Patent Publication Number: US-2002006181-A1

Title: Method and device for estimating bone mineral content of the calcaneus

Description:
CROSS REFERENCE TO RELATED U.S. PATENT APPLICATIONS  
     [0001] This patent application is a continuation-in-part application of U.S. patent application Ser. No. 09/235,236 filed on Jan. 22, 1999 entitled METHOD AND DEVICE FOR ESTIMATING BONE MINERAL CONTENT OF THE CALCANEUS, now allowed, which relates to United States provisional patent application Ser. No. 60/072,312 filed on Jan. 23, 1998 entitled METHOD AND DEVICE FOR ESTIMATING BONE MINERAL CONTENT OF THE CALCANEUS. 
    
    
     
       FIELD OF THE INVENTION  
       [0002] The present invention relates in general to a low dose, in situ and noninvasive method and device for estimating human bone mineral content and more particularly the present invention relates to a method for monitoring osteoporosis by analyzing X-ray backscatter to estimate the calcium content of the calcaneus, specifically an average volumetric bone mineral density.  
       BACKGROUND OF THE INVENTION  
       [0003] Osteoporosis is a condition of the human skeleton that is characterized by deleterious loss, over time, of bone mineral content, particularly calcium. The disease, while most prevalent in women past menopause, is commonly considered an aging disease present in both men and women. Individuals exhibiting osteoporosis are very prone to fractures, most commonly in the wrist, spine and hips. Death rates among men and women due to complications associated with osteoporosis are quite significant, numbering in the tens of thousands a year in North America. Experience has revealed no single measure of bone quality or quantity that is a reliable indicator of fracture risk. For example, microcracks from prior stresses increase risk but are not “visible” in most measurements. Nevertheless, it is widely accepted that the strength of bone (i.e., its resistance to fracture) is roughly proportional to the mass density of the bone mineral and this, in turn, is proportional to the calcium concentration.  
       [0004] New treatments and therapies have recently been, and are currently being, developed to treat osteoporosis. Two basic approaches to treatment are taken; one relates to intervening in order to reduce the amount of bone loss which accompanies aging, and the other involves replacing lost calcium or increasing calcium content. Early detection of bone mineral loss would be very advantageous, particularly if steps can be taken in the very early stages to slow down calcium depletion. The ability to measure, noninvasively and in situ, bone mineral content is crucial to early detection of osteoporosis and other related skeletal degenerative diseases.  
       [0005] There are several techniques available for measurement of bone mineral content. Computed tomography (CT) involves measurement of X-rays transmitted through the different parts of the anatomy detected by arrays of detectors whereupon cross-sectional images are constructed of internal structures of the body from transmitted X-ray data from which mineral loss data is obtained. Dual energy X-ray absorptometry (DXA) uses a dual energy approach in order to correct for tissue variations and to permit quantification of bone mass.  
       [0006] More specifically, U.S. Pat. No. 5,535,750 issued to Matsui et al. is directed to a method and device for monitoring development of osteoporosis using ultrasonic monitoring of a heel or a knee bone. The method involves measurement of velocity differences of acoustic signals transmitted through the subject bones.  
       [0007] U.S. Pat. No. 5,483,965 issued to Weiner et al. teaches insertion of the heel of a person into a water bath in an apparatus containing ultrasonic transducers to perform densitometry. Acoustic signals are transmitted through the user&#39;s foot and a receiver on the other side of the foot detects the signals and measures the transit time and attenuation of a selected frequency thereby obtaining a profile of the bone content.  
       [0008] U.S. Pat. No. 5,335,260 issued to Arnold is directed to a method of quantifying calcium, bone mass and bone mass density via X-ray radiography that involves use of a calibration phantom comprising a material to simulate human tissue. X-rays of sufficient energy and intensity are transmitted through the limb and a detector on the other side of the limb processes the transmitted X-ray data.  
       [0009] U.S. Pat. No. 5,204,888 issued to Tamegai et al. discloses a method for measurement of bone mineral content through irradiating an object with X-rays and measuring the transmitted X-ray intensity. The device uses an X-ray generator that produces X-rays over a continuous spectrum and a detector placed on the other side of the object being provided to measure transmitted X-ray intensities.  
       [0010] U.S. Pat. Nos. 4,510,450 and 4,635,643, both issued to Brown teach use of nuclear magnetic resonance for determining mineral content of bone. U.S. Pat. No. 4,510,450 claims a rotor device which acts as a holder for the assay during the test and U.S. Pat. No. 4,635,643 claims the actual method of probing for mineral content using  31 P NMR.  
       [0011] U.S. Pat. No. 5,521,955 issued to Gohno et al. discloses an apparatus for bone density measurement and non-destructive inspection using a computed tomography (CT) scanner. The method requires scanning a calibration sample produced by mixing a water equivalent material (a material having the same X-ray transmission rate as that of water) with different ratios of a standard material equivalent to bone mineral mass (a material having the same X-ray transmission rate as that of bone mineral mass) and determining the bone density relative to the standard samples.  
       [0012] U.S. Pat. No. 4,829,549 issued to Vogel et al. is directed to a densitometer for predicting osteoporosis by measurement of bone mineral content by transmission of X-rays/gamma rays through the heel bone. A foot holder is provided with a radioactive source holder mounted in the foot holder along with a detector mounted in the foot holder opposite the source holder,  
       [0013] U.S. Pat. No. 5,351,689 issued to MacKenzie teaches a method and apparatus for low dose estimates of bone minerals using gamma ray backscattering. The method disclosed in this patent relies upon measuring the backscattering from bones and comparing the intensities in two areas of the backscatter spectrum. One area, A 1 , derives most of its intensity from Rayleigh scattering while the other area, A 2 , combines the events from both Rayleigh and Compton scattering. The shape parameter, W=A 1 /A 2 , is approximately a linear function of bone mineral content because most of the Rayleigh scattering is due to calcium content of the bone mineral.  
       [0014] A drawback to many of the above-mentioned devices and procedures for measuring bone content is the need for very expensive, large and heavy equipment and in some cases high radiation doses. Such systems, for example the whole body or axial DXA and CT systems require a dedicated centralized location and require attendance by specialized technicians to oversee the scanning process. This results in availability being restricted to medical facilities that are financially well supported. Furthermore, DXA systems, which have the highest market penetration, provide an areal bone density measurement in units of grams per square centimeter because of the transmission nature of the technique. Ideally a volumetric measurement is required so that artifacts are not introduced due for example to differences in bone thickness or orientation.  
       [0015] Therefore, it would be very advantageous to provide an in vivo, low dose, rapid and inexpensive method and device for monitoring volumetric bone mineral content that is portable and does not require sophisticated analysis techniques for interpreting the results. Such a device would readily lend itself to large scale use and may be used by any age group for monitoring bone development and would be very useful as a first tool in a program for early detection and prevention of osteoporosis as well as for monitoring the effectiveness of any dietary or pharmaceutical therapeutic program in respect of impact on bone mineral content.  
       SUMMARY OF THE INVENTION  
       [0016] It is an object of the present invention to provide a method and apparatus for estimating bone mineral content of certain bones, with a high trabecular bone content.  
       [0017] It is also an object of the present invention to provide a method for monitoring osteoporosis using the measured X-ray radiation backscattered from the calcaneus.  
       [0018] The present invention provides a non-destructive, low dose, in-situ method of estimating bone mineral content by measuring the intensity of X-rays backscattered from certain trabecular bones.  
       [0019] In one aspect of the present invention there is provided a low dose in vivo method for estimating bone mineral content of certain trabecular bones. The method comprises the steps of:  
       [0020] a) immobilizing a person&#39;s anatomical part containing trabecular bone;  
       [0021] b) providing a source of X-rays wherein at least some of said X-rays emitted therefrom have an energy in a range so that absorption of said X-rays by calcium competes with scattering of said X-rays by calcium and other constituents making up trabecular bone;  
       [0022] c) irradiating a target trabecular bone in an anatomical part with a low radiation dose from said X-ray source;  
       [0023] d) measuring an intensity spectrum of backscattered X-ray radiation from a person&#39;s anatomical part;  
       [0024] e) providing a theoretical model having model parameters for backscattering of X-rays from said target trabecular bone which accounts for a thickness of soft tissue between said target trabecular bone and said source of X-rays; and  
       [0025] f) determining a thickness of soft tissue between said target trabecular bone and said source of X-rays and using said theoretical model and said thickness of soft tissue to calculate a bone mineral concentration in said target trabecular bone from the intensity spectrum of backscattered X-ray radiation.  
       [0026] In this aspect of the invention the step of irradiating a target trabecular bone may include irradiating the target trabecular bone with X-ray radiation from an X-ray tube.  
       [0027] In another aspect of the invention there is provided an apparatus for low dose in vivo measurement of bone mineral content of trabecular bones, comprising:  
       [0028] a support frame for holding a person&#39;s anatomical part containing a trabecular bone;  
       [0029] an X-ray source mounted on said support frame for providing a continuous energy spectrum of X-rays:  
       [0030] a detection means mounted on said support frame for detecting an energy spectrum I n  (E n ) of X-rays backscattered from said trabecular bone, wherein I n  is the intensity at energy value E n  and n is an integer with a range of values such that E n  spans a preselected range of energies being detected by said detection means, said X-ray source and said detection means being positioned with respect to each other so that a beam of X-rays produced by said X-ray source is directed away from said detector into a person&#39;s immobilized anatomical part, wherein at least some of said X-rays in said beam have an energy in a range so that absorption of the X-rays by calcium competes with scattering of said X-rays by calcium and other constituents making up a trabecular bone; and  
       [0031] computer control and processing means connected to said detection means for receiving data from said detection means and calculating a bone mineral concentration in the trabecular bone from said energy spectrum of the backscattered X-rays.  
       [0032] In another aspect of the invention there is provided an apparatus for in vivo measurement of bone mineral content of trabecular bones, comprising:  
       [0033] a support frame for holding and immobilizing a person&#39;s anatomical part containing a trabecular bone to said support frame;  
       [0034] a detector mounted on said support frame for detecting an intensity of X-rays;  
       [0035] an X-ray source positioned with respect to said detector so that a beam of X-rays is directed away from said detector into a person&#39;s immobilized anatomical part, the detector being positioned with respect to said X-ray source to measure an intensity of X-rays backscattered from said trabecular bone, wherein at least some of said X-rays in said beam have an energy in a range so that absorption of the X-rays by calcium competes with scattering of said X-rays by calcium and other constituents making up a trabecular bone;  
       [0036] thickness measurement means for measuring a thickness of soft tissue covering said trabecular bone; and  
       [0037] a processor for calculating a bone mineral concentration in the trabecular bone from said intensity of backscattered X-rays.  
       [0038] In this aspect of the invention the thickness measurement means is an ultrasound source and detector mounted on said support frame, said ultrasound source and detector adapted to produce an ultrasound signal wherein said detector detects an ultrasound signal reflected from said trabecular bone, and wherein said soft tissue thickness is determined from a transit time for said ultrasound signal through said soft tissue and back from said trabecular bone. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0039] The method and device for estimating calcium content of trabecular bones will now be described, by way of example only, reference being made to the following drawings:  
     [0040]FIG. 1 shows a vertical view of the device for estimating calcium in a person&#39;s calcaneus constructed in accordance with the present invention;  
     [0041]FIG. 2 is a view along line  28  of FIG. 1:  
     [0042]FIG. 3 shows a view of an alternative embodiment of a device for estimating calcium in a person&#39;s calcaneus constructed in accordance with the present invention;  
     [0043]FIG. 3 a  is a detailed blow-up view of the device of FIG. 3;  
     [0044]FIG. 4 is a view from the left of FIG. 3;  
     [0045]FIG. 5 is block diagram of the apparatus of FIGS. 3 and 4;  
     [0046]FIG. 6 is a one-dimensional model of the heel showing soft tissue covering a semi-infinite slab of bone, suitable for mathematical analysis;  
     [0047]FIG. 7 a  shows a top view of an ultrasonic source/detector pressed up against a user&#39;s foot for measuring the thickness of the soft tissue between the skin and bone;  
     [0048]FIG. 7 b  shows a blow-up of the ultrasound waveform shown in FIG. 7 a;  and  
     [0049]FIG. 8 shows an intensity spectra of backscattered radiation for two different bone mineral densities. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
     [0050] The present invention provides a method and device for an in situ, low dose estimation of bone mineral content of certain trabecular bones by measuring the intensity of X-rays backscattered from the trabecular bone. Periodic measurements of the person using the present method and device permits one to monitor changes in bone density as the person ages.  
     [0051] Referring to FIG. 1 an apparatus for estimating calcium content of trabecular bones such as the calcaneus (heel bone) is shown generally at  10 . Apparatus  10  includes a platform  12  which provides a foot and leg support for a user&#39;s foot  30 . A housing  14  encloses a radioactive source/detector assembly  18  mounted therein. The source/detector assembly  18  comprises an axially symmetric heavy-metal radioactive source holder (collimator)  20  containing a radioactive source mounted on the cylindrical axis  28  of a cylindrically symmetric radiation detector  22 , for example, a NaI(TI) scintillation counter and photomultiplier. Source/detector assembly  18  is connected to a control circuit  24  which while shown mounted in housing  14  may be located away from the housing. Control circuit  24  is connected to detector  22  and includes timing circuits and processors to process the data from the detector. Restraining straps  26  are used to hold the user&#39;s foot  30  immobile on apparatus  10 .  
     [0052] Measuring the calcium concentration of the calcaneus is preferred for reasons to be discussed hereinafter. The source holder/detector assembly  18  is mounted in housing  14  so that when a user&#39;s foot  30  is immobilized on apparatus  10  the source-holder  20 , which is spring-loaded using a spring  44  to compress the soft tissue in region  34 , is held firmly against the centre of the rear of the patient&#39;s heel so the X-rays penetrate through the soft tissue  36 . An alignment mechanism  38  allows assembly  18  to be raised and lowered and moved side-to-side and oriented in the vertical plane to allow adjustment to differently sized feet. Referring to FIG. 2, two alignment beams  40  are disposed on each side of the person&#39;s foot on platform  12  and spring biased inwardly so that when a user places his or her foot on the platform it is held in alignment by beams  40 .  
     [0053] The apparatus exploits the cylindrical symmetry of the source containing collimator  20  and detector  22  and uses shadowing or geometric hindrance by the heavy-metal collimator to prevent both primary X-rays from the source and X-rays backscattered from the soft tissue under the skin covering the calcaneus in region  34  (FIG. 1) from reaching detector  22 . The shape of the source holder  20  can be designed to give the desired amount of collimation of the X-ray beam. The beam of X-rays emanating from collimator  20  is backscattered from the constituents making up the calcaneus, as can be seen from the broken ray lines in FIG. 1. The backscattered X-rays can be counted very efficiently by detector  22 , provided that these X-rays reach the detector without being absorbed.  
     [0054] The radioactive source may be  109 Cd that emits the K X-rays of silver (22 to 25 Kev) but other suitable radioactive sources or an X-ray tube may be used. The collimator  20  directs the cone of primary X-rays along the axis  28  of the detector  22  but in the opposite direction away from the detector. The method relies upon measuring the intensity of X-rays backscattered from the various components making up the calcaneus (heel bone)  32  and relating this intensity to the concentration of calcium present. All of the tissues of the human body are very weak absorbers of 20 keV X-rays with the sole exception of bone. Even the bone is a weak absorber except for that part of the bone that is in the form of a mineral called apatite. Apatite comprises mainly calcium phosphate of which calcium is the main X-ray absorber and therefore to a good approximation the observed counting rate provides a measure of the calcium content of the heel; the more calcium, the lower the counting rate and this inverse relationship has been observed to be smoothly varying such that for a given soft tissue thickness there is a unique inverse relationship between counting rate and calcium concentration. Such relationships have been determined using phantoms to represent the calcaneus and its covering of soft tissue.  
     [0055] X-rays are backscattered primarily via Compton scattering (although Rayleigh scattering also contributes to scattering) and are detected by the scintillation detector. The end portion of the detector/source assembly  18  containing the collimator  20  is held firmly against an anatomically determined position on the person&#39;s heel so that the X-rays penetrate through the compressed soft tissue  36  in region  34  (FIG. 1) and in a direction more or less parallel to the sole of the foot  30 . This means that the X-rays are transmitted into the calcaneus after penetration of typically 8 mm of soft tissue  36  that covers the calcaneus in region  34 . Most of the transmitted X-rays will collide with electrons in the chemical constituents of the calcaneus in the process of Compton scattering. In this process, the X-rays lose some of their energy, the loss depending on the angle at which they are scattered Those X-rays from an X-ray tube that are scattered back toward the detector  22  have a distribution of energies centred approximately around 22 keV.  
     [0056] For purposes of monitoring osteoporosis in humans, the calcaneus is the preferred bone to monitor because it has the highest percentage of spongy or trabecular bone in the human body which because of its high surface area is prone to mineral loss due to osteoporosis. Also clinical studies have shown a good correlation between bone mineral density of the calcaneus and the risk of fracture of other bones in the human body. In addition to the mineral constituent of calcium phosphate, the calcaneus also comprises collagen, a biological polymer, and bone marrow, which is primarily fat. Both collagen and bone marrow are normally classified as soft tissue.  
     [0057] Referring to FIGS. 3, 3 a  and  4  an alternative embodiment of an apparatus for estimating calcium content of trabecular bones is shown generally at  50 . Apparatus  50  includes a foot-well  52  (FIG. 4) which provides a foot and leg support for a users foot  54 . A housing  56  (FIG. 4) encloses an X-ray source/detector assembly  58  mounted therein. The source/detector assembly  58  provides an x-ray beam from source  60  through collimator  62  with cylindrical axis  64  and detection aperture  66  for a cylindrically symmetric radiation detector  68 , for example, a NaI(TI) scintillation counter and photomultiplier. Source/detector assembly  58  is connected to a control circuit  70  that while shown mounted outside housing  14  may be mounted inside housing  56 . A computer control and processor  70  is connected to detector  68  and x-ray source  60  and includes timing and control circuits and processors to process the data from the detector  68 . Restraining means (not shown) may be used to hold the user&#39;s foot  30  immobile on apparatus  50 .  
     [0058] The x-ray source/detector assembly  58  is mounted in housing  56  (FIG. 4) so that when a user&#39;s foot  30  is placed in apparatus  50  the source/detector assembly  58 , which is spring-loaded using a spring  72  to compress the soft tissue in region  74  (FIG. 3), is placed against the patient&#39;s heel so that the X-rays penetrate through the soft tissue  76  (FIG. 3). A mechanism  76  allows assembly  58  to be raised and lowered and shims  78  (FIG. 4) are provided to permit adjustment for differently sized feet.  
     [0059] The geometry of the collimator  62  and detection aperture  66  determines the degree of shadowing or geometric hindrance to prevent primary X-rays from the source and X-rays backscattered from the soft tissue  76  under the skin covering the calcaneus in region  74  (FIG. 3) from reaching detector  68 . The shape of the collimator  62  can be designed to give the desired amount of collimation of the X-ray beam. The beam of X-rays emanating from collimator  62  is backscattered from the soft tissue and the calcaneus within region  74 . The backscattered X-rays can be counted very efficiently by detector  68 , provided that these X-rays reach the detector without being absorbed.  
     [0060] Referring to block diagram of apparatus  50  shown in FIG. 5, the preferred X-ray source is a small X-ray tube  102 , for example model series SXR-80 provided by Superior X-ray Tube Company. The X-ray tube  102  is driven by a high voltage source  104  at 35-40 kV and provides a continuous energy spectrum of X-rays. Detector  68  includes a power supply  69  and detector  68  is connected to a multi-channel analyzer  108 , which is connected to the computer controller and processor  70 . Controller  70  receives the data from the detector and multi-channel analyzer and processes the data. Control signals from controller  70  to the power supply  104 , multi-channel analyzer  108  and detector power supply  69  controls the apparatus in operation.  
     [0061] Other suitable sources of X-rays when total backscattered intensity is measured, rather than an intensity spectrum, are radioactive sources such as  109 Cd that emits the K X-rays of silver in the energy range from 22 to 25 keV. The collimator  62  directs the cone of primary X-rays along the axis  64  in a direction away from the detector. The method relies upon measuring the intensity of X-rays backscattered from the various components making up the calcaneus (heel bone)  32  and covering soft tissue  76  and relating this intensity to the concentration of calcium present. The specific arrangement of the source-holder bearing against the side of the heel at region  74  is highly preferred because it exploits the size and shape of the calcaneus when accessed by X-rays in the above-noted direction. This location is also preferred due to a small amount of soft tissue between the calcaneus and the portion of the skin on the heel against which the source/detector assembly  58  (FIG. 3) is engaged.  
     [0062] Devices  10  (FIG. 1) and  50  (FIG. 3 and  4 ) may include a positioning device with the X-ray source and detector assembly being mounted on the positioning device for adjusting the position of the assembly in an arcuate path with respect to the person&#39;s foot. The positioning device includes a locking mechanism for locking assembly  58  in a selected position with respect to the person&#39;s foot, for example at the back or at the side of the foot depending on where the measurements are to be made.  
     [0063] For monitoring the calcium content of the heel bone there is required an X-ray energy that is capable of penetrating about 1.5 cm into a healthy calcaneus. This will ensure a much deeper penetration into an osteoporotic calcaneus because of the relative lack of calcium and hence decreased photoelectric absorption. The X-ray energy must be low enough to ensure a strong contrast in the absorption of both the primary and scattered X-rays because of the presence of calcium. An X-ray tube providing X-rays in the range of 10 to 40 keV is preferred and a  109 Cd source is also useful since it emits X-rays in the energy range 22 to 25 keV.  
     [0064] Similar to device  10  In FIGS. 1 and 2, the end portion of the detector/source assembly  58  in device  50  in FIGS. 3 and 4 containing the collimator  62  is held firmly against an anatomically determined position on the person&#39;s heel so that the X-rays penetrate through the compressed soft tissue  76  in region  74  (FIG. 3) and in a direction more or less parallel to the sole of the foot  30 . This means that the X-rays are transmitted into the calcaneus after penetration of typically 8 mm of soft tissue  76  that covers the calcaneus in region  34 . Most of the transmitted X-rays will collide with electrons in the chemical constituents of the calcaneus in the process of Compton scattering. In this process, the X-rays lose some of their energy, the loss depending on the angle at which they are scattered. Those X-rays from an X-ray tube that are scattered back toward the detector  22  have a distribution of energies centred approximately around 22 keV.  
     [0065] As mentioned above, it is predominantly Compton scattering that causes scattered X-rays to be directed back to the detector  22  in device  10  of FIG. 1 and detector  68  in device  50  of FIG. 3. The greater the density of the material, the more Compton scattering occurs and so normally it would be anticipated that an increase of bone mineral density would lead to an increase in backscatter intensity. However, the opposite occurs in the present invention because the energy of the X-rays has been chosen such that it is primarily the chance of absorption by calcium (rather than the chance of scattering) that determines the backscattered X-ray intensity.  
     [0066] It is noted that the contrast is not due to the difference of absorption and scattering by the calcium alone. Even in a non-osteoporotic calcaneus, most of the scattering is done by the other components making up the calcaneus rather than the calcium. So the objective is to achieve a situation in which absorption by calcium competes on more or less equal terms with scattering by the combination of these other components and calcium. Therefore, by making periodic measurements of the calcium content of the person&#39;s calcaneus the present invention can be used to monitor the development of osteoporosis based on changes in the measured X-ray radiation backscattered from the calcaneus resulting from varying concentrations of calcium phosphate over time.  
     [0067] In the X-ray measurement, the main effect is that the volume of the target that is “sampled” by the X-rays is determined by the total absorption if the target has a lower absorption (such as an osteoporotic heel) the counts are received from a larger volume of the calcaneus. As calcium content increases (progressively more healthy calcanei) the sample volume keeps its general shape but the volume decreases because backscattered photons are absorbed before they can reach the detector.  
     [0068] More specifically, with respect to shadowing, the collimator/aperture geometry is designed to provide sufficient shielding to prevent the primary photons from going directly to the detector in numbers that would mask the signals originating from the backscatter in the target. The geometry is also designed to reduce backscatter from soft tissue close to the detection aperture since this backscatter signal contains no information pertaining to bone mineral density and its effect is to reduce the sensitivity of the backscatter to bone mineral or calcium concentration. Since the thickness of soft tissue covering the calcaneus varies from person to person and tends to be thicker for larger heavier people the method and apparatus pertaining to the current invention recognizes the differences in people&#39;s soft tissue thickness and allows for soft tissue thickness explicitly in the estimation of calcium concentration or bone mineral density of the calcaneus.  
     [0069] Calibration of the backscatter count rate against calcium concentration and soft tissue thickness can be achieved using suitable calibration phantoms. These comprise, for example, finely powdered calcium phosphate (CaHPO 4 ) evenly dispersed in petroleum jelly contained in Nalgene bottles to represent the heel bone and water bags of different thicknesses to represent the soft tissue. The functional form of this calibration and its dependence on key parameters such as dimensions and materials composition can be understood in terms of the following mathematical model the application of which to estimate bone mineral density being part of the present invention.  
     [0070] For a one dimensional model the detected backscattered radiation is directed at 180° to the incident x-ray beam from the collimator, and it is assumed that the Compton backscattered radiation has the same energy as the incident beam and that no distinction is made between the Rayleigh and Compton backscattered components. FIG. 6 shows a one-dimensional representation of the heel anatomy with incident radiation intensity spectrum I O  (E) directed at a layer of soft tissue  76  (FIG. 3) of thickness T over a bone layer  32 , thickness B which is large compared to T and a geometric shadow or dead zone with thickness h. The parameters μ t , k t  and μ b , k b  are the absorption and backscattering coefficients respectively for the soft tissue and bone layers and  
     μ b =μ m α+μ s (1−α)  
       k   b   =k   m   α+k   s (1−α) 
     [0071] where the subscripts m and s refer to the mineral and soft tissue (e.g. marrow) content of the calcaneus and α is the fraction by volume of the bone comprising bone minerals. A straightforward physical argument leads to the formula for the backscattered intensity I B (E)  
       Equation 1:                 I   B          (   E   )           I   O          (   E   )         =           k   t       2        μ   t              (              -   2          μ   i        h       -            -   2          μ   i        T         )       +           k   .     b       2        μ   b                     -   2          μ   i        T                         
 
     [0072] This formula provides a functional relationship exhibiting the dependence of the backscattered intensity on the volumetric bone mineral concentration as represented by α and the soft tissue thickness T. Also involved is the shadow depth h which is a property of the apparatus and can be measured. The absorption and scattering parameters of the anatomical constituents can be estimated from their atomic composition, and may be simulated by the construction of phantoms as indicated above.  
     [0073] The soft tissue thickness T in region  36  at the back of the heel in FIG. 1 or region  76  at the side of the heel in FIG. 3 may be measured directly, using an ultrasound transducer  60  as shown in FIG. 4 situated near the collimator  62  and detector aperture  66  on the source/detector assembly  58 . Referring to FIGS. 7 a  and  7   b,  an ultrasound pulse emitted by the transducer  92  in intimate contact with the soft tissue in region  76  of the foot  30  is reflected from the calcaneus  32  and detected by the transducer  92 . Ultrasound is a quick and reliable mean for thickness gauging and typical operational frequencies are between 500 KHz and 100 MHZ, using piezoelectric transducers to generate bursts of sound waves when excited by electrical pulses. The present X-ray bone mineral densitometer device  60  uses 2.25 MHz and 5.0 MHz frequencies for optimizing both penetration and precision requirement in the highly attenuating and scattering soft tissue material.  
     [0074] The soft tissue thickness is then estimated by measuring the time required for a short ultrasonic pulse generated by a transducer to travel through the thickness of the soft tissue, reflect from the heel bone surface, and be returned to the transducer. The measured two-way transit time is divided by two to account for the down-and-back travel path, and then multiplied by the velocity of sound in the test material, The result is expressed in the well-known relationship: D=V*T/2 where D=the thickness of the soft tissue, V=the velocity of sound waves in the soft tissue, T=the measured round-trip transit time. The speed of sound in soft tissue is 1.54 mm/μs. For most adults, soft tissue thickness at the heel side is between 5 mm to 13 mm with an average of about 9 mm. The down-and-back travel time is about 6 to 16 μs.  
     [0075] The above equation (Equation 1) may be used to estimate calcium concentration or bone mineral density from the ratio of backscattered radiation I B  to the incident intensity I O . The first term represents backscatter from the soft tissue layer, while the second term represents backscatter from the bone layer assuming that thickness B is relatively large. Clearly by inserting numerical values for the intensities, the absorption and scattering constants and soft tissue thickness T, this equation can be solved for α, the average fractional concentration by volume of bone mineral in bone.  
     [0076] The one dimensional model as depicted in FIG. 6 with the model Equation 1 are approximations herein included to illustrate the method. Those skilled in the art will readily appreciate that this model may be extended to include the effects of the backscatter angle being less that 180°; the solid geometry of the collimator and detection aperture; the separation of the Compton and Rayleigh scattering contributions; and the energy dependence of the absorption and backscatter coefficients in the Compton scattering contribution.  
     [0077] Another embodiment of the present invention avoids the use of an ultrasound-based measurement of the soft tissue thickness T, and instead estimates bone mineral density directly from the backscattered radiation intensity energy spectrum, examples of which are shown in FIG. 8. The energy spectrum is denoted by the vector I n (E n ) wherein I n  is the intensity at energy value E n  and n is an integer with a range of values such that E n  spans the range of energies being detected. A preferred energy range is from about 10 to 30 keV. The method for estimating bone mineral density from the backscattered intensity vector I n  (E n ) follows the following steps:  
     [0078] 1. Use the theoretical model described above to calculate I n  (E n ) for a range of values of bone mineral concentration α, and soft tissue thickness T.  
     [0079] 2. Perform measurements of I O  (E O ) using phantoms with a similar range of values of α, and T.  
     [0080] 3. Modify model parameters so that the results of the first two steps are numerically similar.  
     [0081] 4. Invert the results of Step 3 with simple numerical formulae which express α, and T as functions of the intensity vector I n  (E n ), i.e.  
     α= f   1 (I n (E n ))  
     T=f 2 (I n (E n )) 
     [0082] 5. Refine this functional description by parameterizing the vector I n  (E n ) using two parameters CR, the total count rate and SF, the shape factor such that:  
     α=f 3 (CR, SF)  
     T=f 4 (CR, SF) 
     [0083]  where  
       CR   =       ∑     a           n                I   n          (     E   n     )                       
 
     [0084]  and SF is a vector formed from the normalized vector:  
             I   n          (     E   n     )                       ie   .              SF       =       1   CR            I   η          (     E   n     )                       
 
     [0085]  which for ease of computation may be further parameterized for example, as  
       SF   =       1   CR            ∑     k   =   1     N            I   k          (     N   -   k   +   1     )                         
 
     [0086]  where N is a suitably chosen cutoff value.  
     [0087] It will be understood that the parameterized equation for SF above is only one example or way of representation the shape factor SF and those skilled in the art will appreciate that there are numerous parameterization equations that may be used.  
     [0088] In this embodiment, from a measurement of the backscattered intensity spectrum I n  (E n ) using for example a multi-channel analyser the two parameters CR and SF can easily be computed and an estimate of volumetric bone mineral concentration α, can be determined using the function f 3  defined above.  
     [0089] In view of the fact that the strength of a bone (i.e., its resistance to fracture) is proportional to the mass density of the bone mineral and this, in turn, is proportional to the calcium content, the method disclosed herein for measurement of the intensity and intensity spectrum of the backscattered X-rays is a good indicator of the weakness of the bone, with the weaker bones giving higher backscattered X-ray intensities for the same soft tissue thickness.  
     [0090] The present invention measures an X-ray backscattering intensity that decreases with the mean volumetric density of bone mineral and hence the results can be expressed in units of grams/cubic centimeter. In contrast the DXA method provides an areal mineral density in units of grams/square centimeter. This is performed by measuring via transmission the mineral content with a measured surface area of bone. Clearly the same volumetric density can lead to different areal densities with different bone thicknesses or orientations.  
     [0091] Therefore, while the present invention has been described and illustrated with respect to the preferred embodiments for estimating mineral content of trabecular bones, it will be appreciated that numerous variations of these embodiments may be made depending on the application without departing from the scope of the invention as described herein.