Chapter 1. Use of Computer-Assisted Tomography in Studying Water Movement around Plant Roots
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L. A. G. AYLMORE
I. INTRODUCTION
An appreciation of the physical, chemical, and biological factors determining the supply, availability, and movement of water in soil/plant ecosystems, together with suitable techniques for the measurement of the
forces involved, is essential to the development of an understanding of the
mechanisms and dynamics of water movement in soils and their biological
implications. The importance of this field of study cannot be overemphasized, particularly in semiarid and saline environments, where the availability of scarce water resources for agriculture makes it imperative that the
most efficient water utilization by plants is achieved, and where limits to
growth and production are most commonly set by limitations on our
knowledge of such factors.
A serious difficulty encountered in attempts to relate soil water to plant
response is the fact that the water content in a plant root zone varies
markedly in both time and space. Slatyer (1967) emphasized the importance of the soil water potential at the root/soil interface as the main soil
characteristic controlling the availability of soil water for plant growth,
with its value depending on both the soil water potential of the bulk soil
and the potential gradient from the bulk soil to the root surface, which
develops as a result of water removal by the root. Philip (1966) also
suggested that the value of the water potential at the root surfaces was
critical to the distribution of water potential (and to the possibility of
wilting) throughout much of the plant domain. Furthermore, although the
soil water tension, or matric suction, at a given depth in the root zone may
correlate well with plant response in some circumstances and provide a
useful basis for imgation, a clearer understanding of water availability to
plants requires some means of resolving changes in soil suction or water
content over the entire root zone.
Unfortunately, progress in this area has been severely limited because of
the difficulties associated with direct experimental measurement of soil
water content or potential at the root/soil interface and in the soil immediately around the root. Until recently, techniques for the direct measurement of soil water content or potential have either been destructive (and
hence lacked continuity), have perturbed the sensitive balance being examined, were too slow in their response time, or simply lacked the dimensional resolution necessary for meaningful definition of water content
distributions. Although Dunham and Nye (1973) were able to measure
one-off drawdowns in proximity to curtains of roots by destructive sectioning and So et al. (1976, 1978) were able to determine water potentials
at the root surface by extrapolation using a collar tensiometer - potometer
system, these techniques provided only very limited insights into the dy-
CAT STUDIES OF WATER MOVEMENT
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namics of the availability of soil water for plant growth. Consequently,
questions concerning the relative magnitudes of soil and plant resistances
to water movement under different conditions of soil water potential and
transpirational demand (Newman, 1969a,b), concerning the nature of the
water driving forces (Nobel, 1974), and concerning the extent to which
root/soil contact resistance (Herkelrath et al., 1977), accumulation of soil
solute concentrations (osmotic potentials) (Passioura and Frere, 1967),
etc., influence water availability have remained largely unresolved. Furthermore, conflicting results obtained predominantly by the indirect measuring procedures that previously were the only available techniques
(Dunham and Nye, 1973; So et af., 1976, 1978) raise questions as to the
validity of the physical concepts on which theoretical treatments (Molz,
1981) have been based.
Similar problems had long existed in medical diagnostic radiology in
seeking a method by which the interior of a section of the human body
could be viewed in a nondestructive manner without interference from
other regions. With advances in X-ray physics, detector technology, and
mathematical reconstruction theory, a solution to the problem was essentially achieved in the early 1970s by Hounsfield (1972), who developed the
technique known as computer-assisted tomography (CAT), or more simply, computed tomography (CT). (The word tomography is derived from
two Greek words: tomo, meaning slice or section, and graphy, meaning to
write or display.) CAT enables the three-dimensional, nondestructive
imaging of the internal structure of the object under examination using
measurements of the attenuation of a beam of radiation. The application
of the technique to the attentuation of X-rays (colloquially referred to as
CAT scanning) allowed dramatic advances in medical diagnostic capability
and benefited the medical profession greatly by reducing the need for
exploratory surgery to examine the internal structures of the human body.
For this work Godfrey Hounsfield shared the 1979 Nobel Prize for Medicine with A. M. Cormack, who had earlier, in 1963, developed and applied
a mathematical model that allowed the determination of absorption coefficients at specific points in scanned sections from the measured attenuation of collimated beams of 6oCoy-radiation.
Tomographic imaging in various forms is applicable to a number of
different types of energy beams, including electrons, protons, a particles,
lasers, radar, ultrasound, and nuclear magnetic resonance. However, because of its convenience and versatility in medical, industrial, and scientific applications, most attention has been directed to X-ray CT. In recent
years, the opportunity to use CAT scanning for nonmedical applications
has blossomed, particularly in the United States, Canada, Europe, Australia, and Japan. Hopkins et al. (1981) and Davis et af.(1986) demonstrated
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L. A. G . AYLMORE
its application to industrial problems, particularly for nondestructive testing of timber poles, plastics, concrete pillars, steel-belted automobile tires,
and electronic components. Onoe e? al. (1983) described the use of a
portable X-ray CAT scanner for measuring annual growth rings of live
trees.
The potential applications of CAT scanning in the soil and plant
sciences have also attracted increasing interest over the past decade. Numerous workers (Petrovic er al., 1982; Hainsworth and Aylmore, 1983,
1986; Crestana er al., 1985; Anderson e? al., 1988, 1990; Tollner e? al.,
1987; Tollner and Verma, 1989) have demonstrated that commercially
available X-ray medical scanners can provide excellent resolution for some
studies of the spatial distributions of bulk density and water content in soil
columns, including in particular those near plant roots (Hainsworth and
Aylmore, 1983, 1986; Aylmore and Hamza, 1990; Hamza and Aylmore,
1991, 1992a,b). The quantitative usefulness of such systems in soil studies
has, however, been limited by the polychromatic nature of the X-ray beam
and its inability to distinguish between changes in water content and bulk
density in swelling soils. Furthermore; these instruments are prohibitively
expensive (about $2 million) and hence have not been generally accessible
to soil and plant scientists. Consequently, work in several laboratories has
sought to provide experimentally more suitable systems and to reduce
vastly the cost of the equipment, by the modification of “conventional” y
scanning systems (Gurr, 1962; Groenevelt et al., 1969; Ryhiner and Pankow, 1969) to utilize the CAT approach (Hainsworth and Aylmore, 1983,
1988; Crestana e? al., 1986). pRays are essentially monochromatic, and
the ready availability of sources providing large differentials in energy level
offers the potential to distinguish quantitatively between simultaneous
changes in water content and bulk density. However, the relatively low
photon emission from pray sources compared with X-ray tubes requires
much longer scanning times and has as yet limited measurements by this
means to slow or steady-state processes.
Despite these current limitations there is no doubt that the application of
this exciting new technique will, with further developments, provide a
major tool for soil and plant scientists and has the potential to resolve the
major controversies with respect to the physics of water uptake by plant
roots.
11. COMPUTER-ASSISTED TOMOGRAPHY
The theory and use of the CAT technique for medical purposes has been
reviewed in some detail by Budinger and Gullberg (1974), Brooks and Di
Chiro (1975, 1976), and Panton (198 l), and complete reviews of various
CAT STUDIES OF WATER MOVEMENT
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aspects of CAT scanning have been presented by Newton and Potts (198 1)
and Kak and Slaney (1988). Brief reviews of CAT scanning theory as it
relates to the determination of soil water content have been presented by
Hainsworth and Aylmore (1983), Crestana er al. (1983, and Anderson et
al. (1988). However, as the technique has only recently been introduced in
soil science, an outline of the theory of CAT is given here to familiarize
readers with the technique.
A. THEORY
OF ATTENUATION
In conventional radiography the transmission of radiation through a
three-dimensional object is used to produce a two-dimensional image of
the internal features of the object on a radiation-sensitivefilm. Attenuation
occurs because the photons in the incident beam may be absorbed by the
material and disappear, or may be deflected out of the path of the beam,
leading to a decrease in the detected radiation intensity (Fig. 1). The image
formation relies on the spatial variation of radiation attenuation in the
object, which gives rise to a contrast in the transmitted radiation recorded
on the film. The physical quantity that characterizes the attenuation of
radiation by matter is called the linear attenuation coefficient (p).
The three principal mechanisms of radiation attenuation in matter are
photoelectric absorption, Compton scattering, and electron- positron pair
production (Cullity, 1978). In photoelectric absorption, the photon collides
directly with an atom of the absorber and transfers all of the energy to one
of the orbital electrons, which is ejected from the atom. This is the most
important process for low-energy photons (<500 keV). Because photons
with energy in excess of that required to eject an electron are unlikely to be
absorbed, the photoelectric absorption coefficient decreases rapidly with
Incident
beam
Transmitted
beam
absorbed
scattered
Figure 1. Attenuation of a narrow beam of radiation by absorption and scattering.
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L. A. G. AYLMORE
increasing photon energy. Compton scattering is the predominant scattering process in which a photon collides with an atom and is deflected from
its original direction with the loss of only a portion of its energy. This
energy is transferred to an atomic electron, which recoils out of the atom.
The absorption of photons by Compton scattering is most probable for
intermediate-energy photons (500- 1000 keV). The photon continues on
at a reduced energy to undergo additional Compton scattering or to be
absorbed by photoelectric interaction with a second electron. Of secondary
importance may be Rayleigh scattering, in which a photon may be deflected with no loss of energy and the whole atom recoils under the impact.
This can occur for photons of low energy, i.e., in the region where the
photoelectric effect is dominant. At very high photon energy, > 1000 keV,
a photon may be absorbed in the neighborhood of an atomic nucleus or
atomic electron and produce an electron-positron pair. In soil water
studies, the highest photon energy used is 662 keV from a y-radiation
source of I3’Cs, thus electron- positron production is not important in the
attenuation process.
The attenuation of a collimated beam of monoenergetic photons
of intensity I,, as a result of passing through a sample of material of thickness D, yields a transmitted intensity I behind the sample, as illustrated in
Fig. 2a (Anderson et al., 1988); this can be described by Beer’s Law,
I = I, exp(-pD)
(1)
where p, the linear attenuation coefficient (often referred to as attenuation coefficient),represents the fractional attenuation per unit length of the
material traversed by the radiation. The value of p depends primarily on
the energy of the radiation, the electron density, and the packing density of
the material. Equation (1) assumes that the material is homogeneous in
composition and density over the distance D. For heterogeneous materials,
one can subdivide the length D into n subdivisions (of length d), each
having a different linear attenuation coefficient, and can describe the
attenuation over the length D as the sum of the attenuation of these small
subdivisions (Fig. 2b). The transmitted radiation intensity is then
For real objects, such as soil, the attenuating material is continuously
rather than discretely distributed, so EQ. (2) takes the form of an integral
C A T STUDIES OF WATER MOVEMENT
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I
:
I\
EDEDI
Y
Figure 2. Schematic representation of the attenuation of monochromatic radiation of
initial intensity I,, by (a) homogeneous material, (b) nonhomogeneous material consisting of
discrete units with different attenuation coefficients,and (c) nonhomogeneous material consisting of a variable attenuation coefficient,p x , over the distance x from the source. (Afler
Anderson et aL, 1988.)
(Fig. 2c),
where x is the distance from the radiation source and varies between 0 and
D, the thickness of the sample.
Equation (3) can be rearranged to yield
The logarithm of Zo/Z is effectively a sum of the attenuation coefficients
along the ray path and is called a ray sum or ray projection. Obviously, a
single ray sum cannot give any information about the distribution of
attenuation coefficientsat discrete points within the material along the ray
path. Thus interpretative difficulties can arise because the image obtained
is really a two-dimensional projection of a three-dimensional object. The
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L. A. G. AYLMORE
Figure 3. Coordinate system for calculation of the photon attenuation coefficient at a
given point. Points within the object are described by fixed (x, y ) coordinates. Rays (dashed
lines) are specified by their angle (4)with the y axis and their distance (r)from the origin. The
S coordinate denotes distance along the way.
aim of the CAT technique is to overcome this difficulty and to reveal the
spatial distribution of attenuation coefficients unambiguously.
B. PRINCIPLES
OF COMPUTER-ASSISTED
TOMOGRAPHY
In CAT, multiple scans from different angles in a given plane provide a
large number of ray sums or projections. Using these projections, a two-dimensional image of the slice is reconstructed numerically to give the
distribution-of attenuation coefficients at discrete points within the slice.
For image reconstruction, an (x, y ) coordinate system (Fig. 3) is used to
describe points in the slice. As the slice is scanned, ray paths through the
slice can be defined by 4, the angle of the ray with respect to the y axis, and
r, its distance from the origin. The distance of a point from the source on
any ray path is given by the coordinate S, which varies from 0 to S.
The contribution of each point to the attenuation of a ray ( I , 4) with
initial intensity Z, and transmitted intensity I is denoted by
Equation ( 5 ) can be rearranged to obtain the projection value, p, of the
CAT STUDIES OF WATER MOVEMENT
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Figure 4. Schematic illustration of a parallel-beam CAT scanning procedure showing a
single projection consisting of a set of parallel ray sums and the linear and rotational
movementsinvolved in the collection of data prior to image reconstruction for a cross-section
of the object.
ray ,(I
4)
P(r, 4) = W o / ~ , +=)
I,
AX,V ) ds
(6)
In Eq. (6),p(x, y) is determined using many independent views or projections through the object. In the simplest scanning systems these are obtained using a scanning procedure involving both linear and rotational
movements of the source detector system (Fig. 4). A complete set of
parallel ray sums represents a single projection for that view of the crosssectional layer of the object.
Ideally, p(x, y) is a continuous two-dimensional function and an infinite
number of projections are required for reconstruction. Because in practice
it is physically impossible to obtain an infinite number of projections,
p(x, y ) is calculated at a finite number of points from a finite number of
projections. If the object is confined to a circular domain of diameter d,
and the image is reconstructed at points arranged rectangularly with spacing w, then there are n = d / w points along a principal diameter. Each
square cell of width w is called a pixel (an acronym for picture element). It
is also assumed that there are rn projections spaced equally from 0 to 180",
each consisting of n ray sums at intervals w. The minimum number of
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L. A. G. AYLMORE
rotations required for accurate image reconstruction is given by an/4
(Panton, 1981).
1. Numerical Reconstruction
In theory, if p(r, 4) is known for every line of width w passing through a
pixel of dimension w, then p(x, y) can be determined if Eq. (6) can be
inverted (Panton, 198I). Bracewell (1956) was the first to devise a numerical reconstruction technique for determining,u(x, y ) from Eq. (6), and with
subsequent advances there are now more than a dozen different approaches available for reconstructing p(x, y ) (Budinger and Gullberg,
1974). However, these approaches can be classified broadly into three
methods: ( 1) back-projection, (2) iterative reconstruction, and (3) filtered
back-projection (Brooks and Di Chiro, 1975, 1976).
a. Back-Projection Reconstruction
In the back-projection method, reconstruction is performed by applying
the magnitude of each projection to all points that make up the ray, or, in
other words, the back-projected p(x, y ) value is obtained by superimposing
projections together. The process can be described by Eq. (7),
+
where rj = x cos 4j y sin 4j,the distance of the ray from the origin; $ j is
the jth projection angle and A 4 is the angular distance between projections
(i.e., A 4 = a/m)and the summation extends over all rn projections.
Back-projection, however, does not produce a good reconstruction because each ray sum or projection is applied not only to points of high
density but to all points along the ray. This defect shows up most strikingly
with discrete areas of high density, producing a star artifact. The star
artifact causes the density function to vary from the true density function
by an intolerable margin, hence this method is rarely used these days.
b. Iterative Reconstruction
In the iterative methods of reconstruction, the basic strategy is to apply
corrections to arbitrary initial p(x, y) values in an attempt to match the
measured ray projections. Because former matchings are lost as new
corrections are made, the procedure is repeated until the calculated projections agree with the measured ones within the desired accuracy. Iterative
methods are primarily classified according to the sequence in which
corrections are made and incorporated during an iteration, as this choice
CAT STUDIES OF WATER MOVEMENT
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has a significant effect on the performance of the method. Three such
variations have been proposed:
1. Simultaneous correction: all projections are calculated at the beginning of the iteration and corrections are applied simultaneously to all
points (x, y). This method has sometimes been referred to as the iterative
least-squares technique (ILST) (Goitein, 1972).
2. Point-by-point correction: each point is corrected simultaneously for
all rays passing through it and corrections are incorporated before moving
to other points. This technique was introduced in electron microscopy by
Gilbert ( 1972), who named it the simultaneous iterative reconstruction
technique (SIRT).
3. Ray-by-ray correction: a given set of ray projections is calculated and
corresponding corrections are applied to all points. The updated p ( x , y )
values are then used for calculating the next projection. Ray-by-ray correction was used in the original version of the EM1 scanner (Hounsfield, 1972)
and was independently discovered in electron microscopy by Gordon et al.
( I 970), who named it the algebraic reconstruction technique (ART). The
iterative reconstruction methods are slow and hence are not very popular.
c. Filtered Back-Projection
Filtered back-projection methods are the most commonly used and are
considered to be the most accurate. The basis of the analytical methods
involves a fundamental relationship between the Fourier transform of the
linear attenuation function p(x, y ) and the projection function p(r, 4).
Such a relationship filters the projection, accounting for the portions of the
projection that may pass outside a given pixel, thereby eliminating the star
artifact mentioned earlier in the back-projection reconstruction method.
The filtered projections are then back-projected, i.e., the reconstructed
p ( x , y ) is analogous to Eq. (7) except that the p is replaced by the filtered
version p *:
A number of filtering techniques (Fourier, Radon, convolution filtering,
etc.) have been developed, but the performance of filtered back-projection
is not greatly affected by the choice of filtering technique. Derivation of the
formula for the different filters can be found in works by Brooks and Di
Chiro (1976), Herman (1980), and Kak and Slaney (1988).
A schematic illustration of a reconstructed image with direct back-projection and back-projection after filtration of projections (profiles) measured for a homogeneous cylinder is shown in Fig. 5. After direct back-
L. A. G . AYLMORE
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a
b
Figure 5. Schematic illustration of a reconstructed image with (a) direct back-projection
and (b) back-projectionafter filtration of profiles measured for a homogeneous cylinder.
projection of the profiles measured, image details would be smeared if no
further corrections were carried out. For this reason, back-projection is
preceded by a filtration or convolution process.
Filtered back-projection has the advantage that the data can be processed as they are collected and the image can be built up and displayed
projection by projection, thus allowing a useful saving in measurement
time, particularly when data rates are low. An added advantage is that the
final image is ready virtually immediately after the scans are completed
and image quality can be progressively assessed. Iterative techniques need a
larger data set before image reconstruction can commence, but are capable
of giving better results from fewer projections than is normally required for
the convolution method (Gilboy, 1984).
2. Aliasing Artifacts
Reconstruction procedures are only as good as the data on which they
are based and a number of errors or artifacts can arise through the availability of insufficient data or by the presence of random noise in the
measurements. An insufficiency of data may occur either through undersampling of projection data or because not enough projections are
recorded. The distortions that arise as a result of inadequate data are called
aliasing artifacts and generally appear as streaks, blumng, rings, or interference patterns in the reconstructed image. Aliasing distortions may also
be caused by using an undersampled grid for displaying the reconstructed
image (Brooks and Di Chiro, 1976; Kak and Slaney, 1988). Regions of
overestimated or underestimated attenuation associated with sharp
changes in attenuation and appearing as rings or oscillations are called the
Gibbs effect. Moire patterns are interference patterns that can dominate
the entire image. The occurrence of these effects depends largely on the
relative number of projections and rays in each projection, and it has been
shown (Kak and Slaney, 1988) that a balanced image reconstruction re-