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Tecnicas de Medicina
             Nuclear
      Bases y fundamentos
Procedimiento de obtención de imágenes médicas
Gammagrafía
Tomografia Computarizada por Emision de Fotones
     Simples (SPECT)
Tomografía por Emisión de Positrones . PET
Aprender conceptos básicos sobre cómo se generan
   las imágenes de Medicina Nuclear: gammagrafías,
   SPECT y PET
La Medicina Nuclear (MN) utiliza sustancias
radiactivas: isótopos (iso = igual; topos = lugar)

Fines: diagnósticos, terapéuticos y de
investigación.

Estassustancias radiactivas (radionúclidos o
trazadores) se introducen (in vivo) en la parte
del cuerpo que se quiere estudiar y se hace la
imagen detectando la radiación que emite.
 Es mínimamente invasiva (inyección).
 Es una técnica funcional: no estudia la
  anatomía sino su funcionamiento.
 Abarca en la practica, la totalidad del
  organismo.
 El nivel de radiación es similar al de
  otras técnicas radiológicas (ej. RX)
INTRODUCCIÓN

Algunos de los elementos más usados en MN:

Radionúclido Energía   T(1/2)                   Estudios
              (keV)
   99m
       Tc      140      6 horas    Cerebro, tiroides, riñón, pulmón
     131
         I     364     8´04 días          Tiroides y riñon
    67
       Ga       39     3´25 días        Tumores y abscesos
   133
       Xe       81      5´3 días                Pulmón
    201
        Tl   30-140    72 horas          Estudios cardíacos
Fines diagnósticos:




Renograma isotópico de un
paciente con HTA              Imágenes    de   Medicina   nuclear
secundaria, que muestra una   normales.
atrofia renal derecha
INTRODUCCIÓN
Diferencias (MN, rayos X):
  •MN usa radiación gamma ():
                  Energías           Frecuencias
        MN: [104 - 107 eV]       [1019 - 1022 Hz]
     Rayos X: [10 - 104 eV]      [1015 - 1019 Hz]

  •En MN la fuente de radiación es interna (en el interior del
  cuerpo del paciente), en rayos X es externa.

  •Trazador con radiofármaco: permite obtener una representación
  morfológica o información funcional o dinámica. (En rayos X
  contraste)
Esquema básico de un sistema de
                 IMN
 Sustancia
 radiactiva      Colimador


                                    Tubo                Analizador     Contador de
   órgano              Cristal de
                                    fotomultiplicador
                       centelleo                        de amplitud     impulsos
seleccionado
                 Radiación                                           Gammagrafía
Imágenes en Medicina Nuclear




Uso de Rx, radionucleidos y de
radiofarmacos en obtención de imágenes
Con las imagnes de Medicina Nuclear pueden observarse procesos fisiologicos,
como asimismo de Estructuras anatomicas.
En estas tecnicas se inyectan en los pacientes por via
Intravenosa, drogas radiactivas (Radiofarmacos) que emiten rayos gamma
Una vez que son captados por el tejido, organo o sistema de interes.
La cantidad de radionucleidos inyectados, se encuentran en el orden de
concentraciones
de nano a picomolar, de manera de disminuir los riesgos para los pacientes
Durante el estudio de los procesos fisiologicos delos mismos.

El semiperiodo fisico de estos materiales radiactivos es de solo unos pocos
Minutos a semanas. The time course of the
process being studied and the radiation dose to the target are
considered. The nuclear camera then, in effect, takes a time-exposure
"photograph" of the pharmaceutical as it enters and concentrates in
these tissues or organs. By tracing this blood flow activity, the
resulting nuclear medicine image tells physicians about the biological
activity of the organ or the vascular system that nourishes it. Nuclear
Medicine has a wide variety of uses, including the diagnosis of cancer,
 studying heart disease, circulatory problems, detecting kidney
 malfunction, and other abnormalities in veins, tissues and organs.
Medicina Nuclear: camara gamma
Radiofarmacos

EtOOC                 O            COOEt
                  N       NH

                  99mTc



                  S       S



        Aplicacion: perfusion cerebral
Imagen nuclear de
Cuerpo completo
SPECT: single photon emission
          computerized tomography

SPECT esta basada en una tecnica convencional de imagenes nucleares
Y usando ademas la tecnica y metodos de reconstruccion tomografica.
a
                              d
                      b
                          c



                                        Collimator

Electronics                           NaI(Ti)
                                      crystal
                                        PMT
    Y

                                  Counts/pixel
              X
Características de Rendimiento de los
   sistemas de imágenes de Medicina Nuclear
Resolución Espacial – Es la medida del grado de detalles provistos por la
imagen final reconstruida y por lo tanto del tamaño de lesiones que
potencialmente pueden ser detectadas. En otras palabras: cual es el grado
de detalle en el cual puede ser Observada una imagen o cuanto puede ser
resuelta o separada.

Sensibilidad, tiempo muerto – describe de que manera y con que eficiencia
se Detectan los decaimientos radiactivos y la distribucion del trazador, para
Formar finalmente la imagen.

Una fuente isotropica irradia en forma igual hacia todas las direcciones del
espacio. Los detectores, recolectan parte del total de los decaimientos,
dentro de un angulo Solido limitado por los colimadores.
Algunos de estos eventos se pierden debido a que el sistema necesita de
un tiempo de procesamiento entre la deteccion de un evento y el siguiente.
(dead time o Tiempo Muerto).
Signal to Noise ratio (SNR) - The relative strength of the information
and the noise. If the lesion is small compared with the spatial resolution
the contrast is reduced because the high lesion activity blurred into the
neighborhood by the detector response.

Uniformity, Linearity - The image of an object should be independent
of its position in the field of view. This is not true in real systems.

This can be assessed in calibration measurements to derive correction
factors. This reduces non-uniformity from 10% to 3%.
The conventional nuclear medicine imaging process.
Typical radionuclides used are 140 KeV Tc-99m and 70 KeV photons
from Tl-201.

The gamma ray photons emitted from the radiopharmaceutical
penetrate through the patient body and are detected by a set of
collimated radiation detectors. The emitted photon experience
interaction within the body by the photoelectric effect which stops
their emergence from the body or compton scattering which
transfers part of the energy to free electrons and the photon is
scattered into a new direction. These photons are also detected
by the camera and cause blurring of the image if un-treated with
image reconstruction and processing tools.
q
             Pixel I
             Activity ai
             Intersected area fi


    r


    P(r,q)
In 2-D tomographic imaging, the 1D detector array rotates around
the object distribution f(x,y) and collects projection data from various
 projection angles q. The integral transform of the object distribution
to its projections is given by:
                                                      



Ç
                         p' (t ,q )  ct I 0 exp[    z
                                                      
                                                            ( x , y )ds]

Which is called the Radon transform. The goal of image
reconstruction is to solve the inverse Radon transform. The solution
is the constructed image estimate f(x,y) of the object distribution
f(x,y).
The measured projection data can be written as the integral of
radioactivity along the projection rays.
The measured projection data can be written as the integral of
radioactivity along the projection rays.


                                                 z
                                                 
                                p(t ,q )  ce  ( x , y )ds
                                                 
In SPECT attenuation coefficient is not so important, so it can
be considered as constant in the body region under inspection.



                                    z
                                   
                      p(t ,q )  ce  ( x , y ) exp[  l ( x, y )]ds
                                   

l(x,y) is the pathlength between the point (x,y) and the edge of the
attenuator (or patient’s body) along the direction of the projection
ray.
The image reconstruction problem is further complicated by the non
stationary properties of the collimator detector and scatter response
functions and their dependence on the size and composition of the
patient’s body.
PROCEDIMIENTO DE OBTENCIÓN DE IMÁGENES MÉDICAS



  Cristal de centelleo (Yoduro de sodio con talio-
C INa(Ta))
  Transductor de energía  en energía luminosa.

    El cristal está acoplado a un conjunto de
     fotomultiplicadores de sección exagonal.
     Transductor de energía luminosa en electrones.

    Salida del fotomultiplicador: impulsos eléctricos
      amplitud proporcional a la energía de la
     radiación 
      y número proporcional a la actividad del
     elemento radiactivo en el punto analizado.

    Llevando estas señales a un circuito de
     posicionamiento, obtenemos las coordenadas X e
     Y, que indican la posición donde se ha detectado
     el fotón.
PROCEDIMIENTO DE OBTENCIÓN DE IMÁGENES MÉDICAS




Colimador tipo pinhole.
                              Colimadores de múltiples
La imagen es invertida y el   orificios paralelos,
tamaño dependiente dela       convergentes y divergentes
distancia al plano objeto.
 Gammagrafía
 SPECT
 PET
 Es la técnica mas simple.
 Su funcionamiento es similar al de las
  radiografías, una sola imagen por
  volumen.
 Varios tipos dependiendo de la zona:
    › Osea (tumores de hueso)
    › Pulmonar (trombos en las arterias
      pulmonares)
    › Tiroidea (nódulos en la tiroides)
    › Renal (función de los riñones)
Renograma isotópico de un
Gammagrafía de un
                           paciente con HTA secundaria,
adenoma suprarrenal
                           que muestra una clara atrofia
causante de hipertensión
                           renal derecha. La pequeña
arterial secundaria
                           cantidad de contraste isotópico
                           que se observa ha llegado por
                           vía del pedículo suprarrenal.
 Gammacámara que puede
  realizar movimientos de rotación
  alrededor del cuerpo del paciente
  o anillo.
 Imagen de la distribución del
  trazador en 3D utilizando la
  combinación de imágenes
  obtenidas desde diversas
  orientaciones. Pueden obtenerse
  imágenes de cortes axiales,
  sagitales, coronales.
 Mediante los algoritmos de
  retroproyección, similares a los TC,
  se puede reconstruir la imagen.
Ejemplo de un escáner de SPECT
fotón            Positrón



                                     fotón 

                     Detectores de
                     radiación 




Detección de positrones mediante dos gammacámaras
Tipos de cámaras PET:
  a) un par
  b) un anillo hexagonal giratorio alrededor del paciente
  c) Anillo circular que rodea al paciente
 PET generates images depicting the
  distributions of positron-emitting nuclides in
  patients
 In the typical scanner, several rings of
  detectors surround the patient
 PET scanners use annihilation coincidence
  detection (ACD) instead of collimation to
  obtain projections of the activity distribution
  in the subject
 Positrons emitted in matter lose most of their
  kinetic energy by causing ionization and
  excitation
 When a positron has lost most of its kinetic
  energy, it interacts with an electron by
  annihilation
 The entire mass of the electron-positron pair
  is converted into two 511-keV photons,
  which are emitted in nearly opposite
  directions
 If both annihilation photons interact with
  detectors, the annihilation occurred close
  to the line connecting the two interactions
 Circuitry within the scanner identifies
  interactions occurring at nearly the same
  time, a process called annihilation
  coincidence detection
 Circuitry of the scanner then determines the
  line in space connecting the locations of
  the two detector interactions
 ACD establishes the trajectories of the
  detected photons, a function performed by
  collimation in SPECT systems
 Much less wasteful of photons than
  collimation
 Avoids degradation of spatial resolution
  with distance from the detector that occurs
  when collimation is used to form projection
  images
 A true coincidence is the simultaneous
  interaction of emissions resulting from a
  single nuclear transformation
 A random coincidence, which mimics a
  true coincidence, occurs when emissions
  from different nuclear transformations
  interact simultaneously with the detectors
 A scatter coincidence occurs when one or
  both of the photons from a single
  annihilation are scattered, but both are
  detected
 Scintillation crystals coupled to PMTs are
  used as detectors in PET
 Signals from PMTs are processed in pulse
  mode to create signals identifying the
  position, deposited energy, and time of
  each interaction
 Energy signal is used for energy
  discrimination to reduce mispositioned
  events due to scatter and the time signal is
  used for coincidence detection
   Early PET scanners coupled each
    scintillation crystal to a single PMT
    › Size of individual crystal largely determined
      spatial resolution of the system
 Modern designs couple larger crystals to
  more than one PMT
 Relative magnitudes of the signals from the
  PMTs coupled to a single crystal used to
  determine the position of the interaction in
  the crystal
 Material must emit light very promptly to
  permit true coincident interactions to be
  distinguished from random coincidences
  and to minimize dead-time count losses
  at high interaction rates
 Must have high linear attenuation
  coefficient for 511-keV photons in order
  to maximize counting efficiency
   Most PET systems use crystals of bismuth
    germanate (Bi4Ge3O12, abbreviated BGO)
    › Light output 12% to 14% that of NaI(Tl), but
      greater density and average atomic number
      give it higher efficiency at detecting 511-keV
      photons
   Other inorganic scintillators being
    investigated: lutetium oxyorthosilicate and
    gadolinium oxyorthosilicate – faster light
    emission than BGO produces better
    performance at high interaction rates
 Energy signals sent to energy discrimination
  circuits which can reject events in which
  the deposited energy differs significantly
  from 511 keV to reduce effect of photon
  scatter in patient
 Energy window may be adjusted to include
  part of the Compton continuum, increasing
  sensitivity but also increasing the number of
  scattered photons detected
 Time signals of interactions not rejected by
  the energy discrimination circuits are used
  for coincidence detection
 When a coincidence is detected, the
  circuitry or computer of the scanner
  determines a line in space connecting the
  two interactions
    › PET system collects data for all projections
      simultaneously
   Projection data used to produce transverse
    images of the radionuclide distribution as in
    x-ray CT or SPECT
 In 2D (slice) data acquisition, coincidences
  are detected and recorded within each
  detector ring or small groups of adjacent
  detector rings
 PET scanners designed for 2D data
  acquisition have thin annular collimators
  (typically tungsten) to prevent most
  radiation emitted by activity outside a
  transaxial slice from reaching the detector
  ring for that slice
 Fraction of scatter coincidences reduced
  because of the geometry
 Coincidences within one or more pairs of
  adjacent detector rings may be added to
  improve sensitivity
 Data from each pair of detector rings are
  added to that of the slice midway between
  the two rings
 Increasing the number of adjacent rings
  used in 2D acquisition reduces the axial
  spatial resolution
 In 3D (volume) data acquisition, axial
  collimators are not used and
  coincidences are detected between
  many or all detector rings
 Greatly increases the number of true
  coincidences detected; may permit
  smaller activities to be administered to
  patients
   For the same administered activity, the
    increased interaction rate increases
    random coincidence fraction and dead-
    time count losses
    › 3D acquisition may require less activity to be
      administered
   Scatter coincidence fraction is much larger
    and number of interactions from activity
    outside the FOV is increased
    › Activity outside the FOV causes few true
      coincidences, but increases rate of random
      coincidences and dead-time count losses
 3D acquisition may be most useful in low-
  scatter studies, such as pediatric and
  brain studies
 Some PET systems are equipped with
  retractable axial collimators, permitting
  them to perform 2D or 3D acquisition
 For 2D data acquisition, image
  reconstruction methods are similar to SPECT
 For 3D data acquisition, special 3D analytic
  or iterative reconstruction techniques are
  required
 In PET, the correction for nonuniform
  attenuation can be applied to the
  projection data before reconstruction; in
  SPECT, the correction for nonuniform
  attenuation is intertwined with and
  complicates the reconstruction process
    Whole-body PET systems achieve a spatial
     resolution slightly better than 5 mm FWHM in
     the center of the detector ring
    Spatial resolution limited by:
    a) intrinsic spatial resolution of detectors
    b) distance traveled by positrons before annihilation
    c) the fact that annihilation photons are not emitted in
        exactly opposite directions from each other
    Intrinsic resolution of detectors most significant
 Spatial resolution of PET is best in the center
  of the detector ring and decreases slightly
  with distance from the center
 This occurs because of detector thickness
  and inability to determine the depth in the
  crystal where an interaction occurs
 Uncertainty in depth of interaction causes
  uncertainty in the line of response for
  annihilation photons that strike the
  detectors obliquely
 Distance traveled by positron before
  annihilation also degrades the spatial
  resolution
 Distance is determined by maximal positron
  energy of the radionuclide and density of
  the tissue
 Radionuclide that emits lower energy
  positrons yields superior resolution
 Activity in denser tissue yields higher
  resolution than activity in less dense tissue
 Although positrons lose nearly all of their
  momentum before annihilation, the positron
  and electron possess some residual
  momentum when they annihilate
 Conservation of momentum predicts that
  the resultant photons will not be emitted in
  exactly opposite directions
 This causes a small loss of resolution, which
  increases with the diameter of the detector
  ring
   Point source of positron-emitting radionuclide in air
    midway between two identical detectors
   True coincidence rate is
                         RT  2 AG   2

    where A is the activity of the source, G is the
    geometric efficiency of either detector, and  is the
    intrinsic efficiency of either detector
   Because the rate of true coincidences detected is
    proportional to the square of the intrinsic efficiency,
    maximizing the intrinsic efficiency is very important
 Differs in PET from SPECT, because both
  annihilation photons must escape the
  patient to cause a coincidence event to
  be registered
 Probability of both photons escaping the
  patient without interaction is the product
  of the probabilities of each escaping:
            e ) e
               x       d  x )
                                      ) e    d
 For a 20-cm path in soft tissue, the chance
  of both annihilation photons of a pair
  escaping the tissue without interacting is
  about 15%
 Attenuation causes a loss of information
  and, because the loss is not the same for all
  lines of response, causes artifacts in the
  reconstructed transverse images
 Loss of information also contributes to
  statistical noise in the images
   Some PET systems provide one or more
    retractable positron-emitting sources to
    measure the transmission of annihilation
    photons through the patient
    › Gamma-ray emitting source (Cs-137) may be
      used
 Sources revolve around the patient so
  attenuation is measured along all lines of
  response through the patient
 Attenuation correction cannot
  compensate for increased statistical noise;
  increases imaging time
   SPECT with high-energy collimators or
    multihead SPECT cameras with
    coincidence detection capability
    › Less acceptable for brain imaging or evaluation
      and staging of neoplasms
   Dedicated PET systems that are less
    expensive than those with full rings of BGO
    detectors, but which provide better
    coincidence detection sensitivity than
    double-head scintillation cameras
   PET scanner more efficient than scintillation
    camera due to use of annihilation
    coincidence detection instead of
    collimation; also yields superior spatial
    resolution
   Spatial resolution in SPECT deteriorates from
    edge toward center; PET is relatively
    constant across transaxial image, best at
    center
   Attenuation less severe in SPECT; accurate
    attenuation correction possible in PET (with
    transmission source)
   Cost: SPECT ~US$500,000; PET ~US$1M - $2M
 Main factors limiting availability of PET are
  the relatively high cost of a dedicated PET
  scanner and, in many areas, the lack of
  local sources of F-18 FDG
 Multihead SPECT cameras with coincidence
  circuitry and SPECT cameras with high-
  energy collimators provide less expensive,
  although less accurate, alternatives for
  imaging FDG
PET enables physicians to assess chemical or physiological changes
related to metabolism. Since the origins of many diseases are
biochemical in nature, these functional changes often predate or exceed
 structural change in tissue or organs. PET imaging utilizes a variety of
radiopharmaceuticals, called "tracers," to obtain images. PET tracers
mimic the natural sugars, water, proteins, and oxygen found in our
bodies. These tracers are injected into a patient and collect in various
tissues and organs. The PET system takes a time-exposure of the tracer
and generates a "photo" of cellular biological activities. PET images
can be used to measure many processes, including sugar metabolism,
blood flow and perfusion, receptor-ligand binding rates, oxygen
utilization and a long list of other vital physiological activities.
PET scanning uses artificial
radioactive tracers and
radionuclides. Their lifetime is
usually rather short, thus they
need to be produced on site.
Some examples of such materials are:

Radionuclide               Half life Application
Carbon-11                  20.3 min            Positron emitter for metabolism studies
Copper –64                 12.8 hours          clinical diagnostic agent for cancer and
                                               metabolic disorder
Iodine –122                3.76 min            Positron emitter for blood flow study
Iodine –131                8.1 days            Diagnose thyroid disorders including cancer
Iron - 52                  8.2 hours Iron tracer for PET bone marrow imaging
Nitrogen – 13              9.9 min             Positron emitter used as 13NH for heart
                                               perfusion studies
Strontium – 85             64 days             Study of bone formation metabolism
Oxygen – 15                123 sec             Positron emitter used for blood flow
Technetium – 99m 6 hours             The most widely used radiopharmaceutical
                                               In nuclear medicine
PET has a million fold sensitivity advantage over MRI in tracer study
and its chemical specificity, PET is used to study neuroreceptors in
the brain and other body tissues. It is efficient in the nanomolar range
where much of the receptor proteins in the body. Clinical studies
include tumors of the brain, breast, lung, lower GI tract. Additional
study of Alzheimer’s disease, Parkinson’s disease, epilepsy and
coronary artery disease affecting heart muscle metabolism and flow.
PET studies has immeasurably added to the understanding of oxygen
utilization and metabolic changes that accompany disease.
PET imaging starts with the injection of metabolically active tracer – a biologic
molecule that carries with it a positron emitting isotope. Over a few minutes the
isotope accumulates in an area of the body for which the molecule has an affinity.
i.e. glucose labeled with 11C or glucose analogue labeled with 18F, accumulates in the
 brain or tumors, where glucose is used as the primary source of energy. The
radioactive nuclei then decay by positron emission. In positron (positive electron) ,
 a nuclear proton changes into a positive electron and a neutron. The atom maintains
its atomic mass but decreases its atomic number by 1. The ejected positron combines
 with an electron almost instantaneously, and these 2 particles undergo the process of
annihilation. The energy associated with the masses of the positron and electron
particles is 12.022MeV in accordance with E=MC2 . This energy is divided equally
between 2 photons which fly away from one another at 1800 angle. Each photon has
an energy of 511 keV. These high energy gamma rays emerge from the body in
opposite directions and recorded simultaneously by pair of detectors.
The annihilation event that gave rise to them must have occurred somewhere
along the line connecting the detectors. Of course if one of the photons is scattered,
then the line of coincidence will be incorrect. After 100,000 or more annihilation
events are detected, the distribution of the positron-emitting tracer is calculated by
tomographic reconstruction procedures. PET reconstructs a 2 dimensional image
from the one dimensional projections seen at different angles. 3-D reconstructions
 can be done using 2D projections from multiple angles.
Tagged                                  Positron
metabolic                               annihilation
activity                        -
                                        photons (1800
                                +
                     N                  0.250)
                 P
11C   nucleus
                         
                               Lead
                               shield




  Scintillator
                             Tungsten
                             septum
 Detector crystal width
 Anger logic
 Photon noncolinarity
 Positron range
 Reconstruction algorithm
Acquisition




Calibration data
                                             Sinogram
                   Correction data




                                               Counts/ray
                   Reconstruction



                                     Image
SA reconstructed slices
• Blood volumes
• Oxygen consumption
• Perfusion
• Glucose consumption
CENTELLEADOR

FOTOMULTIPLICADOR
   RADIOISÓTOPOS
        β+ DE
  ELECTRÓNICA
     VIDA CORTA




      2 RAYOS γ
     COLINEALES
CICLOTRÓN      Radioisótopo        Inyección
 Radioisótopos         +                 al
      β+           Trazador           Paciente




Reconstrucción    Detección      Decaimiento β+
    de la             de                 y
   Imagen        Coincidencias   Aniquilación (2γ)
IMAGEN FUNCIONAL:

DISTRIBUCIÓN DEL TRAZADOR
     EN EL ORGANISMO

     APLICACIONES:

 -DETECCIÓN DE TUMORES
   - FUNCIÓN CEREBRAL
-EFICIENCIA DEL DETECTOR
- SENSIBILIDAD DEL SISTEMA
- RESOLUCIÓN TEMPORAL
- RESOLUCIÓN ESPACIAL
- RITMO DE RECUENTO
Punto
          Paralelepípedo




             Esfera
            ¿Dentro         No
           de Esfera?
                   Sí
                                 PROGRAMA DE
               Rayo
               Θ,φ                SIMULACIÓN
n veces

            Intersección
          Detectores-Rayo         MÉTODO
                                 MONTECARLO

              Detector
              ¿Dentro
                 de         No
                    Sí
              planos?

            Numeración
             Detectores

           Guardar datos
DETECTOR IDEAL
        LOR
                 2γ COLINEALES


EJE Y


                    Datos



         EJE X
EJE X   EJE Y
π/3

  π/3
υxr
                                    F1

                                y                                            υy
                                                                                             υxr
                                                            EQUIVALENTES
                                                  F2
                       f(x,y)        φ
                                                                                             υx
                                            x



             
                        2i xr xr                       2i xr xr            
f ( x, y )     d xr e             xr W ( xr )  dxr e
                                                                          p( xr , ) d
                                                                                      
             0                                                                 
φ

                φ



                                    0
                       xr




                    Transformada de Radon       0            xr

                
P( xr ,  )      f ( x, y) ( x cos   ysen  x )dxdy
                
                                                    r
PROYECCIÓN   RETROPROYECCIÓN
Sobremuestreo en el         Tipos de Filtros
origen de frecuencias

    υy

            Δφ

                                     Filtro rampa
            υx

                 Δυxr              Ventana Hamming



                        0                       υ
p(xr,φ)                p·cos




                xr             xr



          cos(2 N xr )
4

                                                                     2
                                  xr = x·cosφ +y·senφ
             
                        2i xr xr                       2i xr xr            
f ( x, y )     d xr e             xr W ( xr )  dxr e
                                                                          p( xr , ) d
                                                                                      
             0                                                                 
                                                                     1
                                                    3

                                                    5
                            φ
                                                              (x, z)
                            υxr
                                                                 3
                            xr
                             1                                   4

                             2                                   5
6 mm   4 mm   3 mm
FWHM ≈ 3 mm
xr (cm)




          φ (rad)
CORREGIDA
    POR
NORMALIZACIÓN
xr (cm)




          φ (rad)
CORREGIDA
    POR
NORMALIZACIÓN
CONCLUSIONES:

- Simulación de la Emisión y Detección de
  Gammas en P.E.T.


- Reconstrucción de Imágenes con FBP en
  Modo 2D.

- Estudios Realizados: Resolución,
  Normalización, Filtros.
Imágenes PET de un cerebro activo en varios estados, tras inyección
   intravenosa de 18F, con deoxy-glucosa. (de Shung-92)
Low Pet Scan of Patient.
 The Positron Emission Tomography
Lab at Mount Sinai Medical
Center is located in New York City.
We are dedicated to the study of
Alzheimers, Schizophrenia and
general questions regarding how
the brain changes with age. This
research is accomplished through
the co-registration of PET and MRI
modalities. We have developed
software in order to better aid in
this research
http://neurosurgery.mgh.harvard.edu/pet-hp.htm
   Parkinson's Disease
http://neurosurgery.mgh.harvard.edu/pet-hp.htm
   Huntington's disease
 Sitio caliente: sala de preparación de
  radiofármacos
 Sala de pacientes
 Sala de exploraciones
 Sala de almacenamiento de residuos
  radiactivos
 Equipo humano: Especialista y técnico

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Tecnologias mn

  • 1. Tecnicas de Medicina Nuclear Bases y fundamentos
  • 2. Procedimiento de obtención de imágenes médicas Gammagrafía Tomografia Computarizada por Emision de Fotones Simples (SPECT) Tomografía por Emisión de Positrones . PET
  • 3. Aprender conceptos básicos sobre cómo se generan las imágenes de Medicina Nuclear: gammagrafías, SPECT y PET
  • 4. La Medicina Nuclear (MN) utiliza sustancias radiactivas: isótopos (iso = igual; topos = lugar) Fines: diagnósticos, terapéuticos y de investigación. Estassustancias radiactivas (radionúclidos o trazadores) se introducen (in vivo) en la parte del cuerpo que se quiere estudiar y se hace la imagen detectando la radiación que emite.
  • 5.  Es mínimamente invasiva (inyección).  Es una técnica funcional: no estudia la anatomía sino su funcionamiento.  Abarca en la practica, la totalidad del organismo.  El nivel de radiación es similar al de otras técnicas radiológicas (ej. RX)
  • 6. INTRODUCCIÓN Algunos de los elementos más usados en MN: Radionúclido Energía T(1/2) Estudios (keV) 99m Tc 140 6 horas Cerebro, tiroides, riñón, pulmón 131 I 364 8´04 días Tiroides y riñon 67 Ga 39 3´25 días Tumores y abscesos 133 Xe 81 5´3 días Pulmón 201 Tl 30-140 72 horas Estudios cardíacos
  • 7.
  • 8. Fines diagnósticos: Renograma isotópico de un paciente con HTA Imágenes de Medicina nuclear secundaria, que muestra una normales. atrofia renal derecha
  • 9. INTRODUCCIÓN Diferencias (MN, rayos X): •MN usa radiación gamma (): Energías Frecuencias MN: [104 - 107 eV] [1019 - 1022 Hz] Rayos X: [10 - 104 eV] [1015 - 1019 Hz] •En MN la fuente de radiación es interna (en el interior del cuerpo del paciente), en rayos X es externa. •Trazador con radiofármaco: permite obtener una representación morfológica o información funcional o dinámica. (En rayos X contraste)
  • 10. Esquema básico de un sistema de IMN Sustancia radiactiva Colimador Tubo Analizador Contador de órgano Cristal de fotomultiplicador centelleo de amplitud impulsos seleccionado Radiación  Gammagrafía
  • 11. Imágenes en Medicina Nuclear Uso de Rx, radionucleidos y de radiofarmacos en obtención de imágenes
  • 12. Con las imagnes de Medicina Nuclear pueden observarse procesos fisiologicos, como asimismo de Estructuras anatomicas. En estas tecnicas se inyectan en los pacientes por via Intravenosa, drogas radiactivas (Radiofarmacos) que emiten rayos gamma Una vez que son captados por el tejido, organo o sistema de interes. La cantidad de radionucleidos inyectados, se encuentran en el orden de concentraciones de nano a picomolar, de manera de disminuir los riesgos para los pacientes Durante el estudio de los procesos fisiologicos delos mismos. El semiperiodo fisico de estos materiales radiactivos es de solo unos pocos Minutos a semanas. The time course of the process being studied and the radiation dose to the target are considered. The nuclear camera then, in effect, takes a time-exposure "photograph" of the pharmaceutical as it enters and concentrates in these tissues or organs. By tracing this blood flow activity, the resulting nuclear medicine image tells physicians about the biological activity of the organ or the vascular system that nourishes it. Nuclear Medicine has a wide variety of uses, including the diagnosis of cancer, studying heart disease, circulatory problems, detecting kidney malfunction, and other abnormalities in veins, tissues and organs.
  • 14. Radiofarmacos EtOOC O COOEt N NH 99mTc S S Aplicacion: perfusion cerebral
  • 16. SPECT: single photon emission computerized tomography SPECT esta basada en una tecnica convencional de imagenes nucleares Y usando ademas la tecnica y metodos de reconstruccion tomografica.
  • 17. a d b c Collimator Electronics NaI(Ti) crystal PMT Y Counts/pixel X
  • 18. Características de Rendimiento de los sistemas de imágenes de Medicina Nuclear Resolución Espacial – Es la medida del grado de detalles provistos por la imagen final reconstruida y por lo tanto del tamaño de lesiones que potencialmente pueden ser detectadas. En otras palabras: cual es el grado de detalle en el cual puede ser Observada una imagen o cuanto puede ser resuelta o separada. Sensibilidad, tiempo muerto – describe de que manera y con que eficiencia se Detectan los decaimientos radiactivos y la distribucion del trazador, para Formar finalmente la imagen. Una fuente isotropica irradia en forma igual hacia todas las direcciones del espacio. Los detectores, recolectan parte del total de los decaimientos, dentro de un angulo Solido limitado por los colimadores. Algunos de estos eventos se pierden debido a que el sistema necesita de un tiempo de procesamiento entre la deteccion de un evento y el siguiente. (dead time o Tiempo Muerto).
  • 19. Signal to Noise ratio (SNR) - The relative strength of the information and the noise. If the lesion is small compared with the spatial resolution the contrast is reduced because the high lesion activity blurred into the neighborhood by the detector response. Uniformity, Linearity - The image of an object should be independent of its position in the field of view. This is not true in real systems. This can be assessed in calibration measurements to derive correction factors. This reduces non-uniformity from 10% to 3%.
  • 20. The conventional nuclear medicine imaging process. Typical radionuclides used are 140 KeV Tc-99m and 70 KeV photons from Tl-201. The gamma ray photons emitted from the radiopharmaceutical penetrate through the patient body and are detected by a set of collimated radiation detectors. The emitted photon experience interaction within the body by the photoelectric effect which stops their emergence from the body or compton scattering which transfers part of the energy to free electrons and the photon is scattered into a new direction. These photons are also detected by the camera and cause blurring of the image if un-treated with image reconstruction and processing tools.
  • 21.
  • 22.
  • 23.
  • 24. q Pixel I Activity ai Intersected area fi r P(r,q)
  • 25. In 2-D tomographic imaging, the 1D detector array rotates around the object distribution f(x,y) and collects projection data from various projection angles q. The integral transform of the object distribution to its projections is given by:  Ç p' (t ,q )  ct I 0 exp[  z   ( x , y )ds] Which is called the Radon transform. The goal of image reconstruction is to solve the inverse Radon transform. The solution is the constructed image estimate f(x,y) of the object distribution f(x,y). The measured projection data can be written as the integral of radioactivity along the projection rays.
  • 26. The measured projection data can be written as the integral of radioactivity along the projection rays. z  p(t ,q )  ce  ( x , y )ds  In SPECT attenuation coefficient is not so important, so it can be considered as constant in the body region under inspection. z  p(t ,q )  ce  ( x , y ) exp[  l ( x, y )]ds  l(x,y) is the pathlength between the point (x,y) and the edge of the attenuator (or patient’s body) along the direction of the projection ray. The image reconstruction problem is further complicated by the non stationary properties of the collimator detector and scatter response functions and their dependence on the size and composition of the patient’s body.
  • 27.
  • 28. PROCEDIMIENTO DE OBTENCIÓN DE IMÁGENES MÉDICAS Cristal de centelleo (Yoduro de sodio con talio- C INa(Ta)) Transductor de energía  en energía luminosa.  El cristal está acoplado a un conjunto de fotomultiplicadores de sección exagonal. Transductor de energía luminosa en electrones.  Salida del fotomultiplicador: impulsos eléctricos amplitud proporcional a la energía de la radiación  y número proporcional a la actividad del elemento radiactivo en el punto analizado.  Llevando estas señales a un circuito de posicionamiento, obtenemos las coordenadas X e Y, que indican la posición donde se ha detectado el fotón.
  • 29. PROCEDIMIENTO DE OBTENCIÓN DE IMÁGENES MÉDICAS Colimador tipo pinhole. Colimadores de múltiples La imagen es invertida y el orificios paralelos, tamaño dependiente dela convergentes y divergentes distancia al plano objeto.
  • 30.
  • 32.  Es la técnica mas simple.  Su funcionamiento es similar al de las radiografías, una sola imagen por volumen.  Varios tipos dependiendo de la zona: › Osea (tumores de hueso) › Pulmonar (trombos en las arterias pulmonares) › Tiroidea (nódulos en la tiroides) › Renal (función de los riñones)
  • 33. Renograma isotópico de un Gammagrafía de un paciente con HTA secundaria, adenoma suprarrenal que muestra una clara atrofia causante de hipertensión renal derecha. La pequeña arterial secundaria cantidad de contraste isotópico que se observa ha llegado por vía del pedículo suprarrenal.
  • 34.  Gammacámara que puede realizar movimientos de rotación alrededor del cuerpo del paciente o anillo.  Imagen de la distribución del trazador en 3D utilizando la combinación de imágenes obtenidas desde diversas orientaciones. Pueden obtenerse imágenes de cortes axiales, sagitales, coronales.  Mediante los algoritmos de retroproyección, similares a los TC, se puede reconstruir la imagen.
  • 35. Ejemplo de un escáner de SPECT
  • 36. fotón  Positrón fotón  Detectores de radiación  Detección de positrones mediante dos gammacámaras
  • 37. Tipos de cámaras PET: a) un par b) un anillo hexagonal giratorio alrededor del paciente c) Anillo circular que rodea al paciente
  • 38.  PET generates images depicting the distributions of positron-emitting nuclides in patients  In the typical scanner, several rings of detectors surround the patient  PET scanners use annihilation coincidence detection (ACD) instead of collimation to obtain projections of the activity distribution in the subject
  • 39.
  • 40.
  • 41.
  • 42.
  • 43.  Positrons emitted in matter lose most of their kinetic energy by causing ionization and excitation  When a positron has lost most of its kinetic energy, it interacts with an electron by annihilation  The entire mass of the electron-positron pair is converted into two 511-keV photons, which are emitted in nearly opposite directions
  • 44.
  • 45.  If both annihilation photons interact with detectors, the annihilation occurred close to the line connecting the two interactions  Circuitry within the scanner identifies interactions occurring at nearly the same time, a process called annihilation coincidence detection  Circuitry of the scanner then determines the line in space connecting the locations of the two detector interactions
  • 46.  ACD establishes the trajectories of the detected photons, a function performed by collimation in SPECT systems  Much less wasteful of photons than collimation  Avoids degradation of spatial resolution with distance from the detector that occurs when collimation is used to form projection images
  • 47.  A true coincidence is the simultaneous interaction of emissions resulting from a single nuclear transformation  A random coincidence, which mimics a true coincidence, occurs when emissions from different nuclear transformations interact simultaneously with the detectors  A scatter coincidence occurs when one or both of the photons from a single annihilation are scattered, but both are detected
  • 48.
  • 49.  Scintillation crystals coupled to PMTs are used as detectors in PET  Signals from PMTs are processed in pulse mode to create signals identifying the position, deposited energy, and time of each interaction  Energy signal is used for energy discrimination to reduce mispositioned events due to scatter and the time signal is used for coincidence detection
  • 50. Early PET scanners coupled each scintillation crystal to a single PMT › Size of individual crystal largely determined spatial resolution of the system  Modern designs couple larger crystals to more than one PMT  Relative magnitudes of the signals from the PMTs coupled to a single crystal used to determine the position of the interaction in the crystal
  • 51.
  • 52.  Material must emit light very promptly to permit true coincident interactions to be distinguished from random coincidences and to minimize dead-time count losses at high interaction rates  Must have high linear attenuation coefficient for 511-keV photons in order to maximize counting efficiency
  • 53. Most PET systems use crystals of bismuth germanate (Bi4Ge3O12, abbreviated BGO) › Light output 12% to 14% that of NaI(Tl), but greater density and average atomic number give it higher efficiency at detecting 511-keV photons  Other inorganic scintillators being investigated: lutetium oxyorthosilicate and gadolinium oxyorthosilicate – faster light emission than BGO produces better performance at high interaction rates
  • 54.
  • 55.  Energy signals sent to energy discrimination circuits which can reject events in which the deposited energy differs significantly from 511 keV to reduce effect of photon scatter in patient  Energy window may be adjusted to include part of the Compton continuum, increasing sensitivity but also increasing the number of scattered photons detected
  • 56.  Time signals of interactions not rejected by the energy discrimination circuits are used for coincidence detection  When a coincidence is detected, the circuitry or computer of the scanner determines a line in space connecting the two interactions › PET system collects data for all projections simultaneously  Projection data used to produce transverse images of the radionuclide distribution as in x-ray CT or SPECT
  • 57.
  • 58.  In 2D (slice) data acquisition, coincidences are detected and recorded within each detector ring or small groups of adjacent detector rings  PET scanners designed for 2D data acquisition have thin annular collimators (typically tungsten) to prevent most radiation emitted by activity outside a transaxial slice from reaching the detector ring for that slice  Fraction of scatter coincidences reduced because of the geometry
  • 59.
  • 60.  Coincidences within one or more pairs of adjacent detector rings may be added to improve sensitivity  Data from each pair of detector rings are added to that of the slice midway between the two rings  Increasing the number of adjacent rings used in 2D acquisition reduces the axial spatial resolution
  • 61.
  • 62.  In 3D (volume) data acquisition, axial collimators are not used and coincidences are detected between many or all detector rings  Greatly increases the number of true coincidences detected; may permit smaller activities to be administered to patients
  • 63.
  • 64. For the same administered activity, the increased interaction rate increases random coincidence fraction and dead- time count losses › 3D acquisition may require less activity to be administered  Scatter coincidence fraction is much larger and number of interactions from activity outside the FOV is increased › Activity outside the FOV causes few true coincidences, but increases rate of random coincidences and dead-time count losses
  • 65.  3D acquisition may be most useful in low- scatter studies, such as pediatric and brain studies  Some PET systems are equipped with retractable axial collimators, permitting them to perform 2D or 3D acquisition
  • 66.  For 2D data acquisition, image reconstruction methods are similar to SPECT  For 3D data acquisition, special 3D analytic or iterative reconstruction techniques are required  In PET, the correction for nonuniform attenuation can be applied to the projection data before reconstruction; in SPECT, the correction for nonuniform attenuation is intertwined with and complicates the reconstruction process
  • 67. Whole-body PET systems achieve a spatial resolution slightly better than 5 mm FWHM in the center of the detector ring  Spatial resolution limited by: a) intrinsic spatial resolution of detectors b) distance traveled by positrons before annihilation c) the fact that annihilation photons are not emitted in exactly opposite directions from each other  Intrinsic resolution of detectors most significant
  • 68.  Spatial resolution of PET is best in the center of the detector ring and decreases slightly with distance from the center  This occurs because of detector thickness and inability to determine the depth in the crystal where an interaction occurs  Uncertainty in depth of interaction causes uncertainty in the line of response for annihilation photons that strike the detectors obliquely
  • 69.
  • 70.  Distance traveled by positron before annihilation also degrades the spatial resolution  Distance is determined by maximal positron energy of the radionuclide and density of the tissue  Radionuclide that emits lower energy positrons yields superior resolution  Activity in denser tissue yields higher resolution than activity in less dense tissue
  • 71.
  • 72.  Although positrons lose nearly all of their momentum before annihilation, the positron and electron possess some residual momentum when they annihilate  Conservation of momentum predicts that the resultant photons will not be emitted in exactly opposite directions  This causes a small loss of resolution, which increases with the diameter of the detector ring
  • 73. Point source of positron-emitting radionuclide in air midway between two identical detectors  True coincidence rate is RT  2 AG 2 where A is the activity of the source, G is the geometric efficiency of either detector, and  is the intrinsic efficiency of either detector  Because the rate of true coincidences detected is proportional to the square of the intrinsic efficiency, maximizing the intrinsic efficiency is very important
  • 74.  Differs in PET from SPECT, because both annihilation photons must escape the patient to cause a coincidence event to be registered  Probability of both photons escaping the patient without interaction is the product of the probabilities of each escaping: e ) e  x   d  x ) ) e  d
  • 75.
  • 76.  For a 20-cm path in soft tissue, the chance of both annihilation photons of a pair escaping the tissue without interacting is about 15%  Attenuation causes a loss of information and, because the loss is not the same for all lines of response, causes artifacts in the reconstructed transverse images  Loss of information also contributes to statistical noise in the images
  • 77. Some PET systems provide one or more retractable positron-emitting sources to measure the transmission of annihilation photons through the patient › Gamma-ray emitting source (Cs-137) may be used  Sources revolve around the patient so attenuation is measured along all lines of response through the patient  Attenuation correction cannot compensate for increased statistical noise; increases imaging time
  • 78.
  • 79. SPECT with high-energy collimators or multihead SPECT cameras with coincidence detection capability › Less acceptable for brain imaging or evaluation and staging of neoplasms  Dedicated PET systems that are less expensive than those with full rings of BGO detectors, but which provide better coincidence detection sensitivity than double-head scintillation cameras
  • 80.
  • 81. PET scanner more efficient than scintillation camera due to use of annihilation coincidence detection instead of collimation; also yields superior spatial resolution  Spatial resolution in SPECT deteriorates from edge toward center; PET is relatively constant across transaxial image, best at center  Attenuation less severe in SPECT; accurate attenuation correction possible in PET (with transmission source)  Cost: SPECT ~US$500,000; PET ~US$1M - $2M
  • 82.  Main factors limiting availability of PET are the relatively high cost of a dedicated PET scanner and, in many areas, the lack of local sources of F-18 FDG  Multihead SPECT cameras with coincidence circuitry and SPECT cameras with high- energy collimators provide less expensive, although less accurate, alternatives for imaging FDG
  • 83.
  • 84.
  • 85. PET enables physicians to assess chemical or physiological changes related to metabolism. Since the origins of many diseases are biochemical in nature, these functional changes often predate or exceed structural change in tissue or organs. PET imaging utilizes a variety of radiopharmaceuticals, called "tracers," to obtain images. PET tracers mimic the natural sugars, water, proteins, and oxygen found in our bodies. These tracers are injected into a patient and collect in various tissues and organs. The PET system takes a time-exposure of the tracer and generates a "photo" of cellular biological activities. PET images can be used to measure many processes, including sugar metabolism, blood flow and perfusion, receptor-ligand binding rates, oxygen utilization and a long list of other vital physiological activities.
  • 86. PET scanning uses artificial radioactive tracers and radionuclides. Their lifetime is usually rather short, thus they need to be produced on site.
  • 87. Some examples of such materials are: Radionuclide Half life Application Carbon-11 20.3 min Positron emitter for metabolism studies Copper –64 12.8 hours clinical diagnostic agent for cancer and metabolic disorder Iodine –122 3.76 min Positron emitter for blood flow study Iodine –131 8.1 days Diagnose thyroid disorders including cancer Iron - 52 8.2 hours Iron tracer for PET bone marrow imaging Nitrogen – 13 9.9 min Positron emitter used as 13NH for heart perfusion studies Strontium – 85 64 days Study of bone formation metabolism Oxygen – 15 123 sec Positron emitter used for blood flow Technetium – 99m 6 hours The most widely used radiopharmaceutical In nuclear medicine
  • 88. PET has a million fold sensitivity advantage over MRI in tracer study and its chemical specificity, PET is used to study neuroreceptors in the brain and other body tissues. It is efficient in the nanomolar range where much of the receptor proteins in the body. Clinical studies include tumors of the brain, breast, lung, lower GI tract. Additional study of Alzheimer’s disease, Parkinson’s disease, epilepsy and coronary artery disease affecting heart muscle metabolism and flow.
  • 89. PET studies has immeasurably added to the understanding of oxygen utilization and metabolic changes that accompany disease.
  • 90. PET imaging starts with the injection of metabolically active tracer – a biologic molecule that carries with it a positron emitting isotope. Over a few minutes the isotope accumulates in an area of the body for which the molecule has an affinity. i.e. glucose labeled with 11C or glucose analogue labeled with 18F, accumulates in the brain or tumors, where glucose is used as the primary source of energy. The radioactive nuclei then decay by positron emission. In positron (positive electron) , a nuclear proton changes into a positive electron and a neutron. The atom maintains its atomic mass but decreases its atomic number by 1. The ejected positron combines with an electron almost instantaneously, and these 2 particles undergo the process of annihilation. The energy associated with the masses of the positron and electron particles is 12.022MeV in accordance with E=MC2 . This energy is divided equally between 2 photons which fly away from one another at 1800 angle. Each photon has an energy of 511 keV. These high energy gamma rays emerge from the body in opposite directions and recorded simultaneously by pair of detectors.
  • 91. The annihilation event that gave rise to them must have occurred somewhere along the line connecting the detectors. Of course if one of the photons is scattered, then the line of coincidence will be incorrect. After 100,000 or more annihilation events are detected, the distribution of the positron-emitting tracer is calculated by tomographic reconstruction procedures. PET reconstructs a 2 dimensional image from the one dimensional projections seen at different angles. 3-D reconstructions can be done using 2D projections from multiple angles.
  • 92. Tagged Positron metabolic annihilation activity - photons (1800 + N 0.250) P 11C nucleus  Lead shield Scintillator Tungsten septum
  • 93.  Detector crystal width  Anger logic  Photon noncolinarity  Positron range  Reconstruction algorithm
  • 94. Acquisition Calibration data Sinogram Correction data Counts/ray Reconstruction Image
  • 95.
  • 97. • Blood volumes • Oxygen consumption • Perfusion • Glucose consumption
  • 98. CENTELLEADOR FOTOMULTIPLICADOR RADIOISÓTOPOS β+ DE ELECTRÓNICA VIDA CORTA 2 RAYOS γ COLINEALES
  • 99. CICLOTRÓN Radioisótopo Inyección Radioisótopos + al β+ Trazador Paciente Reconstrucción Detección Decaimiento β+ de la de y Imagen Coincidencias Aniquilación (2γ)
  • 100. IMAGEN FUNCIONAL: DISTRIBUCIÓN DEL TRAZADOR EN EL ORGANISMO APLICACIONES: -DETECCIÓN DE TUMORES - FUNCIÓN CEREBRAL
  • 101. -EFICIENCIA DEL DETECTOR - SENSIBILIDAD DEL SISTEMA - RESOLUCIÓN TEMPORAL - RESOLUCIÓN ESPACIAL - RITMO DE RECUENTO
  • 102.
  • 103. Punto Paralelepípedo Esfera ¿Dentro No de Esfera? Sí PROGRAMA DE Rayo Θ,φ SIMULACIÓN n veces Intersección Detectores-Rayo MÉTODO MONTECARLO Detector ¿Dentro de No Sí planos? Numeración Detectores Guardar datos
  • 104. DETECTOR IDEAL LOR 2γ COLINEALES EJE Y Datos EJE X
  • 105. EJE X EJE Y
  • 107.
  • 108.
  • 109. υxr F1 y υy υxr EQUIVALENTES F2 f(x,y) φ υx x    2i xr xr    2i xr xr  f ( x, y )     d xr e  xr W ( xr )  dxr e  p( xr , ) d  0    
  • 110. φ φ 0 xr Transformada de Radon 0 xr  P( xr ,  )    f ( x, y) ( x cos   ysen  x )dxdy  r
  • 111. PROYECCIÓN RETROPROYECCIÓN
  • 112. Sobremuestreo en el Tipos de Filtros origen de frecuencias υy Δφ Filtro rampa υx Δυxr Ventana Hamming 0 υ
  • 113. p(xr,φ) p·cos xr xr cos(2 N xr )
  • 114. 4 2 xr = x·cosφ +y·senφ    2i xr xr    2i xr xr  f ( x, y )     d xr e  xr W ( xr )  dxr e  p( xr , ) d  0     1 3 5 φ (x, z) υxr 3 xr 1 4 2 5
  • 115. 6 mm 4 mm 3 mm
  • 116. FWHM ≈ 3 mm
  • 117. xr (cm) φ (rad)
  • 118. CORREGIDA POR NORMALIZACIÓN
  • 119. xr (cm) φ (rad)
  • 120. CORREGIDA POR NORMALIZACIÓN
  • 121. CONCLUSIONES: - Simulación de la Emisión y Detección de Gammas en P.E.T. - Reconstrucción de Imágenes con FBP en Modo 2D. - Estudios Realizados: Resolución, Normalización, Filtros.
  • 122. Imágenes PET de un cerebro activo en varios estados, tras inyección intravenosa de 18F, con deoxy-glucosa. (de Shung-92)
  • 123. Low Pet Scan of Patient. The Positron Emission Tomography Lab at Mount Sinai Medical Center is located in New York City. We are dedicated to the study of Alzheimers, Schizophrenia and general questions regarding how the brain changes with age. This research is accomplished through the co-registration of PET and MRI modalities. We have developed software in order to better aid in this research
  • 126.  Sitio caliente: sala de preparación de radiofármacos  Sala de pacientes  Sala de exploraciones  Sala de almacenamiento de residuos radiactivos  Equipo humano: Especialista y técnico