# FFF.1 General Concepts of X-Ray Angiography

This chapter describes the general concepts of the X-Ray Angiography equipment and the way these concepts can be encoded in SOP Instances of the Enhanced XA SOP Class. It covers the time relationships during the image acquisition, the X-Ray generation parameters, the conic projection geometry in X-Ray Angiography, the pixel size calibration as well as the display pipeline.

The following general concepts provide better understanding of the examples for the different application cases in the rest of this Annex.

## FFF.1.1 Time Relationships

### FFF.1.1.1 Time Relationships of a Multi-frame Image

The following figure shows the time-related attributes of the acquisition of X-Ray multi-frame images. The image and frame time attributes are defined as absolute times, the duration of the entire image acquisition can be then calculated.

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Figure FFF.1.1-1Time Relationships of a Multi-frame Image

### FFF.1.1.2 Time Relationships of one Frame

The following figure shows the time-related attributes of the acquisition of an individual frame “i” and the relationship with the X-Ray detector reading time and simultaneous ECG waveform acquisition.

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Figure FFF.1.1-2Time Relationships of one Frame

Notes: 1. Positioner angle values, table position values etc… are measured at the Frame Reference Datetime.

2. Dose of the frame is the cumulative dose: PRE-FRAME + FRAME

## FFF.1.2 Acquisition Geometry

This chapter illustrates the relationships between the geometrical models of the patient, the table, the positioner, the detector and the pixel data.

The following figure shows the different steps in the X-Ray acquisition that influences the geometrical relationship between the patient and the pixel data.

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Figure FFF.1.2-1Acquisition Steps Influencing the Geometrical Relationship Between the Patient and the Pixel Data

### FFF.1.2.1 Patient Description

Refer to Annex A for the definition of the patient orientation.

A point of the patient is represented as: P = (P left , P posterior , P head ).

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Figure FFF.1.2-2Point P Defined in the Patient Orientation

### FFF.1.2.2 Patient Position

#### FFF.1.2.2.1 Table Description

The table coordinates are defined in the section C.8.7.4.1.4 of PS 3.3.

The table coordinate system is represented as: (O t , X t , Y t , Z t ) where the origin O t is located on the tabletop and is arbitrarily defined for each system.

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Figure FFF.1.2-3Table Coordinate System

#### FFF.1.2.2.2 Options for Patient Position on the X-Ray Table

The position of the patient in the X-Ray table is described in the section C.7.3.1.1.2 of PS 3.3.

The table below shows the direction cosines for each of the three patient directions (Left, Posterior, Head) related to the Table coordinate system (X t , Y t , Z t ), for each patient position on the X-Ray table:

 Patient Position Patient left direction Patient posterior direction Patient head direction Recumbent - Head First - Supine (1, 0, 0) (0, 1, 0) (0, 0, 1) Recumbent - Head First - Prone (-1, 0, 0) (0, -1, 0) (0, 0, 1) Recumbent - Head First - Decubitus Right (0, -1, 0) (1, 0, 0) (0, 0, 1) Recumbent - Head First - Decubitus Left (0, 1, 0) (-1, 0, 0) (0, 0, 1) Recumbent - Feet First - Supine (-1, 0, 0) (0, 1, 0) (0, 0, -1) Recumbent - Feet First - Prone (1, 0, 0) (0, -1, 0) (0, 0, -1) Recumbent - Feet First- Decubitus Right (0, -1, 0) (-1, 0, 0) (0, 0, -1) Recumbent - Feet First -Decubitus Left (0, 1, 0) (1, 0, 0) (0, 0, -1)

### FFF.1.2.3 Table Movement

#### FFF.1.2.3.1 Isocenter Coordinate System

The Isocenter coordinate system is defined in section C.8.19.6.13.1.1 of PS 3.3.

#### FFF.1.2.3.2 Table Movement in the Isocenter Coordinate System

The table coordinate system is defined in section C.8.19.6.13.1.3 of PS 3.3 where the table translation is represented as (T X ,T Y ,T Z ). The table rotation is represented as (At 1 , At 2 , At 3 ).

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Figure FFF.1.2-4At1: Table Horizontal Rotation Angle

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Figure FFF.1.2-5At2: Table Head Tilt Angle

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Figure FFF.1.2-6At3: Table Cradle Tilt Angle

A point (P Xt , P Yt , P Zt ) in the table coordinate system (see Figure FFF.1.2-7) can be expressed as a point (P X , P Y , P Z ) in the Isocenter coordinate system by applying the following transformation:

(P X , P Y , P Z ) T = (R 3 . R 2 . R 1 ) T . (P Xt , P Yt , P Zt ) T + (T X , T Y , T Z ) T

And inversely, a point (P X , P Y , P Z ) in the Isocenter coordinate system can be expressed as a point (P Xt , P Yt , P Zt ) in the table coordinate system by applying the following transformation:

(P Xt , P Yt , P Zt ) T = (R 3 . R 2 . R 1 ) . ( (P X , P Y , P Z ) T - (T X , T Y , T Z ) T )

Where R 1 , R 2 and R 3 are defined as follows:

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Figure FFF.1.2-7Point P in the Table and Isocenter Coordinate Systems

### FFF.1.2.4 Positioner Movement

#### FFF.1.2.4.1 Positioner Movement in the Isocenter Coordinate System

The positioner coordinate system is defined in section C.8.19.6.13.1.2 of PS 3.3 where the positioner angles are represented as (Ap 1 , Ap 2 , Ap 3 ).

A point (P Xp , P Yp , P Zp ) in the positioner coordinate system can be expressed as a point (P X , P Y , P Z ) in the Isocenter coordinate system by applying the following transformation:

(P X , P Y , P Z ) T = (R 2 . R 1 ) T . ( R 3 T . (P Xp , P Yp , P Zp ) T )

And inversely, a point (P X , P Y , P Z ) in the Isocenter coordinate system can be expressed as a point (P Xp , P Yp , P Zp ) in the positioner coordinate system by applying the following transformation:

(P Xp , P Yp , P Zp ) T = R 3 . ( (R 2 . R 1 ) . (P X , P Y , P Z ) T )

Where R 1 , R 2 and R 3 are defined as follows:

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#### FFF.1.2.4.2 X-Ray Incidence and Image Coordinate System

The following concepts illustrate the model of X-Ray cone-beam projection:

The X-Ray incidence represents the vector going from the X-Ray source to the Isocenter.

The receptor plane represents the plane perpendicular to the X-Ray Incidence, at distance SID from the X-Ray source. Applies for both image intensifier and digital detector. In case of digital detector it is equivalent to the detector plane.

The image coordinate system is represented by (o, u, v), where “o” is the projection of the Isocenter on the receptor plane.

The source to isocenter distance is called ISO. The source image receptor distance is called SID.

The projection of a point (P Xp , P Yp , P Zp ) in the positioner coordinate system is represented as a point (P u , P v ) in the image coordinate system.

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Figure FFF.1.2-8Projection of a Point of the Positioner Coordinate System

A point (P Xp , P Yp , P Zp ) in the positioner coordinate system (O p , X p , Y p , Z p ) can be expressed as a point (P u , P v ) in the image coordinate system by applying the following transformation:

P u = (SID / (ISO – P Yp ) ) . P Xp

P v = (SID / (ISO – P Yp ) ) . P Zp

The ratio SID / (ISO - P Yp ) is also called magnification ratio of this particular point.

### FFF.1.2.5 Field of View Transformations

#### FFF.1.2.5.1 Detector

The following concepts illustrate the model of the X-Ray detector:

Physical detector array (or physical detector matrix) is the matrix composed of physical detector elements .

Note: Not all the detector elements are activated during an X-Ray exposure. The active detector elements are in the detector active area, which can be equal to or smaller than the physical detector area.

Physical detector element coordinates represented as (i det, j det ) are columns and rows of the physical detector element in the physical detector array.

Detector TLHC element is the detector element in the Top Left Hand Corner of the physical detector array and corresponds to (i det, j det ) = (0,0).

The attribute Detector Element Physical Size (0018,7020) represents the physical dimensions in mm of a detector element in the row and column directions.

The attribute Detector Element Spacing (0018,7022) contains the two values Δ jdet and Δ idet , which represent the physical distance in mm between the centers of each physical detector element:

• Δ idet = detector element spacing between two adjacent columns;

• Δ jdet = detector element spacing between two adjacent rows.

The attribute Detector Element Physical Size (0018,7020) may be different from the Detector Element Spacing (0018,7022) due to the presence of spacing material between detector elements.

The attribute Position of Isocenter Projection (0018,9430) contains the point (ISO_P idet, ISO_P jdet ), which represents the projection of the Isocenter on the detector plane, measured as the offset from the center of the detector TLHC element. It is measured in physical detector elements.

The attribute Imager Pixel Spacing (0018,1164) contains the two values Δ j and Δ i , which represent the physical distance measured at the receptor plane between the centers of each pixel of the FOV image:

• Δ i = imager pixel spacing between two adjacent columns;

• Δ j = imager pixel spacing between two adjacent rows.

The zoom factor represents the ratio between Imager Pixel Spacing (0018,1164) and Detector Element Spacing (0018,7022). It may be different from the detector binning (e.g., when a digital zoom has been applied to the pixel data).

• Zoom factor (columns) = Δ i / Δ idet ;

• Zoom factor (rows) = Δ j / Δ jdet .

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Figure FFF.1.2-9Physical Detector and Field of View Areas

#### FFF.1.2.5.2 Field of View

The following concepts illustrate the model of the field of view:

The field of view (FOV) corresponds to a region of the physical detector array that has been irradiated.

The field of view image is the matrix of pixels of a rectangle circumscribing the field of view. Each pixel of the field of view image may be generated by multiple physical detector elements.

The attribute FOV Origin (0018,7030) contains the two values (FOV idet, FOV jdet ), which represent the offset of the center of the detector element at the TLHC of the field of view image, before rotation or flipping, from the center of the detector TLHC element. It is measured in physical detector elements. FOV Origin = (0,0) means that the detector TLHC element is at the TLHC of a rectangle circumscribing the field of view.

The attribute FOV Dimension (0018,9461) contains the two values FOV row dimension and FOV column dimension, which represent the dimension of the FOV in mm:

• FOV row dimension = dimension in mm of the field of view in the row direction;

• FOV column dimension = dimension in mm of the field of view in the column direction.

FOV pixel coordinates represented as (i , j) are columns and rows of the pixels in the field of view image.

FOV TLHC pixel is the pixel in the Top Left Hand Corner of the field of view image and corresponds to (i , j) = (0,0).

As an example, the point (ISO_P i, ISO_P j ) representing the projection of the Isocenter on the field of view image, and measured in FOV pixels as the offset from the center of the FOV TLHC pixel, can be calculated as follows:

ISO_P i = (ISO_P idet - FOV idet ) . Δ idet / Δ i - (1 - Δ idet / Δ i ) / 2

ISO_P j = (ISO_P jdet - FOV jdet ) . Δ jdet / Δ j - (1 - Δ jdet / Δ j ) / 2

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Figure FFF.1.2-10Field of View Image

#### FFF.1.2.5.3 Field of View Rotation and Flip

The attribute FOV Rotation (0018,7032) represents the clockwise rotation in degrees of field of view relative to the physical detector.

The attribute FOV Horizontal Flip (0018,7034) defines whether or not a horizontal flip has been applied to the field of view after rotation relative to the physical detector.

The attribute Pixel Data (7FE0,0010) contains the FOV image after rotation and/or flipping.

Pixel data coordinates is the couple (c,r) where c is the column number and r is the row number.

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Figure FFF.1.2-11Examples of Field of View Rotation and Horizontal Flip

## FFF.1.3 Calibration

The X-Ray projection pixel calibration macro of the PS 3.3 C.8.19.6.9 specifies the attributes of the image pixel size calibration model in X-Ray conic projection, applicable to the Enhanced XA SOP Class.

In this model, the table plane is specified relative to the Isocenter. As default value for the attribute Distance Object to Table Top (0018,9403), the half distance of the patient thickness may be used.

Oblique projections are considered in this model by the encoding of the attribute Beam Angle (0018,9449), which can be calculated from Positioner Primary Angle (0018,1510) and Positioner Secondary Angle (0018,1511) as follows:

For Patient Positions HFS, FFS, HFP, FFP:Beam Angle = arcos( |cos(Positioner Primary Angle)| * |cos(Positioner Secondary Angle)| ).

For Patient Positions HFDR, FFDR, HFDL, FFDL:Beam Angle = arcos( |sin(Positioner Primary Angle)| * |cos(Positioner Secondary Angle)| ).

The resulting pixel spacing, defined as Δ Px * SOD / SID , is encoded in the attribute Object Pixel Spacing in Center of Beam (0018,9404). Its accuracy is practically limited to a beam angle range of +/- 60 degrees.

## FFF.1.4 X-Ray Generation

This chapter illustrates the relationships between the X-Ray generation parameters:

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Figure FFF.1.4-1Example of X-Ray Current Per-Frame of the X-Ray Acquisition

Values per frame are represented by the following symbols in this section:

In the Frame Content Sequence (0020,9111):

• Frame Acquisition Duration (0018,9220) in ms of frame « i » = Δt i

In the Frame Acquisition Sequence (0018,9417):

The following shows an example of calculation of the cumulative and average values per image relative to the values per-frame:

## FFF.1.5 Pixel Data Properties and Display Pipeline

This chapter describes the concepts of the display pipeline.

The X-Ray intensity (I) at the image receptor is inversely proportional to the exponential function of the product of the object’s thickness (x) traversed by the X-Ray beam and its effective absorption coefficient (μ): I ~ e - μ x .

The X-Ray intensity that comes into contact with the image receptor is converted to the stored pixel data by applying specific signal processing. As a first step in this conversion, the amplitude of the digital signal out of the receptor is linearly proportional to the X-Ray intensity. In further steps, this digital signal is processed in order to optimize the rendering of the objects of interest present on the image.

The Enhanced XA IOD includes attributes that describe the characteristics of the stored pixel data, allowing to relate the stored pixel data to the original X-Ray intensity independently from the fact that the image is “original” or “derived”.

When the attribute Pixel Intensity Relationship (0028,1040) equals LIN:

• P ~ I : The pixel values (P) are approximately proportional to X-Ray beam intensity (I).

When the attribute Pixel Intensity Relationship (0028,1040) equals LOG:

• P ~ x : The pixel values (P) are approximately proportional to the object thickness (x).

In order to ensure consistency of the displayed stored pixel data, the standard display pipeline is defined.

On the other side, the stored pixel data is also used by applications for further analysis like segmentation, structure detection and measurement, or for display optimization like mask subtraction. For this purpose, the Pixel Intensity Relationship LUT described in PS 3.3 C.7.6.16.2.13.1 defines a transformation LUT enabling the conversion from the stored pixel data values to linear, logarithmic or other relationship.

For instance, if the image processing applied to the X-Ray intensity before storing the Pixel Data allows returning to LIN, then a Pixel Intensity Relationship LUT with the function “TO_LINEAR” is provided. The following figure shows some examples of image processing, and the corresponding description of the relationship between the stored pixel data and the X-Ray intensity.

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Figure FFF.1.5-1 Examples of Image Processing prior to the Pixel Data Storage

No solution is proposed in the Enhanced XA SOP Class to standardize the subtractive display pipeline. As the Enhanced XA image is not required to be stored in a LOG relationship , the Pixel Intensity Relationship LUT may be provided to convert the images to the logarithmic space before subtraction. The creation of subtracted data to be displayed is a manufacturer-dependent function.

As an example of subtractive display, the pixel values are first transformed to a LOG relationship, and then subtracted to bring the background level to zero and finally expanded to displayable levels by using a non-linear function EXP similar to an exponential.

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Figure FFF.1.5-2 Example of Manufacturer- Dependent Subtractive Pipeline with Enhanced XA