging plate readers, and cooled CCD cameras. Most of these instruments provide up to 16-bit (65,536 gray levels) digital data to take advantage of their broad dynamic range. For a detailed discussion of dynamic range, see the "Cameras and Scanners" chapter.

If the amount of incident illumination can be precisely quantified, we can measure both incident and transmitted illumination in gray levels, and then create an optical density ratio as described in equation 3. Measurements of incident illumination are possible in systems that pass a beam of coherent or highly collimated light over the specimen (scanning densitometers). However, incident illumination measurements are not practical in camera-based systems, which illuminate the specimen with diffuse light. Therefore, camera-based image analyzers start with uncalibrated gray levels. These can be used, directly, or are converted to uncalibrated transmittance or density values.

Gray level transmittance or reflectance (GLT or GLR) can be measured as follows (equation 4):

 

 

Gray level transmittance or reflectance go up as brightness increases. Therefore, we usually prefer to convert GLT or GLR to relative optical densities (ROD) as follows (equation 5):

 

 

Note that, in using GLT, GLR, or ROD, specimen density values are referenced to the dynamic range of the imaging system, and not to any external reference. Therefore, a GLT, GLR, or ROD value tells us very little about the OD which would be measured by a densitometer. With a camera, there is no measurement of incident illumination, so a given specimen may yield a ROD value of 0.5 under one set of lighting conditions, and 0.8 under different conditions.

To summarize, camera-based imaging systems express density (levels, GLT, GLR, and ROD) as purely relative values, reflecting only a ratio of incident illumination to maximum system response. In addition to changing with any alteration in the lighting conditions, the relative values are affected by nonlinearities in any component of the measurement chain. For these reasons, camera-based imaging systems require external calibration if stable and replicable density measurements are to be obtained.

Valid Density Measurements

The history of biological densitometry is a record of attempts to improve both the validity and efficiency (speed, convenience) of density measurements. Early systems used spot (Bryan and Kutyna, 1983; Haas, Robertson and Myers, 1978; Reivich, et al., 1969) or computer-controlled scanning spot (Goochee, Rasband and Sokoloff, 1980; Leitz DADS) densitometers. These systems were often quite precise, but were very slow and tedious to use. Today, scanning laser densitometers have replaced most of the earlier scanner-based systems. Scanning laser densitometers are nicely packaged (smaller, faster, cheaper, and more reliable than the old scanners), yield highly replicable OD values (incident illumination is measured), and are linear. These systems provide reliable density values across a wide range of staining intensities, reaction product densities, or autoradiographic exposures. However, they are slow and tedious to use. They also use a scanning beam that is relatively large (e.g. 50 m m), so they are not suitable for small specimens (e.g. microscopic sections, rodent brain autoradiographs).

Camera-based systems are very attractive because they are much faster than laser densitometers, and can digitize an entire specimen in a fraction of a second. They can also be used with small specimens (using lenses to magnify). However, cameras lack the wide linear dynamic range of scanners. Under bright field conditions (the situation is different at low light levels), the high densities (above about 1D) are compressed. The higher the actual density, the more nonlinear is the camera's response. This characteristic results from physical and electronic properties inherent to the camera, and from optical aberrations (flare). Unlike collimated or coherent beam scanning systems, the camera-based system is illuminating and acquiring large areas of the specimen simultaneously. Therefore, it is subject to flare (internal reflections within the lens and scattered light that does not pass through the specimen).

With the limitation in dynamic range understood, and with a reasonable amount of care, a camera-based imaging densitometer can yield highly accurate density measurements. At the very least, the camera-based system must be proven to be linear prior to use. That is, the sensitivity of the camera (the ability to discriminate between shades of gray) must be constant across the density measurement range found in the specimens. This linearity can be demonstrated by calibrating the system, as discussed in the next section.

Calibrating Optical Density Values

Optical density values must be replicable. That is, a particular image analyzer should always report the same OD values for a given specimen. However, a camera-based system does not measure both incident and transmitted illumination to form an OD ratio, and the camera may be responding nonlinearly. That is, it is more sensitive in some parts of its range than in others. For these reasons, camera-based density measurements are unlikely to replicate without external calibration.

For example, labeled spinal cord cells contralateral to a cortical lesion transmit 64/256 gray levels (GLT = 0.25), while labeled cells ipsilateral to the lesion transmit 128/256 gray levels (GLT = 0.5). We would wish this relation between the two sides of our specimen (one side yields twice the density value of other) to be dependent upon treatment condition, not upon illumination intensity. Similarly, in analyzing gels and blots, it is important that the difference between the peak density of a band and the baseline density reflect only the amount of substance, not the illumination level of the specimen. Without external calibration, we would probably find that the density characteristics of our specimens (ipsilateral vs. contralateral cells, peak vs. baseline) change as illumination changes.

What type of external calibration should be used? At minimum, a calibration to diffuse density standards can establish that our optical density measurements are linear. Once an external calibration is established, the camera-based densitometer is yielding OD (as opposed to ROD) values (e.g. Baskin and Wimpey, 1989). The calibrated OD values are corrected for nonlinearity, and should be the same as those obtained by measuring both incident and transmitted illumination. That is, they should be precisely replicable.

A better way to perform external calibration is to use concentration standards. After all, we are trying to use OD as an operational definition of tissue properties (binding levels, metabolic rate, etc.). However, even the most rigorously measured OD has no intrinsic biological meaning. In contrast, calibration to concentration standards defines a relation between ROD (the image analyzer's uncalibrated measurement scale) and tissue properties.

Calibration to external standards is usually possible at the macro level. Large density step tablets and concentration standards are available and easily used. At the micro level, density calibration is more problematic. Microscopic density references are not easily obtained, though we have some of these available. Even with microscopic density standards, the complex optics of microscopes do not lend themselves to precise calibration. For these reasons, microscope densitometry is often performed without external calibration. The best you can do is to establish that the imaging system is linear across the range of illumination intensities seen through the microscope. Linearity should be documented with any report of uncalibrated density values (Table 2).

 

Table 2: Conditions for reading density.

Procedure Instrument Replicability
Internal calibration Scanning densitometer, phosphor plate imager, other types of scanner high
No calibration Camera, simple densitometer very low
External calibration to diffuse density standards Camera, or any without internal calibration high - assumptions must be made about biological relevance
External calibration to concentration standards Camera, or any without internal calibration high - direct measurement of biologically relevant data

 

Semiquantitative Densitometry

In semiquantitative densitometry, we make density measurements without calibrating the system to a range of concentration standards. As commonly used, semiquantitative densities demonstrate regions in which a target molecule is localized. At best, densities obtained with semiquantitative methods are proportional to the amount of the target molecule. Without a standard curve, however, the relation between the concentration of the target molecule and the tissue density cannot be known. In semiquantitative densitometry, our first goal is to obtain replicable and sensitive measurements which reflect (but do not quantify) tissue biology.

Strategies for Semiquantitative Densitometry

High levels of error variance can result from unpredictable influences of exposure, incubation, development, etc. Ideally, we would minimize these problems by calibrating to concentration standards. Even without calibration, however, error variance can be minimized to yield more sensitive experiments. A few strategies are given below.

Use tightly controlled conditions (e.g. Brown and Fishman, 1990)

The specimen processing, lighting, and sensing conditions are exactly the same for all readings. This approach is very prone to error, as many irrelevant and subtle factors (especially those associated with tissue processing) can affect the density of specimens.

Normalization

Uncalibrated densities are normalized to an internal standard and inter-condition comparisons are formed from the resulting ratios. Theoretically, the normalization process removes contributions of non-specific density variation (e.g. background density) from the ratio data. Therefore, it is the ratios, as opposed to the absolute density values, that are used for group comparisons (e.g. Burke et al., 1990; King et al., 1989; Reis, et al., 1982). It is important that linear system response be demonstrated, if normalization is to yield replicable ratios.

Normalization and tight control

It is often possible to combine minimization of processing-induced variation with normalization. For example, brain hemispheres from experimental and control conditions could be glued together before sectioning, processing, and side-to-side ratio formation (Tatton and Greenwood, 1991).

Issues in Normalization

In quantifying reaction product (e.g. immunostaining), a within-section reference provides the best control for extraneous influences. An example would be reaction product density in cells ipsilateral vs. contralateral to a treatment (e.g. Garrison, Dougherty and Carlton, 1993; Mize and Luo, 1992). In whole body autoradiography, the blood is often used as a reference. In semi-quantitative brain autoradiography, each regional density could be normalized to the mean density of the entire brain (e.g. Ramm and Frost, 1983, 1986).

Try to ensure that specimen preparation, illumination intensity, label density, and other conditions are held as constant as possible across specimens. The density of the reference region should be highly sensitive to irrelevant factors, such as development and exposure, but insensitive to the independent variable. This can be easily tested by comparing density values of the reference region across exposure/processing conditions (irrelevant variables), and across treatment conditions. We want to observe a significant relation between irrelevant variables and our reference density. In contrast, we should fail to observe a relation between the reference density and the treatment conditions of our experiment.

Normalization to an internal reference would, theoretically, allow us to obtain the same value from a given target each time we measure it. However, this is only true if the system density response is linear across the entire range of measurements. Any nonlinearities will affect the ratio between our reference and target regions. As a precondition of semiquantitative densitometry, both the reference and target values must fall within the linear response range, and it should be shown that system response was linear over the entire measurement range used in the experiment. This set of conditions should be achieved automatically, with most internally calibrated scanners. Cameras and other devices without internal calibration should be calibrated to a set of density standards, before reading data.

 

Quantitative Densitometry

Quantitative densitometry is performed by calibrating to a set of concentration standards before reading density values in the unit of calibration. The most common form of quantitative densitometry is isotope autoradiography, using radioisotope standards exposed with each film to establish a standard curve. Attempts have also been made to perform fully quantitative immunocytochemistry using biochemical calibration of staining intensity (e.g. Benno et al., 1982; Laborde et al., 1990; Reis et al., 1982), antigen concentration standards (Nabors, Songu-Mize and Mize 1988; Huang, Chen and Tietz, 1996), or chemiluminescence (Norman, Khosla, Klug and Thompson, 1994). However, quantitative immunocytochemistry remains relatively rare, because of the difficulties involved in establishing the exact relation between tissue densities and the amount of the target molecule.

MCID and AIS offer very flexible functions for quantitative densitometry. The systems may be calibrated to any standards. They also incorporate operational equations for the conversion of calibrated density values to rates of local cerebral glucose utilization, protein synthesis, or blood flow.

Density Standards

A good density calibration provides a ratio scale (a scale with fixed 0 point and equal step intervals), and allows the reading of density values in units of concentration. Calibration creates a table of ROD values paired with the concentration values of the standards. The table should span the entire range of densities found in the specimen (see the left side, Figure 1).

Figure 1: An AIS screen, showing a calibration to 14C standards (Amersham Microscales) exposed on autoradiographic film. The calibrated values of the standards are shown at left, under "Std. Value". The relative optical density values seen by the system are shown under "Value Read". The graph, at right, shows the relation between relative optical density and the calibrated values. A smoothed cubic spline function has been used to interpolate between the standard values.

 

Interpolation or Approximation

We use interpolation or approximation to calculate density values which lie between the steps provided by the calibration reference. MCID and AIS offer a variety of methods for fitting interpolation or approximation functions to the calibration values. A graph shows how well a selected fitting function fits the concentration values of the reference. A numerical estimate of goodness of fit is available from the last column in the calibration table (under Rel. Error in the above example). With any good fit, the error proportions will be low.

Calculating the Density Value

In reading from a photometer, the entire sensor area is integrated to yield a single voltage. This voltage is compared with the calibration table to yield a single concentration value. This is termed the integrated optical density (IOD) of the specimen. In an imaging system, this is equivalent to taking the mean gray level values of all the pixels in a sample window, and then converting this single mean gray level value to a concentration.

Gray level IOD: Calculate mean gray level value, then convert to concentration.

 

In a sample window taken with an imaging system, we have a great deal more information than is available from a photometer window. Instead of just a single voltage, we have discrete density values for each of the pixels within the window. Therefore, we can calculate discrete concentration values by comparing each pixel with the calibration table. Only after all of the pixels have been converted to concentrations do we calculate the mean of the sample window.

Concentration IOD: Convert each pixel to a concentration value, then calculate the mean.

 

 

The concentration IOD is usually preferable, for the following reasons.

1. Use all available information

In any group of pixels, some may fall within the non-linear portion of the calibration. For example, we have a calibration table as follows:

 

Gray levels Concentration (nCi/g)

10 100

15 50

20 45

35 10

 

Let us create a sample window with four pixels, one each of 10, 15, 20 and 35 gray levels. The mean of this window is 10 + 15 + 20 + 35 / 4 = 20 gray levels. We look up 20 gray levels in our calibration table and obtain a concentration for the window of 45 nCi/g. Now compare what happens when we look up each pixel in the calibration table before taking the mean. The result is 100 + 50 + 45 + 10 / 4 = 51.25 nCi/g. The difference results from nonlinearities in the relation between gray levels and concentration.

A simple mean of gray levels ignores what we know about calibration linearity. Therefore, the concentrations calculated from a mean of gray levels and from discrete pixel concentrations will differ by increasing amounts as the proportion of nonlinear pixels in the sample window increases.

2. Requirement for operations using single pixel quantities

Imaging systems offer many ways to manipulate discrete pixel data. For example, we could work with only those pixels representing a given range of concentrations, or we could check for multiple receptor populations by examining a histogram showing the distribution of concentration values within a sample window. It is important that the data obtained from such discrete pixel operations be equivalent to the data obtained from the integration of pixels. This is only possible if the IOD(c) is used.

3. Multi-image operations using single pixel quantities

Many multi-image procedures require that pixel-by-pixel calculations be performed using concentrations. Examples are creation of a specific binding image by subtracting non-specific from total binding, or combining pixels across a series of concentration images to yield images of Kd or Bmax (e.g. Toga, Santori and Samaie, 1986). These are termed derived images, as they are calculated from other images. Imagine that we are sampling data from a derived image. The values obtained should be exactly the same as if we were to sample the data from the original images, and then pass those data through the calculations used in creating the derived image. This equivalence is only possible if the IOD(c) is used.

The IOD(c) cannot be used when there is extreme nonlinearity in the calibration. In measuring cerebral blood flow, for example, gray level values are linearly related to flow values up to a point. They then become very nonlinear, so that a small change in gray level can represent a very large change in flow rate. Under these conditions, it would be possible for single pixels to have fairly wild flow rates, and to exert an unreasonable inlfuence on the flow rate values obtained from a sample window. Therefore, MCID/AIS calculate a mean gray level for the entire sample window, before doing a flow rate calculation.

 

Limitations in Densitometric Imaging

Limiting factors for densitometric accuracy originate within the imaging system, and within the specimen. The following discussion summarizes some of the major limitations.

System-generated random noise

Cameras and digitizers exhibit a certain amount of random noise, seen as changes in single pixel density values on successive image acquisitions. This noise is minimized by the use of high quality cameras, and by image processing (frame and spatial averaging).

Limited digital precision

Many imaging systems offer only 8-bit/pixel depth. That is, they represent the entire range of densities with 256 gray levels. This yields a best possible sensitivity (limited by the Nyquist criterion) of one part in 128. This may not be a major problem with receptor autoradiography of brain sections. In receptor binding analysis, ligand concentrations and film exposures can usually be adjusted so that specimens occupy a fairly narrow range (less than about 1 OD unit) of densities, and one part in 128 may be sufficient within this narrow range. However, many specimens (e.g. whole body and gel autorads, fluorescent materials) contain a broader range of densities. This is especially true when the imaging system is interfaced to devices such as digital cameras, scanning densitometers and imaging plate readers. Under these conditions, a precision of one part in 128 becomes a severe limitation, and much greater sensitivity is required. MCID and AIS offer up to 16-bits/pixel (64K gray levels).

Limited dynamic range

Dynamic range limitations are most evident with film. Imaging plate readers, fluorescence imagers, and other scanner types tend to offer a broader dynamic range.

Film is most accurate when exposed to medium density. With overexposure, the film compresses its response so that sensitivity (ability to discriminate variation in concentration) becomes very low. With very light exposures, it is common for variations in film background to be larger than effects of interest. Therefore, reading from over- or underexposed regions is dangerous.

Film or plate noise

There are random variations from place to place on the specimen medium. At macro-level magnifications, the imaging plates or fast films used for quantitative autoradiography may exhibit variations of more than 20% from pixel to pixel. This noise results primarily from random variations in grain structure, and is exacerbated at high magnifications, with high speed films, or with phosphor plates.

Random density variations are minimized by using film with the lowest possible grain, at the sacrifice of exposure speed. For example, Kodak’s TL or OM film is much finer in grain, lower in noise, and slower than SB film. The problem is also minimized by reading from larger regions (Ramm et al., 1984). Theoretically, noise decreases as the square root of the number of pixels. Assuming only random grain noise, we could read from 25 pixels and obtain film noise of about 1/5 the single pixel value. This is termed "spatial averaging". We recommend a combination of frame averaging to reduce noise originating within the imaging system, and spatial averaging to reduce noise originating within the film or plate.

Systematic Background Variation

Non-random variations in background density are common. Background adjacent to specimens is often slightly different than that adjacent to the standards, and background at the media edges may differ from background at other points (a sign of poor processing or exposure conditions). These types of non-random variations cannot be corrected and, without great care in specimen preparation, these variations tend to limit the accuracy of background calibration to within a few gray percent. Therefore, there is a good chance that readings of data that lie within a few percent of background (e.g. very light non-specific binding) will be inaccurate.

The Clipping Problem

During calibration to the lightest reference standard, we encounter a range of pixel values. For example, in reading film background as a 0 concentration reference, we might obtain values from .01 - .10 ROD, normally distributed about a mean value of .06 ROD (Figure 2).

Figure 2: Histogram of pixel density values in a region of film background. The mean is .058 ROD, shown by a line at the center of the histogram. The second set of vertical lines is at one standard deviation.

 

 

In calibrating to background, we use the mean density for the pixels in the above histogram. Now, whenever the system sees a pixel of .058 ROD, it will know that its concentration is 0. But a sample window will contain pixels that are lighter than .058 ROD. What do we do with those pixels?

The simplest approach is to set pixels that are lighter than the mean background value to the mean background value. The same strategy could be used at the maximum limit of the calibration. Those pixels that are darker than the maximum calibrated ROD value are set to the maximum. This approach to extreme values is termed "clipping" (Figure 3).

Figure 3: Histogram of calibrated pixel values from film background. During calibration, film background (concentration 0 nCi/g) had a ROD value of .058. When we then read data from film background, some of the pixel values fall below .058 ROD, the 0 concentration reference. These values have been adjusted upwards, or "clipped" to 0, resulting in a large peak at 0. Because we have adjusted the value of some pixels upwards, our mean density value for this sample window now overestimates its true density.

 

 

The consequence of clipping is that readings taken from regions at the light limit will tend to overestimate concentration. We are selectively increasing the values of those pixels which lie below the calibration limit. Similarly, readings taken from regions approaching the high concentration reference will tend to underestimate the true concentration. We are selectively decreasing those pixels which lie above the calibration limit.

Avoid exposing specimens to the point that regions of interest approach the minimum or maximum calibrated density. With care, clipping-induced errors will be minimal. However, rather large clipping errors can occur if the pixel noise is high in our images (Figure 4) and/or if we attempt to work with image data that lie very close to our calibration limits. Under these conditions, a considerable proportion of pixels will lie beyond the calibration limits. As a consequence of clipping these pixels, the concentration values that we obtain from the imaging system can differ between media (different films, phosphor plates), and will also differ from the gold standard of liquid scintillation counting.

Figure 4: Histograms of film background taken from a relatively low noise specimen (left, Hyperfilm imaged with a Xillix digital camera), and (right) from a Fuji BAS 3000 phosphor plate imager with much higher noise. Note that the film values are distributed within about 20 fmol of the zero point, while the BAS range from about -45 fmol to about 100 fmol. Clipping the BAS data will have a greater effect than clipping the film data. This could cause density values obtained from the two technologies to differ.

 

 

 

 

 

Recognizing that real-world images are often noisy, or contain very light and very dark data, we must implement some procedure that minimizes the effects of clipping. The simplest approach is to warn the user, so that any windows containing clipped data can be regarded with caution. MCID/AIS warn (by showing the density value in red) whenever pixel values in a sample window extend beyond the calibration limits.

Extrapolation

Beyond simply warning that the data in a window are suspect, there are things we can do to minimize the effects of poor data upon densitometric accuracy. Extrapolation is extension of the calibration function beyond the calibration limits. Pixels that are lighter than the lower calibration limit will be assigned a negative concentration value. Pixels that are darker than the maximum calibration value will be assigned values higher than the maximum calibration value. The use of extrapolation makes the value obtained from a poor specimen more closely approach the concentration value that would be obtained from a liquid scintillation counter. It also minimizes the differences observed when the same specimen is exposed on media with different noise properties.

MCID and AIS allow clipping, or various forms of extrapolation. Selection of extrapolation is up to you. If you choose to extrapolate at the low extreme, pixels lighter than the zero concentration reference will be assigned negative values during the calculation of the sample window mean. If you extrapolate at the high end, pixels darker than the maximum concentration reference will be given higher values estimated by the extrapolation function. In our experience, extrapolation works much better than clipping (Table 3).

Table 3: Comparison of the effects of clipping and extrapolation upon density values obtained from two different imaging technologies (film and phosphor plate). A set of calibrated Amersham 3H Microscales were exposed to Hyperfilm (3 weeks) and to a Fuji BAS 3000 phosphor plate imager (4 days). Although the two imaging technologies are very different (film is low noise, high resolution, narrow dynamic range vs. plate is noisier, low-medium resolution, broad dynamic range), we would like to obtain similar results so that we can select an appropriate imaging medium for specific tasks.

MCID was calibrated to images of the concentration standards, and was then used to read from the minimum and maximum standards. Note that the extrapolated concentration reading is better with both the film and plate technology. Also, the film and plate do not match each other, unless extrapolation is used.

  Concentration standard

(fmol/mg)

Clipped reading Extrapolated reading
Hyperfilm 0 2.2 0.1
  769.2 768.8 769.3
BAS3000 0 8.9 1.1
  769.2 745.32 769.2

 

Appendix: Densitometric Applications

Receptor Analysis

MCID is by far the most popular image analyzer in receptor analysis applications, both because of its proven densitometric accuracy and because of the many specialized functions that it includes. For example, there are many ways in which total and nonspecific binding sections can be aligned with each other, and with stained sections. Then all binding parameters can be read with a single operation.

Total, Nonspecific, and Specific Binding

To obtain specific binding, we have to subtract nonspecific binding from total binding. MCID/AIS offer an extensive set of image alignment functions, which are used to register the total and nonspecific binding images. Once the images are in register, there are two ways to generate specific binding data.

Unless we are creating presentation images of specific binding (slides, publication), we often prefer to use numerical analysis. The image formation process requires subtraction of the nonspecific binding image, and this subtraction is subject to clipping and round-off errors. In contrast, numerical analysis allows extrapolation to operate during density calculation, yielding higher precision. The data are presented as total, nonspecific, specific, and percent specific binding for each region of interest (Figure 5).

Figure 5: Arrangement of data in the receptor study mode.

 

Autoradiographic Measurement of Rates of CGU, CPS, and CBF

In reading rates of glucose utilization, protein synthesis, or blood flow, an initial calibrated density value is passed through an operational equation before being reported as a rate at which some physiological process is occurring. Solution of an operational equation requires that data regarding plasma LSC counts and/or other data be entered into the system.

Cerebral Glucose Utilization

CGU is calculated using Sokoloff's (Sokoloff et al., 1977) original operational equation (Equation 6), or the Savaki (Savaki et al., 1980) modification (Equation 7). The Savaki equation should be used when plasma glucose concentrations vary considerably during the experiment (within a range of about 70 - 250 mg%), especially when the animal becomes progressively hyperglycemic. Keep in mind that the lumped constant changes, increasing in hypoglycemia and decreasing in hyperglycemia (Schuier et al., 1990; Suda et al., 1990).

 

Equation 6: Sokoloff's original operational equation for CGU.

 

 

 

Equation 7: Modified operational equation for CGU.

 

 

Ri is the rate of glucose utilization. T is the time at the termination of the experimental period. Ci* is the total 14C concentration in a single homogeneous tissue of the brain. Cp* and Cp represent the concentrations of [14C]deoxyglucose and glucose in the arterial plasma. l is the ratio of the distribution space of deoxyglucose in the tissue to that of glucose. f is the fraction of glucose which, once phosphorylated, continues down the glycolytic pathway. Km*, Vm*, and Km, Vm, represent the Michaelis-Menten kinetic constants of hexokinase for deoxyglucose and glucose, respectively. The six constants collectively constitute the lumped constant. The solution is presented as follows (Figure 6).

Figure 6: A screen from the MCID program, showing a solution for the CGU operational equation.

 

Changes can be made to any terms in the CGU equation, by entering new values into any portion of the solution screen. For example, the lumped constant is very sensitive to the plasma glucose level and should be modified if hypo or hyperglycemia is present. Enter any relevant changes to the default constants, and press Calculate to re-solve the equation. It is also possible to skip the accessory file entirely, and type in precalculated values for the tissue integrals.

Cerebral Protein Synthesis

Protein synthesis is measured using the autoradiographic [1-14C]leucine method. The procedure is exactly as given for LCGU, above. The method has evolved through various forms (Smith et al., 1980; Ingvar et al., 1985; Smith, 1991). The present form of the operational equation (Equation 8, Smith, 1991) assumes that sections have been washed by repeated immersion in buffered formalin before autoradiography.

Earlier forms of the equation (Ingvar et al., 1985) did not account for reflux of labeled leucine into the precursor pool. This reflux has been shown to occur (Smith et al., 1988). Therefore, the earlier forms of the equation underestimated actual rates of protein synthesis. The most recent form of the leucine operational equation yields values considerably higher than those obtained with the previous equation.

 

Equation 8: Operational equation for measurement of rates of cerebral protein synthesis

 

Ri equals the rate of reaction in tissue i. Pi* (T) is the concentration of labeled leucine incorporated into protein in tissue i during the experimental period (T). This is measured from the washed autoradiographs. The factor li is composed of rate constants and varies from tissue to tissue. Smith (1991) has used a value of .58 for li. Cp and Cp* represent the concentrations of free leucine and [1-14C]leucine, respectively, in arterial plasma.

Blood Flow

1. Capillary blood flow, indicator fractionation

This is a variation of the method introduced by Goldman and Sapirstein (1973). The procedure requires calibration to nCi/g. The withdrawal rate (arterial flow rate in your pump) and LSC counts are taken from an accessory file.

 

Equation 9: Operational equation for indicator fractionation blood flow.

 

The regional rate of blood flow is FB. A(T) is the amount of indicator per unit weight of tissue at time T. WR is the withdrawal rate of your arterial pump. CP is the plasma mean 14C value, across all the sets, calculated as below (equation 10).

 

Equation 10: Calculation of the mean plasma 14C value for indicator fractionation blood flow.

where n: the number of batches

mi: the number of LSC samples for the ith batch

LSCij: the jth LSC sample for the ith batch

bkdi: the background value for the ith batch

 

2. Capillary blood flow, tissue equilibration (Sakurada)

Calculation of cerebral blood flow by the tissue equilibration method is shown (Equation 11, Sakurada et al., 1978). Calibration is to nCi/g or to dpm/g. An accessory file contains times (seconds), sample volume (ul) or weight of filter paper, washout correction factor (/min), and LSC counts (DPM).

 

Equation 11: Operational equation for tissue equilibration blood flow.

 

A(T) is the amount of indicator per unit weight of tissue at time T. l is the estimated equilibrium tissue-blood partition coefficient of the indicator. F is the actual rate of blood flow per unit weight of tissue. Ca(t) is the concentration of indicator in the arterial blood perfusing a tissue at the time t, and T is the time at the end of the experimental period.

3. Capillary blood flow, tissue equilibration (Modified)

This modified form of the Sakurada equation (for details see Jay et al., J. Cereb. Blood Flow Metab. 8:p 124-125, 1988) applies a correction for the distortion of the arterial input function in the catheter.

 

Equation 12: Modified operational equation for tissue equilibration blood flow.

 

where Ci(T) is the tissue concentration of the tracer at a given time, T, after its introduction into the circulation at zero time; C'a is the measured concentration of the tracer in the arterial blood sampled from the distal end of the catheter; l is the tissue/blood partition coefficient for the tracer; r is the rate constant for the monoexponential washout of the catheter dead space; t is the variable time after correction for the transit time through the catheter; and K is a constant that incorporates within it the rate of blood flow in the tissue. The constant K is defined as follows:

where F/W equals the rate of flow per unit mass of tissue; l is the tissue/blood partition coefficient for the tracer; and m is a constant between 0 and 1 representing the extent to which diffusion equilibrium between the blood and tissue is achieved during passage from the arterial to the venous end of the catheter. We use m = 1.

 

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