Fox, M.D., Frizzell, L.A., FrankS, L. A, Darken, L.S., James, R B. "Medical Imaging The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Fox, M..D., Frizzell, L.A., Franks, L.A., Darken, L.S., James, R.B. “Medical Imaging” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
116 Medical lmaging University of Connecticut Leon a. frizzell 116.1 Tomography Larry A Franks Tomography. Single Photon Emission Computed Tomography. Magnetic Resonance Imaging. Imaging Sandia national laboratories 116.2 Ultrasound Larry S Darken Fundamentals of Acoustics. Principles of Pulse-Echo Ultrasound. Future Developments 116.3 Semiconductor Detectors for Radiation measurements Ralph B. James Cryogenic Detectors. True Room-Temperature Detectors sandia national laboratories Silicon Detectors. Prices and Availability 116.1 Tomography M.D. Fox The term tomography derives from the Greek tomos(cutting)and grapho( to write). Originally the term was applied to sectional radiography achieved by a synchronous motion of the x-ray source and detector in order to blur undesired data while creating a sharp image of the selected plane. The term tomography was used to distinguish between such slices and the more conventional plain film radiograph, which represents a two- dimensional shadowgraphic superposition of all x-ray absorbing structures within a volumetric body. Computerized tomography, also known as computerized axial tomography, was introduced by EMI, Ltd. n 1973 and transformed medical imaging by obviating the superposition of intervening structures present conventional radiographic imag in ges. Initially, the clinical application was for imaging the head, but soon the technique found wide application in body imaging As medical imaging has evolved into a multimodality field, the meaning of tomography has broadened to include any images of thin cross-sectional slices, regardless of the modality utilized to produce them. Thus, omographic images can be generated by magnetic resonance imaging(MRI), ultrasound (US), computerized tomography(CT), or such nuclear medicine techniques as positron emission tomography(PET) or single photon emission computerized tomography(SPECT). For the purposes of this discussion we will cover all of the foregoing modalities with the exception of ultrasound, which will be treated separately. Since the power of such computerized techniques was recognized, the practice of radiology has been revo- lutionized by making possible much more precise diagnosis of a wide range of conditions. In this necessarily brief discussion we will describe the basic physical principles of the major tomographic modalities as well as their key clinical applications. Computerized Tomography The basic concept of computerized tomography can be described by consideration of Fig. 116.1. An x-ray source is passed through an aperture to produce a fan-shaped beam that passes through the body of interest absorption along approximately parallel lines. The natural logarithm of the detected intensity will be the intesa of the linear attenuation coefficient of the object along the ray directed from the source to the detector elem If the source and the detector array are synchronously rotated about a point within the object, a number c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 116 Medical Imaging 116.1 Tomography Computerized Tomography • Positron Emission Tomography • Single Photon Emission Computed Tomography • Magnetic Resonance Imaging • Imaging 116.2 Ultrasound Fundamentals of Acoustics • Principles of Pulse-Echo Ultrasound • Future Developments 116.3 Semiconductor Detectors for Radiation Measurements Cryogenic Detectors • True Room-Temperature Detectors • Silicon Detectors • Prices and Availability 116.1 Tomography M. D. Fox The term tomography derives from the Greek tomos (cutting) and grapho (to write). Originally the term was applied to sectional radiography achieved by a synchronous motion of the x-ray source and detector in order to blur undesired data while creating a sharp image of the selected plane. The term tomography was used to distinguish between such slices and the more conventional plain film radiograph, which represents a twodimensional shadowgraphic superposition of all x-ray absorbing structures within a volumetric body. Computerized tomography, also known as computerized axial tomography, was introduced by EMI, Ltd. in 1973 and transformed medical imaging by obviating the superposition of intervening structures present in conventional radiographic images. Initially, the clinical application was for imaging the head, but soon the technique found wide application in body imaging. As medical imaging has evolved into a multimodality field, the meaning of tomography has broadened to include any images of thin cross-sectional slices, regardless of the modality utilized to produce them. Thus, tomographic images can be generated by magnetic resonance imaging (MRI), ultrasound (US), computerized tomography (CT), or such nuclear medicine techniques as positron emission tomography (PET) or single photon emission computerized tomography (SPECT). For the purposes of this discussion we will cover all of the foregoing modalities with the exception of ultrasound, which will be treated separately. Since the power of such computerized techniques was recognized, the practice of radiology has been revolutionized by making possible much more precise diagnosis of a wide range of conditions. In this necessarily brief discussion we will describe the basic physical principles of the major tomographic modalities as well as their key clinical applications. Computerized Tomography The basic concept of computerized tomography can be described by consideration of Fig. 116.1.An x-ray source is passed through an aperture to produce a fan-shaped beam that passes through the body of interest with absorption along approximately parallel lines. The natural logarithm of the detected intensity will be the integral of the linear attenuation coefficient of the object along the ray directed from the source to the detector element. If the source and the detector array are synchronously rotated about a point within the object, a number of M. D. Fox University of Connecticut Leon A. Frizzell University of Illinois Larry A. Franks Sandia National Laboratories Larry S. Darken Oxford Instruments Ralph B. James Sandia National Laboratories
APPARATUS AND METHOD FOR DETECTING CANCER IN TISSUE Raymond V. damadian Patented February 5, 1974 #3,789,832 xcerpts from Raymond Damadian's patent application It has now been found that, by measuring the degree of organization of these selected molecules in cells being studied and comparing this with the degree of organization in a known cancerous cell, cancer cells can be detected. Furthermore, it has now been found that the less the organization the greater the malignancy therefore a scale can be made to provide a standard for basing a decision on the degree of malignancy Further apparatus is provided for scanning throughout the entire body during which time the relaxation times are measured for selected nuclei and compared with standards. In this way a determination can be made of the existence of cancer together with the location and degree of malignancy of the cancerous cells This patent describes a device that uses very powerful magnetic fields to resonate the nuclei in cells in a body. Collapsing the field and measuring the relaxation times gave a comparison to healthy cells Later advances in digital signal processing have resulted in magnetic resonance imaging(MRi)equipment with color-coded image viewing of living tissue and its chemical composition. Copyright o 1995, Dew Ray Products, Inc. Used with permission. lines of data can be collected, each representing the projected density of the object as a function of lateral position and angle number of mathematical techniques can and have been used to recover the two-dimensional distribution of the linear attenuation coefficient from this array of measurements. These include iterative solution of a set of simultaneous linear equations, Fourier transform approaches, and techniques utilizing back-projection followed by deconvolution[Macovski, 1983]. Conceptually, the Fourier transform approach is perhaps the most straightforward, so we will describe it in some detail e 2000 by CRC Press LLC
© 2000 by CRC Press LLC APPARATUS AND METHOD FOR DETECTING CANCER IN TISSUE Raymond V. Damadian Patented February 5, 1974 #3,789,832 Excerpts from Raymond Damadian’s patent application: ...It has now been found that, by measuring the degree of organization of these selected molecules in cells being studied and comparing this with the degree of organization in a known cancerous cell, cancer cells can be detected. Furthermore, it has now been found that the less the organization the greater the malignancy, therefore a scale can be made to provide a standard for basing a decision on the degree of malignancy... ...Further apparatus is provided for scanning throughout the entire body during which time the relaxation times are measured for selected nuclei and compared with standards. In this way a determination can be made of the existence of cancer together with the location and degree of malignancy of the cancerous cells present.... This patent describes a device that uses very powerful magnetic fields to resonate the nuclei in cells in a body. Collapsing the field and measuring the relaxation times gave a comparison to healthy cells. Later advances in digital signal processing have resulted in magnetic resonance imaging (MRI) equipment with color-coded image viewing of living tissue and its chemical composition. (Copyright © 1995, DewRay Products, Inc. Used with permission.) lines of data can be collected, each representing the projected density of the object as a function of lateral position and angle. A number of mathematical techniques can and have been used to recover the two-dimensional distribution of the linear attenuation coefficient from this array of measurements. These include iterative solution of a set of simultaneous linear equations, Fourier transform approaches, and techniques utilizing back-projection followed by deconvolution [Macovski, 1983]. Conceptually, the Fourier transform approach is perhaps the most straightforward, so we will describe it in some detail
A Computerized Tomography(CT) Detector Array Detector Array Source B. Positron Emission Tomography(PET collimator C. Single Photon Emission Computed Tomography FIGURE 116. 1 Comparison of three photon-based tomographic imaging modalities. Fig. 116.1(A)and assuming parallel rays, the intensity picked up by the detector array can be expresse L,()=Io exp[-a(x,y)dx] where a(x,y) represents the linear attenuation coefficient to x-ray photons within the body as a function of x,y position, and Io is the source intensity. Rearranging, we see that a, (y)=a(x, y)dx=In(L (y)/Iol where a(y)is the projected attenuation function Taking a one-dimensional Fourier transform of this projected density function we see that Fa(y)=A(f)=∫∫以xy减e形yb where A, (fy) is the Fourier transform of a single line of detected data. But this can also be written c2000 by CRC Press LLC
© 2000 by CRC Press LLC Using the coordinate system of Fig. 116.1(A) and assuming parallel rays, the intensity picked up by the detector array can be expressed as Id(y) = I0 exp[–Úa(x,y)dx] where a(x,y) represents the linear attenuation coefficient to x-ray photons within the body as a function of x,y position, and I0 is the source intensity. Rearranging, we see that where ap(y) is the projected attenuation function. Taking a one-dimensional Fourier transform of this projected density function we see that where Ap(fy) is the Fourier transform of a single line of detected data. But this can also be written FIGURE 116.1 Comparison of three photon-based tomographic imaging modalities. a y a x y dx I y I p d ( ) ( , ) ln[ ( )/ ] – = = • • Ú 0 F a y A f a x y dx e dy p py j fyy [ ( )] ( ) ( , ) – –– = = • • • • ÚÚ 2p
A,0,)=J∫以x,y减c0b Thus, the one-dimensional Fourier transform of the projection of the linear attenuation function, ap(y), is equal to the two-dimensional Fourier transform of the original attenuation function evaluated along a line in the frequency domain(in this case the f=0 line) It can readily be demonstrated that if we rotate a function a(x,y) through an angle o in the x,y plane, its transform will be similarly rotated through an angle o [Castleman, 1979]. Thus as we rotate the source and detector around the object, each projected density function detected a(p, o can be Fourier transformed to provide one radial line of the two-dimensional Fourier transform of the desired reconstructed image, A(p, oi), where p is a radial spatial frequency. The set of all A(p, o )for small angular displacements o; form a set of spokes in the transform domain which can be interpolated to estimate A(y), the two-dimensional Fourier transform of the image in rectangular coordinates. The image can then be recovered by inverse transformation of A(ffr), which can readily be carried out digitally using fast Fourier transform algorithms, i. e, a(x,y)=F [A(ofr)I While the Fourier transform approach is mathematically straightforward, many commercial scanners utilize the equivalent but more easily implemented back-projection/deconvolution approach, where each ray is traced back along its propagation axis. When all rays have been back-projected and the result summed, one obtains an approximate(blurred)image of that plane. This image can then be sharpened(deblurred)through the use deblurring function. Refer to Macovski [1983]for the details of this procsse an appropriate two-dimensional of an appropriate filter, which is usually implemented by convolving with Clinically, the impact of computerized tomography was dramatic due to the vastly increased density resolu tion, coupled with the elimination of the superposition of overlying structures, allowing enhanced differenti- ation of tissues with similar x-ray transmittance, such as blood, muscle, and organ parenchyma. CT scans of the head are useful for evaluation of head injury and detection of tumor, stroke, or infection. In the body, CT is also excellent in detecting and characterizing focal lesions, such as tumors and abscesses, and for the evaluation of the skeletal system. [Axel et al., 1983]. In recent years the advent of magnetic resonance systems has provided even greater soft tissue contrast, and thus the role of Ct has been constrained by this at times competing modality Positron Emission Tomography Unlike computerized tomography, which relies on photons produced by an external source, in the modalities of positron emission tomography(PET) and single photon emission computed tomography(SPECT), the source of radiation is a radioisotope that is distributed within the body, and thus these modalities are sometimes referred to as forms of emission computed tomography(ECT). While conventional CT can produce images based upon anatomy of organs, emission Ct techniques can quantitate the distribution of tracer materials that can potentially elucidate physiologic function. The positron or positive electron is a positively charged particle that can be emitted from the nucleus of a radionuclide. The positron travels at most a few millimeters before being annihilated by interaction with a egative electron from the surrounding tissue. The product of this event is the emission of 511-keV gamma ray photons which travel in almost exactly opposite directions. The detectors themselves can be either discrete detectors or a modified Anger camera like those used in conventional nuclear imaging. A coincidence detector is employed to limit recorded outputs to cases in which events are detected simultaneously in both detector arrays, thus reducing the pickup of noise or scattering A possible detection scheme is illustrated in Fig. 116. 1(B). The detector arrays shown can be made energy selective to eliminate lower energy scattered gamma rays. While the distribution of radioactivity can be recon- structed using the reconstruction from projection techniques described in the section on CT Hurculak, 1987 e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Thus, the one-dimensional Fourier transform of the projection of the linear attenuation function, ap(y), is equal to the two-dimensional Fourier transform of the original attenuation function evaluated along a line in the frequency domain (in this case the fx = 0 line). It can readily be demonstrated that if we rotate a function a(x,y) through an angle f in the x,y plane, its transform will be similarly rotated through an angle f [Castleman, 1979]. Thus as we rotate the source and detector around the object, each projected density function detected ap(r,fi ) can be Fourier transformed to provide one radial line of the two-dimensional Fourier transform of the desired reconstructed image, A(r,fi ), where r is a radial spatial frequency. The set of all A(r,fi ) for small angular displacements fi form a set of spokes in the transform domain which can be interpolated to estimate A(fx,fy), the two-dimensional Fourier transform of the image in rectangular coordinates. The image can then be recovered by inverse transformation of A(fx,fy), which can readily be carried out digitally using fast Fourier transform algorithms, i.e, a(x,y) = F–1[A(fx,fy)] While the Fourier transform approach is mathematically straightforward, many commercial scanners utilize the equivalent but more easily implemented back-projection/deconvolution approach, where each ray is traced back along its propagation axis. When all rays have been back-projected and the result summed, one obtains an approximate (blurred) image of that plane. This image can then be sharpened (deblurred) through the use of an appropriate filter, which is usually implemented by convolving with an appropriate two-dimensional deblurring function. Refer to Macovski [1983] for the details of this process. Clinically, the impact of computerized tomography was dramatic due to the vastly increased density resolution, coupled with the elimination of the superposition of overlying structures, allowing enhanced differentiation of tissues with similar x-ray transmittance, such as blood, muscle, and organ parenchyma. CT scans of the head are useful for evaluation of head injury and detection of tumor, stroke, or infection. In the body, CT is also excellent in detecting and characterizing focal lesions, such as tumors and abscesses, and for the evaluation of the skeletal system. [Axel et al., 1983]. In recent years the advent of magnetic resonance systems has provided even greater soft tissue contrast, and thus the role of CT has been constrained by this at times competing modality. Positron Emission Tomography Unlike computerized tomography, which relies on photons produced by an external source, in the modalities of positron emission tomography (PET) and single photon emission computed tomography (SPECT), the source of radiation is a radioisotope that is distributed within the body, and thus these modalities are sometimes referred to as forms of emission computed tomography (ECT). While conventional CT can produce images based upon anatomy of organs, emission CT techniques can quantitate the distribution of tracer materials that can potentially elucidate physiologic function. The positron or positive electron is a positively charged particle that can be emitted from the nucleus of a radionuclide. The positron travels at most a few millimeters before being annihilated by interaction with a negative electron from the surrounding tissue. The product of this event is the emission of 511-keV gamma ray photons which travel in almost exactly opposite directions. The detectors themselves can be either discrete detectors or a modified Anger camera like those used in conventional nuclear imaging. A coincidence detector is employed to limit recorded outputs to cases in which events are detected simultaneously in both detector arrays, thus reducing the pickup of noise or scattering. A possible detection scheme is illustrated in Fig. 116.1(B). The detector arrays shown can be made energy selective to eliminate lower energy scattered gamma rays. While the distribution of radioactivity can be reconstructed using the reconstruction from projection techniques described in the section on CT [Hurculak, 1987], A f a x y dx e dy p y j x fyy (, ) (, ) –( ) –– 0 2 0 = + • • • • ÚÚ p