Physics of Diagnostic X-rays For English please visit: http://www.thefreedictionary.com/ For More information about X-rays: http://www.youtube.com/watch?v=7hwzg0yi9ms http://www.youtube.com/watch?v=bc0eojwkxpu http://www.youtube.com/watch?v=i3s5hfq2yme http://www.youtube.com/watch?v=mego38kzg8g (interaction of X-rays) http://www.youtube.com/watch?v=n9fklbaktey http://www.youtube.com/watch?v=_erp1blposu http://www.youtube.com/watch?v=0vuqgknpy2y
Objectives: - Electromagnetic wave spectrum - Pr inciples of x-r ays pr oduction - Atomic gener ation of x-r ays - X-rays spectrum and absorption - Interaction of x-rays with matter - Making an x-r ay image (Rӧntgenogr am) - Dosimetry units - Biological effects of x-rays Refer ences: 1- Medical Physics textbook by Camer on 2- Physics in Biology and Medicine, Thir d Edition by Paul Davidovits 3- Physics of the Human Body, by Ir ving P. Her man
Electr omagnetic r adiation: Electr omagnetic r adiation (EM r adiation or EMR) consists of two electr ic (hor izontal plane) and magnetic (ver tical plane) fields per pendicular to each other and per pendicular to the pr opagation dir ection as shown in figur e. Electr omagnetic r adiation is char acter ized by: 1- In space, it tr avels with the speed of light and under go r efraction, attenuation, diffr action, diffr action, and r eflection. 2- Wavelength (λlambda, measur ed in Length unit (nm) ) is the distance between any two points have the same phase. 3- Fr equency (f) is the number of cycles or vibr ations under gone dur ing one unit of time (Hertz (Hz) or S -1 ) ( Speed of light C = λ(wavelength) x f (fr equency)) 4- Period (T) is the time for one complete cycle (S). 5- Ener gy of electr omagnetic r adiation is calculated by (E=hxf) (h is Planck s constant, h= 6.5821 10-16 ev s)
Electr omagnetic spectr um is shown in the under neath Figur e X-r ays wer e discover ed by Wilhelm Conr ad Röntgen X-r ays have a wavelength in the r ange of 0.01 to 10 nm, cor responding to ener gies in the r ange of 120 ev to 120 kev (please Calculate). X-r ays fr om about 0.12 to 12 kev ar e classified as Soft" x-r ays (low ener gy), and fr om about 12 to 120 kev as Har d" x - r ays, due to their penetr ating abilities. Soft X-r ays har dly penetr ate matter at all. Har d X-r ays can penetr ate solid objects, and their most common use is to take images of the inside of objects in diagnostic r adiogr aphy.
X-r ays applications ar e str ongly dependent on the ener gy and wavelength and object to be imaged (Why?). Differ ent applications use differ ent par ts of the X- ray spectrum [micrometer μm = 10-6 m, nanometer nm = 10-9 m, picometer pm = 10-12 m and femtometer fm = 10-15 m].
X- r ays pr oduction X-r ays is pr oduced in the tr aditional X-r ay tube when high speed (High ener getic ) electr ons collide with a high atomic number element (Tar get). X-r ays ar e pr oduced in the tube shown the Figur e (Cathode) Focal spot (Anode) Tar get Evacuat ed Electr on beam The elements of X-r ays tube ar e: 1- Evacuated Glass Envelop: to avoid the pr oduction of collision between high ener getic electr ons and air molecules, which give r ise to pr oduction of undesir ed r adiation. 2- Heated filament (Cathode) emits electr ons by ther moionic emission, the number of electr ons is contr olled by the electr ic cur r ent in the filament (Contr ol the X-r ays intensity). The higher the electric curr ent, the higher the number of emitted electrons, the higher the X-rays intensity. 3- High voltage to accelerate the emitted electr ons (Contr ol both the X-r ays ener gy and intensity), Explain the effect of potential defer ence on the intensity and ener gy of X-r ays.
4- Anode: it is the component in which the x-r ays ar e pr oduced in a ver y small ar ea on the sur face of the anode known as the focal spot (wher e the accelerated electr ons collide with the tar get). 4-1- Most x-r ay tubes use tungsten ( 184 74W 110 ), which has an atomic number (number of pr otons within its nucleus) of 74, ability to maintain its str ength at high temper atures. 4-2 Anode has two pr imar y functions: 4-3 X-r ays pr oduction thr ough inter action with ener getic electr ons. 4-4 Mor e than 99% of ener getic electr on that str iking the anode is conver ted into heat which may damage the anode. The mater ial for the anode is selected to enhance these functions. Fur thermor e X-r ay tube is equipped with a cooling system and r otating anode. Near ly all x-r ay tubes use tungsten tar gets (W). The Z for tungsten is 74 & its melting point is about 3422 C and high boiling point (5555 o C). Atomic number is defined as The number of pr otons found in the nucleus of the atom. 4-5 The impor tance of r otating the tar get is to spr ead the pr oduced heat over a lar ge ar ea (never theless, this heat will damage the tar get) in or der to over come the over heating effect at the focal spot of the anode (tar get).
- Efficiency of x- r ays pr oduction is defined as The total x-r ay ener gy expr essed as a fr action of the total electr ical ener gy impar ted into the sur face of the anode. - The two factor s that deter mine x-r ays pr oduction efficiency ar e the voltage applied to the tube (KV p ) and the atomic number of the anode (Z). An appr oximate r elationship to calculate the efficiency is: - Efficiency = KV p x Z 10-6 In x-r ay tube the number (quantity) of electr ons accelerated towar d the anode depend on the temper ature of the filament. The intensity of the pr oduce x-r ays when electr ons str ike the anode depends on the anode mater ial. In gener al, the higher the atomic number (Z) and a high melting point of the tar get, the mor e efficiently x-r ays ar e pr oduced. The maximum ener gy of the pr oduce x-r ays photons deter mined by the accelerating voltage [Kilovolt peak (kv p )]. Power (P) put into the sur face of the tar get is given by: P = I x V (Watt) wher e, I is the cur r ent in milli amper es (ma) and V is the voltage (potential differ ence) in volts.
Animation of how x-ray tube works http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html# c1
Atomic generation of X - rays In X-r ay tube, X-r ays ar e pr oduced by two differ ent mechanisms; these ar e: A- Br emsstr ahlung (Continuous or white r adiation): It is pr oduced when ener getic electr ons loss some or all of their kinetic ener gy (1/2mv 2, wher e v is the velocity of electr on)because the attr action for ce between electr ons (negative Char ge) and the nucleus of the tar get atom (Positive Char ge), the differ ence in ener gy will emitted as X-r ays with wide spectr um (Why?) Let the ener gy of incident electr on is 1 and ener gy after and deflection is E 2, 1> 2, then the emitted X-r ays has Ener gy : = = 1-2 The maximum X-r ays ener gy is emitted when an ener getic electr on is completely stopped with in the tar get, 2 = 0. All kinetic ener gy of the electr on will be conver ted into X-r ays = = 1= evp (e is the char ge of electr on) The minimum wavelength of maximum X-r ay ener gy, (C = 3x10 8 m/s., is Velocity of light) The Br emsstr ahlung r adiation is known as white r adiation since it contains a wide r ange of wavelengths (Fr equencies and ener gies).
The Br emsstr ahlung intensity pr oduced for a given number of electr ons str iking the anode depends upon two factor s: (1) Atomic number (Z) of the tar get (the higher the atomic number, the gr eater the deceler ation of the electr ons). (2) Kilovolt peak (KV p ) (The faster the electr ons, the mor e they penetr ate into the r egion of the anode s nucleus), The higher the electr on ener gy, the high the ener gy can r elease. * Deduce the r elation between λ min and the accelerating potential? * Relative x-r ays intensity and accelerating potential (Vp)? λ m in
2- Character istic radiation involves a collision between high-speed (ener getic) electrons and the orbital electrons in the target s atoms. The interaction can occur only if the incoming electron has a kinetic ener gy greater than the binding ener gy of the electron within the atom. When a primary fast moving electron strikes (knocks) an inner bound (K) electron in a target atom and knocks it out of its orbit, the vacancy in the K shell is filled almost immediately by an electron from an outer shell either L or M which, cause ener gy levels in the target to change. In this process, a Character istic K x-ray photon is emitted which have discrete ener gies. For Tung sten, an L shell electron filling K shell vacancy results in characteristic X-ray radiation of energ y The same held for M-Shell hf = E K - she ll - E L - She ll = 69.5 K ev-10.2 k ev = 59.3 k ev
An x-ray photon emitted when an electron falls from the L shell to replace the vacancy in the K shell is called: K α x-ray, and that emitted when an electron falls from the M shell to the K shell is called K β x-ray. Character istic x- rays photon (either αor β) are produced with ener gy equal to the difference in the ener gies of the outer and inner shell electrons. Character istic x-rays are of little use at present except in mammography machine dedicated to breast images. Elect ron binding ener gy is a measure of the ener gy required to free electrons from their atomic orbits Gr aph plotting of x-r ays pr oduced by a moder n x-r ay gener ator (wavelength ver sus r elative intensity) L "K M "K (10-20%) ( Broad smooth curve) (80-90% ) [ Multiple(wide range) wavelengths] 6
Contr ol of x-r ays spectrum: An x-r ay tube is an ener gy conver ter. It r eceives electr ical ener gy and converts it into x- ray and heat. The heat is an undesir able by pr oduct. X-rays tubes ar e designed to maximize x-ray pr oduction and to dissipate heat as r apidly as possible. The quantity (exposur e) and quality (spectr um) of the x-ray can be controlled by adjusting the electr ical quantities [volt & cur rent] (KV p, ma), filament temper ature and exposure time applied to the x-r ay tube: (1) Filament Temper atur e: The higher the filament temper ature, the more electrons are released fr om the cathode which in tur n increases the pr oduction of x-rays. (2) Kilovolt peak (KVp): Incr easing the KV p incr eases the speed of the electr ons that str ike the tar get (anode). The faster the electrons, the more they penetr ate into the r egion of the anode s nucleus. (3) Level of cur rent in milliamper e (ma): Incr easing the ma incr eases the number of electr ons emitted fr om the cathode. This, incr eases the number of x-r ays pr oduced. (4) Time: A timer on the x-rays tube contr ols the number of seconds that electrons are produced by the cathode. This also influences the number of x-rays pr oduced.
Ener gy of x-r ay beam The maximum ener gy (quality) of x-r ays photons pr oduced depends on the accelerating voltage (potential) kilovolt peak (KV p ) applied in the tube. The higher the voltage the mor e efficient x- r ays ar e pr oduced. X-r ays ar e char acter ized by ther e ener gy in KeV. For example, x-r ay tube oper ating at 80 KV p will pr oduce x-r ays with a spectr um of ener gies up to a maximum of 80 KeV KeV is The ener gy an electr on gains or losses in going acr oss a potential differ ence of 1000 volt = 1kilo volt. KeV = 1.6 x 10-16 (joules) = 1.6 x 10-9 (er g) The intensity of the pr oduce x-r ays when electr ons str ike the anode depends on the anode mater ial. In gener al, the higher the atomic number (Z) and a high melting point of the tar get, the mor e efficiently x-r ays ar e pr oduced.
How X-r ays ar e absor bed? X-r ays ar e not well absor bed equally by all mater ials; if they wer e they would not be ver y useful in diagnosis. Heavy elements such as calcium ( atomic number is 20, it is the main component of bone), ar e much better absor ber s of x -r ays than light elements such as car bon (atomic number 6), oxygen (atomic number 8) and hydr ogen (atomic number 1). 1- Str uctur es containing heavy elements, like the bones stand out clear ly in x-r ay. 2- Soft tissues like fat, muscles and tumor s all absor b about equally well and ar e thus they ar e difficult to distinguish fr om each other on an x-r ays image.
Inter action of X-rays with matter X-rays interaction with matter is strongly correlated with both the matter structure (atomic number) and X- rays energy, see the opposite figure. Photoelectr ic effect (PE): Occur s in the intense electr ic field near the nucleus, when the incoming x-r ay encounters and transfers all of its energy to a K electr on. Compton effect (CE): Occurs when x-ray encounters an electron from an outer M - shell Pair production (PP): When a high energy x-ray photon enter s the intense electr ic field of the nucleus.
K inetic energy: ½ mv 2. Binding energy: At the nuclear level, binding energy is the energy required to disassemble a nucleus into the same number of free unbound neutrons and protons. Low x-ray energy and high atomic number materials Photoelectric effect ( PE): when the incoming x-ray ( of energy = hf = hc/λ), encounters and transfers all of its energy to an electron of an inner K shell electron [ therefore disappears ( absorbed)]. This inner bound electron of mass ( m e ) will escape from the atom. The ejected electron is called photoelectron ( PE), its binding energy must be lower than that of the incoming x- ray. Vacancy created in K - shell will be filled by electron from the L - shell, producing characteristic radiation ( Energy of characteristic photon is equal to energy difference between the two shells). PE is more useful than the Compton one, because it permits to see bone and other heavy materials.
Compton effect ( CE): High x- ray energy and low atomic number materials R ecoil electron Higher energy shorter wavelength L ower energy L onger wavelength Compton effect ( CE): Occurs when x-ray encounters an electron from an outer M shell ( loosely bound electron). This electron is ejected and the remaining energy of the incident x-ray will be re-emitted immediately in the form of a ( Compton) scattered x-ray photon. The direction of the emitted x- ray can be anywhere other than that of the original x- ray. Compton scattering results in: 1) Ionization events, 2) recoil electron, 3) positive ion and 4) lower energy scattered photon. In Compton interaction the incoming x- ray photon will be scattered with lesser energy and longer wavelength ( Compton x-ray).
Pair production ( PP): x- ray photon energy must exceed ( more than) 1.022 MeV. PP occurs in high atomic number materials. It leads to formation of two charged particles from a single high- energy photon. Formation of two charged particles from a single high- energy photon E=( m e - + m e + )C 2 = 1.022 ( MeV) X-rays > 1.022 MeV Pair production ( PP): When the energy of a high energy x- ray photon ( exceeds 1.022 MeV) enters the intense electric field of the nucleus, this energy will be converted into two particles e - ( electron) & e + ( positron) ( i.e., energy of x-ray photon is converted into mass). The remaining energy will be given to the particles as kinetic energy. When e + spent its K.E in ionization it annihilates ( collide) with an electron and produce annihilation photons. Both then vanish and their mass energy appears as two photons of 511 K ev each called annihilation radiation, which go in opposite directions.
Attenuation of X-rays is the R eduction in the intensity of x-ray due to absorption and scattering of some of the photons out of the x-ray beam. A simple method to measure the attenuation of x-ray is shown in this figure. It consists of: ( 1) A narrow beam of x-rays produced with an x-ray source this beam goes through a collimator ( a lead plate with hole in it) ( 2) Absorber ( sheets of aluminum introduced into the beam pass) ( 3) X-ray detector to measure the beam s intensity. X- ray source Narrow beam Collimator The exponential equation describes the attenuation curve for a monoenergetic x- ray beam ( photons of a single energy) :I is the radiation intensity after traveling a thickness x and I o is the original radiation I ( Un- attenuated) o I = I o e -μx Absorber ( attenuating material) ( Attenuated) (T% ) Scattered x- rays X-ray detector -intensity. Intensity of x- ray decreases exponentially [ intensity decreases with increasing thickness of absorbing material]. x I [ Graph of the transmitted intensity versus the thickness of attenuator]
The relation between I and I o - The un-attenuated (in front of the absorber) x-rays beam intensity is (I o ). The intensity of the attenuated ( transmitted or scattered) beam ( I) will decrease exponentially. - The lower energy (soft) x-rays are absorbed at once than the higher energy ( hard) x- rays. - The exponential equation describing the attenuation curve for a monoenergetic x-ray beam is: I = I o e -μx - Linear attenuation (absorption) coefficient (μ) of the attenuator (cm -1 ), depends on the energy of x- ray photons and the material of the attenuator. x = thickness of the attenuator in cm and e = 2.718 - If the thick ness ( x) of the absorber material is doubled, the linear attenuation coefficient ( μ) of this material will not change. - Linear attenuation coefficient is the probability of interactions per unit length = mass density [ g/cm 3 ], N A = 6.02 x10 23 [ 1/mol] (Avogadro s number), A = Atomic Weight [ g/mol] and a = Atomic cross section [ cm 2 ].
Since I = I o e -μx I/I o = e -μx ln I/I o = -μx ln I o /I= μx Example: If the intensity of the un-attenuated x-r ay beam is 150 (count/sec) and the intensity after attenuation is 30 (count/sec). Find the thickness of the attenuator, knowing that the linear attenuation coefficient of the attenuator is 0.5 (cm -1 ). Answer: ln I o /I = μx ln (150/30) = 1.6094 x = 1.6094/0.5 = 3.2188 (cm)
Example: Calculate the thickness of the lead (μ= 0.58 cm -1 ) used to attenuate the x- ray intensity to tenth its original value. Answer: ln I o /I= μx I/I o =1/10 I o /I = 10 ln 10 = 0.58 x = 2.3025 Thickness= x = 2.3025/0.58 = 3.9699 4 ( cm)
The half value layer (HVL) for an x-ray beam is defined as the thickness of a given material that will reduce the beam intensity by one- half. HVL is related to the linear attenuation coefficient ( μ) by the following equation: HVL = ln2/μ= 0.693/µ ( cm) The equivalent energy of an x- ray beam is determined by its half- value layer; it is the energy of a monoenergetic x-ray beam with the same half-value layer. Example: For a certain material if the linear attenuation coefficient is 0.562 (cm -1 ). Calculate the half value layer. Answer: HVL= 0.693/0.562= 1.233 ( cm) Example: If the linear attenuation coefficient is 0.05 (cm -1 ). Find the HVL Answer: HVL = ln2/0.05 = 13.8629 13.9 (cm)
Example: What is the linear attenuation coefficient ( μ) of a given material. if you know that the thickness of this material reduced the x-ray beam intensity to its half value is 15 ( cm). Find the thickness ( x) needed from this material to reduce the beam intensity ( I) to the tenth of its original value ( I o ). Answer: HVL = 15 ( cm) then I o /I = 10 I/I o = 1/10 HVL = ln 2/μthen μ= ln 2 / HVL = 0.693 /15 = 0.0462 ( cm - 1 ) ln ( I o /I) = μx then x = ln ( I o /I) / μ= ln ( 10)/0.0462 =2.3025/0.0462 = 49.839 ( cm)
Mass attenuation coefficient (μ m ) Mass attenuation coefficient (μ m ) is used to remove the effect of density (ρ) when comparing attenuation in several materials. μ m equals to the linear attenuation coefficient ( µ) divided by density (ρ= g/cm 3 ) of the material µ m = µ/ρ ( cm 2 /g) then μ= μ m ρ Since I = I o e - μx then I = I o e - ( μ m ρ) x µ m emphasizes that the mass is primarily responsible for attenuating the x-rays. μ m is independent of physical state of material. Example: For a certain material if the linear attenuation coefficient is 0.562 ( cm - 1 ) and its density is 320 ( g/cm 3 ). Calculate the mass attenuation coefficient of this material. Answer: µ m =µ/ρ=0.562/320=0.001756=1.756x10-3 ( cm 2 /g)
Making an x-ray image X-ray source Collimat or Object Film Processing Image ( wrapped in black paper ) It is easy to make an x-r ay image, or Rӧntgenogr am. X-r ays images ar e shadows cast on film by var ious str uctur es in the body. (Differ ent type tissues attenuate X-r ays differ entially) The x-r ay imaging chain is a fair ly simple system consisting of the sour ce, collimator (which blocks the str ay x-r ays), object which the x-r ays inter act with, and the detector (photogr aphic film in this case).
X- ray images Soft tissues Hand X-rays Bone Head X-ray Bone is very dense and absorbs or attenuates a great deal of the x-rays. The soft tissues around the bones is much less dense than bone and that is why it attenuates or absorbs less x- ray. To obtain a satisfactory x- ray image of thick parts such as the abdomen and hips it is necessary to reduce the scattered radiation at the film. The amount of scattered radiation at the film depends on the energy of the x-ray and the thickness of the tissue that the x-ray beam passes through. The thicker the tissue the
What is meant by penumbr a? Penumbr a: is The next to the shadow ar ea. It is the blur r ed edge of the shadow. The width of the Penumbr a can be calculated fr om this equation: P = (f x b)/a Penumbr a (P) can be r educed by incr easing the distance fr om the x-r ay tube to the patient, and minimized the distance between patient and film (detector). But the most effective par ameter is the focal spot, which should be minimized to, minimized the penumbr a (p), See under neath figur e. The focal spot should be as small as conditions per mit, in or der to secur e the shar pest possible definition in the r adiogr aphic image. However, the smaller the focal spot, the less ener gy it will withstand without damage.
Impr ove the image quality by using Gr id to eliminate the scatter ed X-r ays photons X-rays source X-rays photons Patient L ead stripes ( absorb )scattered X- rays Grid Film ( detector) Gr id used to r educe the amount of scatter ed r adiation. It consists of alternating thin lead str ipes and wide plastic str ipes. The un-scatter ed x-r ays pass thr ough the plastic str ipes, while most of the scatter ed x-r ays ar e absor bed by the lead str ipes.
To get a good x-r ay image, the following conditions should be meet: 1- Small focal spot (minimum volume of x-r ay sour ce) (why? Think at Penumbr a) 2- Positioning the patient as close as possible to the film (why? Think at Penumbr a) 3- Incr easing the distance between the x-r ay sour ce and the patient and film as much as possible (why? Think at Penumbr a) 4- Reducing the amount of scatter ed r adiation str iking the film by using a gr id consisting of a ser ies of thin lead and wide plastic str ips. These str ips ar e aligned so that the unscatter ed x-r ays fr om the sour ce will go thr ough the plastic str ips and str ike the film, while most of the scatter ed r adiation will str ike the lead str ips and be absor bed [hence the gr id is used to decr ease the effect of scatter ed r adiation]. 5- It is necessar y to avoid motion of the patient dur ing exposur e, since motion causes blur r ing of the x-r ay image.
The measur e of x-r ays ionizing ability is called exposur e The effect of ionizing r adiation on matter (especially living tissue) is mor e closely r elated to the amount of ener gy deposited r ather than the char ge. This is called absor bed dose. Gr ay (Gy=J/Kg) is the Standar d Inter national (SI) unit of absor bed dose. [1 gr ay=100 r ad]. Gr ay is defined as The amount of r adiation r equir ed to deposit ener gy of 1 Joule in 1 Kilogr am of any kind of matter. Rad [Radiation absor bed dose] It is the tr aditional unit used to measur e r adiation dose = 0.01 Joule of ener gy deposited per kilogr am of mass (J/Kg) = 100 er g of ener gy per gr am of mass.
Radiation to patients fr om X-r ays Gy can be used for any type of radiation and Gy does not descr ibe the biological different radiations. effects of the Quantity Definition New Units Exposure Char ge per unit mass of air Roentgen 1 R = 2.58 x 10-4 C/kg (R) Absor bed dose to tissue T fr om r adiation of type R DT,R Equivalent dose to tissue T H T Effective Dose (E) Ener gy of r adiation R absor bed per unit mass of tissue T: 1 Rad = 100 er gs/g 1 Gy = 1 joule/kg 1 Gy = 100 rads Sum of contr ibutions of dose to T fr om differ ent r adiation types, each multiplied by the r adiation weighting factor (wr) H T = Σ(R wr) DT,R Sum of equivalent doses to or gans and tissues exposed, each multiplied by the appr opr iate tissue weighting factor (wt) Gray (Gy) Siever t (Sv) Siever t (Sv) E = Σ(T wt) H T
Biological effects of radiation Dir ect action R adiation damage to cells may occur directly from a radiation hit on the critical target, this results in ionization and excitation of the molecules inside the nucleus of cells Somatic (Body cells) Cancer is the somatic effect of most concern in r adiation r isk assessment. For chr onic exposur e to r adiation over many year s, the late somatic effects may occur dur ing the ir radiation per iod. Genetic (Germinal cells) genetic effects in childr en of ir radiated par ents. Indir ect action Cr eation of fr ee r adicals (r eactive chemicals) due to inter action of r adiation (xr ays) with water and leads to for mation of H 2 O 2 which is a ver y power ful oxidative agents causing damaging to DNA or undesir ed modification in DNA.
Biological effects of r adiation - Most Human Body cells can be damaged by ionizing r adiation - Different cell can receive different amounts of radiation before damage can occur Immatur e cells (cells that undergo r apid cell division) have a higher sensitivity to r adiation than matur e cells - Lymphocytes (white blood cells) ar e the most r adiosensitive - Repr oductive cells (sper m and ova) ar e highly sensitive - Linings and cover s of body or gans ar e moder ately sensitive - Muscle and ner ve cells ar e least sensitive.