Articles

Articles are a collaborative effort to provide a single canonical page on all topics relevant to the practice of radiology. As such, articles are written and edited by countless contributing members over a period of time. A global group of dedicated editors oversee accuracy, consulting with expert advisers, and constantly reviewing additions.

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Molecular tumbling rate effects on T1 and T2

The average rate at which molecules tumble (and therefore T1 and T2 time) is related to the molecular size. Small molecules (e.g. water/CSF) have a broad distribution of motional frequencies with poor matching with the Larmor frequency and therefore have long T1 values. Medium sized molecules (e...

Factors affecting T1

Factors affecting T1 and T2 relaxation times of different tissues are generally based on molecular motion, size and interactions. The protons giving rise to an NMR signal are mainly those in cell water and lipids (i.e. protons that are free to move), while those in protein and solids usually do...

T1 values (1.5 T)

T1 values are a few hundred milliseconds (ms) for most tissues examined. The following are approximate T1 values (ms) of several tissues for B0 = 1.5 T fat = 260 liver = 500 muscle = 870 brain white matter = 780 brain grey matter = 920 CSF = 2500 Tissues that will have high signal on T1-...

Electromagnetic induction

Electromagnetic induction is the induction of electric current via changing magnetic fields. Magnetic fields are generated by moving charges (equivalent to electrical current). Ampere’s law or Fleming’s right-hand rule determines the magnitude and direction (i.e. clockwise or anti-clockwise) of ...

Longitudinal and transverse magnetization

Longitudinal magnetism and transverse magnetism are components of the net magnetism vector. Longitudinal magnetism Longitudinal magnetization is the component of the net magnetization vector parallel to the magnetic field (z-axis). This is due to a difference in the number of spins in parallel...

Dependence of magnetization (proton density, field strength and temperature)

The dependence of magnetism is based on proton density (PD), field strength and temperature. There is a frictional interchange of energy between the protons and the lattice (spin-lattice interaction), such that a balanced exchange occurs between the two energy states and the thermal equilibrium ...

Magnetic susceptibility

Magnetic susceptibility is the ability of external magnetic fields to affect the nuclei of an atom. This may also be thought of as the “magnetisability” of a material, or the extent to which a material becomes magnetized when placed in an external magnetic field. Magnetic susceptibility is rela...

Nuclear magnetization

Nuclear magnetization refers to the magnetic moment of an atomic nucleus. Magnetic resonance imaging (MRI) makes use of nuclear magnetic resonance (NMR). Some nuclei may have nuclear magnetization depending on their nuclear charge distribution and the spin of their protons and neutrons. Nuclei w...

Magnetic dipole moment

The magnetic dipole moment is a quantity that represents the strength and orientation of the magnetic dipoles. This can be represented by the torque that a material experiences when added to a magnetic field. The stronger the magnetic moment, the stronger the magnetic field and the stronger the ...

Fast spin echo

Fast or turbo spin echo (FSE/TSE) is an adaptation of conventional spin-echo (SE) acquisition technique designed to reduce imaging time. It has largely supplanted the original spin-echo technique due to vastly improved imaging speed. Basic spin echo sequence In a basic SE sequence, a single ec...

Magnetic dipole

Magnetic dipoles are the magnetic equivalent of an electric dipole, where the two charges are positive and negative, with a flow of electric charge and surrounding electric field. Magnets are bipolar, having two poles: north and south. The term dipole means two charges. In a magnetic dipole, th...

Magnetic field

The magnetic field describes the influence a magnet has on its surrounding area. Magnets create a magnetic field or line of force running from the magnetic north to the magnetic south pole of the magnet. Magnetic fields are the result of intrinsic magnetic moments and moving electric charges wit...

David E Kuhl

David E Kuhl (1929-2017) was a pioneering nuclear physician, who played a key role in the development of positron emission tomography (PET), and more generally nuclear medicine. Early life David Edmund Kuhl was born on 27 October 1929 in St Louis, Missouri. He went to Temple University in Phil...

Nobel Prizes for radiology

The Nobel Prizes have been awarded since 1901, and several have been won for scientific discoveries with a direct or indirect importance for the development of radiology. History The Nobel Prizes were originally established in the will of Alfred Nobel (1833-1896), a very wealthy Swedish weapo...

Direct digital radiography

Direct digital radiography (DDR) refers to direct digital registration of the image at the detector with no intermediate processing step required to obtain the digital signals as in computed radiography (CR). There are two primary methods of conversion, either indirect or direct: Indirect conv...

Allan Macleod Cormack

Allan M Cormack (1924-1998) was a South African-American physicist who was instrumental in the development of CT 1,3. Early life Allan Macleod Cormack was born on 23 February 1924 in Johannesburg, South Africa. His parents - teacher Amelia MacLeod and engineer George Cormack - had both emigrat...

Fat-water swapping artifact

Fat-water swapping artifact is seen in a significant proportion of fat/water suppressed sequences using the Dixon method. The artifact follows a computational error in areas of field inhomogeneity resulting in incorrectly determining whether a voxel contains water or fat. The images have geogra...

Spatial resolution (CT)

Spatial resolution in CT is the ability to distinguish between object or structures that differ in density. A high spatial resolution is important for one to discriminate between structures that are located within a small proximity to each other. Factors affecting CT spatial resolution field...

Charles Thurstan Holland

Charles Thurstan Holland (1863-1941) was a pioneering radiologist who played a pivotal role in establishing radiology as a specialty in its own right. Early life Charles Thurstan Holland was born in Bridgwater, Somerset on 7 March 1863. He studied medicine at University College Hospital in...

Units of measurement

For units of measurement the use of SI units (both base and derived units) in articles and cases on Radiopaedia.org is preferred. This is in line with best scientific practice and helps maintain consistency across the site. Terminology By scientific convention: for eponymous units, the full n...

Wall filter

The wall filter in ultrasound is a way of filtering out low or high frequency Doppler signals. In clinical ultrasound, it is usually used to filter out very low frequencies that may add noise to a spectral Doppler waveform. A typical use is removing the low frequency reverberation of an arteria...

Doppler angle

Doppler angle corrects for the usual clinical situation when an ultrasound beam is not parallel to the Doppler signal. For instance, if one wants to evaluate an artery, the best angle for evaluation would be at zero degrees (parallel to the vessel). The strongest signal and best waveforms would...

MKS system

The MKS (or mks) system (or meter-kilogram-second) of units predated the current International System of Units (also known as SI), which is the current iteration of the metric system. Although many fields, including most of the healthcare sciences have abandoned the MKS system for everyday work...

Ionizing radiation

Ionizing radiation is the term given to forms of radiation that are energetic enough to displace orbiting electrons from the atoms in the absorbing medium, thus forming positive ions. The process of ionization is the principal means by which ionizing radiations dissipate their energy in matter a...

Henry (SI unit)

The henry (symbol: H) is the SI derived unit of electrical inductance. Terminology As per all other eponymous SI units when the unit is written out in full it is not capitalized, but when shortened to its symbol it is capitalized. History and etymology The henry is named in honor of Joseph ...

Antoine Henri Becquerel

Antoine Henri Becquerel (1852-1908) was a French scientist renowned for his work and subsequent discovery of radioactivity for which he was awarded the Nobel Prize for physics in 1903. Early life Antoine Henri Becquerel was born on 15 December 1852 in Paris, France to a family of nobility and ...

Pixel

A pixel (or pel or picture element) may refer to either the smallest discrete element of the physical display or to the smallest element of the image. Voxel is its 3-dimensional equivalent, as employed in CT and other cross-sectional imaging modalities. History and etymology The history of the...

Maxwell (CGS unit)

The maxwell (symbol: Mx) is the CGS unit of magnetic flux and was superseded by the weber, the unit in the SI system. Terminology As per all other eponymous measurement units when the unit is written out in full it is not capitalized, but when shortened to its symbol it is capitalized. Histo...

Weber (SI unit)

The weber (symbol: Wb) is the SI derived unit of magnetic flux, and superseded the maxwell, the CGS unit for magnetic flux. Terminology As per all other eponymous SI units when the unit is written out in full it is not capitalized, but when shortened to its symbol it is capitalized. History ...

Gauss (unit)

The gauss (symbol: G or Gs) is a legacy CGS unit of magnetic flux density, which was superseded by the tesla (T). One gauss is defined as one maxwell per cm2 (Mx/cm2), which equates to 10-4 tesla, and is therefore a small unit. This is one of the reasons for its stubborn persistence in some scie...

Tesla (SI unit)

The tesla (symbol T) is the derived SI unit of magnetic flux density, which represents the strength of a magnetic field. One tesla represents one weber per square meter. The equivalent, and superseded, cgs unit is the gauss (G); one tesla equals exactly 10,000 gauss. Most current medical magnet...

Disintegrations per second

Disintegrations per second (dps), also known as decays per second, represents the number of atoms of a radioactive isotope that decay per second. One becquerel is equivalent to one disintegration per second. Counts per second (cps) is the number of disintegrations per second, as measured by a ...

International System of Units

The International System of Units, or the SI units (shortened from the French Système international d'unités) is the globally-adopted system of units of measurement. It is the modern iteration of the metric system. It superseded all prior systems including CGS and MKS, although in certain fields...

CGS system

The CGS (or cgs) system (or centimeter-gram-second) of units predated the current International System (also known as SI units), which is the current iteration of the metric system. Although many fields, including most of the healthcare sciences have abandoned CGS for everyday work, there are s...

Rutherford (unit)

The rutherford (symbol Rd) is an obsolete unit of radioactivity which was superseded by the introduction of the becquerel in 1975. One rutherford was equivalent to 1,000,000 nuclear disintegrations per second, or alternatively one becquerel equated to one microrutherford (μRd). Terminology As...

Curie (unit)

The curie (symbol Ci) was the unit for radioactive decay in the cgs system. One curie was defined as the radioactivity of one gram of pure radium-226; this is equivalent to 3.7 x 1010 decays per second. It was officially replaced by the becquerel in 1975. Terminology One curie was too large t...

Rad (CGS unit)

The rad (symbol rad) is a legacy unit in the cgs system for the absorbed dose of ionizing radiation, although it remains in widespread use in the United States. The rad is defined as the dose represented by 100 ergs of energy being absorbed by one gramme of matter. The erg is the unit of energ...

Rem (unit)

The rem (an acronym for roentgen equivalent man) was the cgs unit of effective dose and was officially replaced by the sievert many years ago. One rem was a large quantity of radiation, and therefore for practical day to day use the millirem (mrem), representing one-thousandth of a rem, was us...

Coulomb per kilogram

The SI unit for exposure to ionizing radiation is coulomb per kilogram (Ckg-1) and curiously unlikely other SI radiation units, a specific name has not been adopted for this unit. This unit officially replaced the old unit, the roentgen in 1975, with an official transition period lasting at leas...

Sievert (SI unit)

The sievert (symbol Sv) is the SI unit of dose equivalent and is dimensionally-equivalent to one joule per kilogram. The sievert represents the stochastic effects of ionizing radiation as adjusted by a tissue weighting factor to account for differing responses of different human tissues to ioniz...

Gray (SI unit)

The gray (symbol Gy) is the SI unit of absorbed dose and is defined as the absorption of one joule of energy, in the form of ionizing radiation, per kilogram of matter, i.e. one gray = 1 J/kg 2. Terminology One gray is a large unit and is usually used with a prefix, e.g. milligray (mGy), micro...

Marie Skłodowska Curie

Marie Skłodowska Curie (1867-1934) was a Polish-born, French scientist known for her pioneering work in radioactivity. Much of her early work was in collaboration with her husband Pierre Curie (1859-1906). Her work shaped medicine, warfare and scientific research for countless generations, earn...

FLAIR vascular hyperintensities

FLAIR vascular hyperintensities are hyperintensities encountered on FLAIR sequences within subarachnoid arteries related to impaired vascular hemodynamics 1,2. They are usually seen in the setting of acute ischemic stroke and represent slow retrograde flow through collaterals (and not thrombus) ...

Size specific dose estimate

Size specific dose estimate (SSDE) measured in mGy, is a method of estimating CT radiation dose that takes a patient's size into account. CTDIvol and DLP are common methods to estimate a patient's radiation exposure from a CT procedure. The exposures are the same regardless of patient size, bu...

Photon starvation

Photon starvation is one source of streak artifact which may occur in CT. It is seen in high attenuation areas, particularly behind metal implants. Because of high attenuation, insufficient photons reach the detector. During the reconstruction process, the noise is greatly magnified in these are...

Synthetic MRI

Synthetic MRI is a technique that generates contrast weighted images based on measurements of tissue properties from a single acquisition. Basic principles With synthetic MRI, different contrast weighted images can be obtained based on quantifications of a single multiple dynamic and multiple ...

Inverse Fourier transformation

The inverse Fourier transform is a mathematical formula that converts a signal in the frequency domain ω to one in the time (or spatial) domain t. A time domain signal f(t) is obtained by demodulating a frequency domain signal F(ω) using a special sinusoidal wave ejωt across all time (from nega...

Fourier transformation

The Fourier transform is a mathematical formula that converts a signal in time (or spatial) domain t to one in the frequency domain ω. A frequency domain signal F(ω) is obtained by modulating the time domain signal f(t) to a special sinusoidal wave e-jωt across all time (from negative infinity ...

Dose length product

Dose length product (DLP) measured in mGy*cm is a measure of CT tube radiation output/exposure. It is related to volume CT dose index (CTDIvol), but CTDIvol represents the dose through a slice of an appropriate phantom. DLP accounts for the length of radiation output along the z-axis (the long a...

Photostimulable phosphors

Photostimulable phosphors (PSP) are materials that store absorbed energy within excited electrons and release it in the form of light on exposure to laser energy. The process can be broken up as follows 1: an x-ray or gamma photon interacts with the PSP and releases high energy secondary elect...

Tube rating

Tube ratings are the defined input parameters (kVp, mA, exposure) that can be safely used during its operation without causing damage to the x-ray tube itself and unique to each individual x-ray tube model. An x-ray tube rating is the maximum allowable kilowatts (kW) in 0.1 second 2. When the ...

Anode angle

The anode angle refers to the angle the target surface of the anode sits at in relation to the vertical. Most x-ray tubes have an anode angle of 12-15 degrees but greater or lesser angles can also be used depending on the application. The degree of angulation of the anode affects the effective...

Dosimeters

Dosimeters are a form of devices to monitor ionizing radiation. They are used regularly for a number of key roles including both patient and personal dosimetry, environmental monitoring, spectroscopy, radiopharmaceutical and equipment checking. Function Energy enters the dosimeter which conve...

Becquerel (SI unit)

The becquerel (symbol: Bq) is the SI unit of radioactivity and is defined as one nuclear disintegration per second 1; it officially replaced the curie (Ci), the unit in the superseded cgs system, in 1975. On Radiopaedia.org we primarily express all radioactive doses in becquerels. However as th...

Computed tomography texture analysis

Computed tomography texture analysis (or CTTA) is a method to obtain new useful biomarkers that provide objective and quantitative assessment of tumor heterogeneity by analyzing the differences and patterns within the pixel values of an image. CTs can be worked with as a matrix of numbers, corre...

Magnetic resonance neurography

Magnetic resonance neurography (MRN) is a relatively new non-invasive imaging technique for dedicated assessment of peripheral nerves. It is used to assess peripheral nerve entrapments and impingements as well as localization and grading of nerve injuries and lesions. Dedicated high-resolution...

Silver recovery

Silver recovery is the process by which pure metallic silver can be recycled from old x-ray films. The modern process is extremely efficient with a recovery of greater than 99.9% silver. Historically all radiographic film media employed silver salts as part of the image-producing process. Alth...

Voxel

Voxel is a portmanteau of contractions of the two words 'volume' and 'element' and was coined as a 3-D equivalent of a pixel. It is an individual point in space on a 3-dimensional, regular matrix. The location of each voxel is encoded by its relative relationship to other voxels. A tensor may b...

Biological effects of ultrasound

The biological effects of ultrasound refer to the potential adverse effects the imaging modality has on human tissue. These are primarily via two main mechanisms: thermal and mechanical. Despite this, ultrasound has a remarkable record for patient safety with no significant adverse bioeffects re...

Reflection

Reflection of a sound wave occurs when the wave passes between two tissues of different acoustic impedances and a fraction of the wave 'bounces' back. This forms one of the major principles of ultrasound imaging as the ultrasound probe detects these reflected waves to form the desired image. An...

Transient elastography

Transient elastography most often refers to a type of elastography which relies on a mechanical pulse generated by an external probe. The principle is similar to shear wave elastography, in that the elastic modulus is generated from shear wave velocity, but the application of the pulse from an ...

Eddy currents

Eddy currents (also known as Foucault currents) are the result of rapidly changing gradient magnetic fields that in turn induce stray currents in the surrounding conducting materials. They form in accordance to Faraday's Law of Induction. Eddy currents are unwanted as they generate their own ma...

Phased array

A phased array ultrasound transducer is typically 2-3 cm long, consisting of 64-128 elements. It is a smaller assembly than a sequential array and can be either linear or curvilinear. A sector field of view is produced by all elements firing to create a single waveform. Small delays in element ...

Convex array

Convex (sequential) arrays, also known as curvilinear or curved linear arrays, are similar to linear arrays but with piezoelectric elements arranged along with a curved transducer head. Ultrasound beams are emitted at 90 degrees to the transducer head. This arrangement results in a trapezoidal f...

Linear array

Ultrasound transducers that produce images via linear array typically contain 256-512 elements, making them the largest assembly. Each element produces a scan line that makes up the ultrasound image. Multiple adjacent elements combine to produce an ultrasound beam that is emitted at 90 degrees ...

Portosystemic shunt ratio

The portosystemic shunt ratio is a measure performed using ultrasound to quantify the abnormal flow of portal venous blood that is shunted away from the hepatic sinusoidal circulation in the context of a congenital portosystemic shunt 1. Measurement The ratio is determined on ultrasound using ...

PET radiotracers

A PET radiotracer (also known as PET tracer) is a positron-emitting radiopharmaceutical used in positron emission tomography (PET). Each tracer consists of a positron-emitting isotope (radioactive tag) bound to an organic ligand (targeting agent). The ligand component of each tracer interacts wi...

Magnetization transfer

Magnetization transfer (MT) imaging is an MRI technique that can be used to exploit the contrast between tissues where 1H protons are present in three states1: bound to macromolecules in free water as water in the hydration layer between the macromolecules and the free water To assess MT, an...

Energy difference between spin up and spin down states

The energy difference between spin up and spin down states of hydrogen are important in understanding net magnetization vector of tissue for magnetic resonance imaging. Each hydrogen atom is formed by one proton and one orbiting electron. Because the atomic number is 1, it has a spin quantum nu...

Grid cutoff

Grid cutoff is an unwanted absorption of x-rays via an x-ray grid, observed when a grid is employed incorrectly, most often seen with parallel grids. The term cutoff stems from the phenomenon in which the primary x-ray beam is 'cut off' by grid lines, leading to an overall decrease in optical de...

Ultrasound transducer

An ultrasound transducer converts electrical energy into mechanical (sound) energy and back again, based on the piezoelectric effect. It is the hand-held part of the ultrasound machine that is responsible for the production and detection of ultrasound waves. It consists of five main components:...

Background radiation equivalent time

Exposing a patient to radiation is a measured, justified means aiding patient care. Each medical imaging examination utilizing ionizing radiation adheres to the fundamental principles of radiation protection. The general public's understanding of ionizing radiation is limited 1; this article pr...

Absorption (ultrasound)

In ultrasound, absorption is the reduction in intensity of the sound waves as it passes through tissue. Most of the energy lost is in the form of heat.

Computed radiography

Computed radiography (CR) is the use of photostimulable phosphor as an image receptor. The image receptor is held in a similar casing (cassette) to that of the traditional film screen. Computed radiography harnesses the absorption of radiation, trapping electrons at energy levels via the process...

Background radiation

Background radiation refers to exposure to ionizing radiation in day-to-day life, excluding occupational exposures. It is measured in millisieverts (mSv). Ionizing radiation occurs naturally in the environment 1,2: radioactive gas (e.g. radon, thoron): 0.2-2.2 mSv/year external terrestrial (e....

Radiation damage (skin injury)

Radiation-induced skin injuries can occur in both radiotherapy and fluoroscopic procedures such as interventional radiology. It is a type of deterministic effect. Acute radiation doses above 2 Gy are known to result in erythema, permanent epilation will occur at 7 Gy and delayed skin necrosis ...

Lead equivalent personal protection equipment

Lead equivalent personal protection equipment (PPE) should be available in all radiology departments and operating suites. There are three traditional principles for ionizing radiation safety: time, distance, and shielding. It is important to remember that all three principles have a part to pla...

Dose limits

Dose limits are recommended by the International Commission on Radiological Protection (ICRP). They are in place to ensure that individuals are not exposed to an unnecessarily high amount of ionizing radiation. Dose limits are a fundamental component of radiation protection, and breaching these ...

Radiation-induced carcinogenesis

Radiation-induced carcinogenesis is widely but not universally believed to occur at exposures from ionizing radiation used in medical imaging. It is thought to be a stochastic effect of ionizing radiation, with the linear no-threshold theory (LNT) proposing no "safe" level of radiation exposure,...

Biomolecular radiation damage

Biomolecular radiation damage may result from exposure of biological tissues to ionizing radiation from direct exposure, or via Compton scattering. Mechanism of tissue radiation damage Direct effect if a biological macromolecule (e.g. DNA, RNA, protein) becomes ionized or excited by an ionizi...

Photon

A photon is, in simple terms, an elementary force-carrying particle i.e. a boson 2 (obeys the statistical law of Bose-Einstein). It has a zero mass (rest mass) and travels at, c, the speed of light in vacuo. It is defined as stable with no electric charge and exhibits both wave-like and particle...

MR fingerprinting

MR fingerprinting (MRF) is a relatively recent approach to the acquisition and evaluation of MRI data aimed at generating quantitative multiparametric data from a single acquisition. The underlying process is acquiring data in a pseudorandom manner resulting in a unique pattern of signal evolu...

Image intensifier

Image intensifiers (II) are utilized to convert low energy x-radiation into visible light images. Frequently the detector portion of an x-ray C-arm used in operating theaters, the image intensifier has a low scatter input portion made of low absorption substances such as titanium or aluminum 1,2...

High voltage generator

X-ray units require a high voltage generator to achieve the necessary power required of an x-ray tube. AC power will supply x-ray units with sinusoidal currents, resulting in 'peaks and troughs', limiting an x-ray tube to produce x-rays only half of the 1/60th of s second cycle. A single-phase...

Entrance skin dose

The entrance skin dose (or entrance surface dose), abbreviated as ESD, is the measure of the radiation dose that is absorbed (measured in milligray) by the skin as it reaches the patient. Entrance skin dose is a directly measurable quantity, often, measured using thermoluminescent dosimeters (TL...

Radiation protection

Radiation protection is based on the three fundamental principles of justification of exposure, keeping doses (of ionizing radiation) as low as reasonably achievable (optimization) and the application of dose limits. The International Commission on Radiological Protection (ICRP) is responsible f...

Milliampere-seconds (mAs)

Milliampere-seconds, also more commonly known as mAs, is a measure of radiation produced (milliamperage) over a set amount of time (seconds) via an x-ray tube. It directly influences the radiographic density, when all other factors are constant. An increase in tube current (mA) results in a hig...

Physics curriculum

The physics curriculum is one of our curriculum articles and aims to be a collection of articles that represent core physics and imaging technology knowledge: physics and imaging technology: x-ray physics and imaging technology: ultrasound physics and imaging technology: CT physics and imagi...

Aliasing artifact (CT)

Aliasing artifact, otherwise known as undersampling, in CT refers to an error in the accuracy proponent of analog to digital converter (ADC) during image digitization. Image digitization has three distinct steps: scanning, sampling, and quantization. When sampling, the brightness of each pix...

Indium-111 oxine labeled white blood cell scan

Indium-111 oxine labeled white blood cell (WBC) scan (or In-111 oxine labeled white blood cell scan) is a nuclear medicine test which attempts to localize infection and/or inflammation by injecting the patient's previously extracted and radioactively-labeled white blood cells. Procedure The p...

Image reconstruction (CT)

The rapid evolution of mathematical methods of image reconstruction in computed tomography (CT) reflects the race to produce an efficient yet accurate image reconstruction method while keeping radiation dose to a minimum and has defined improvements in CT over the past decade. The mathematical ...

Radiation-induced lung cancer

Radiation-induced lung cancers are a potential long-term complication of radiotherapy to the chest. Besides lung cancer, sarcomas (osteosarcomas are the most common arising from the irradiated bones, and malignant fibrous histiocytomas the most frequently arising from the soft tissues), breast...

LaPlace's law

LaPlace's law is useful in thinking about dilated tubular structures, such as the bowel or vessels (e.g. aortic aneurysms). The relationship between wall tension and radius shows why more dilated regions of a tube develop more wall stress and therefore are at higher risk for perforation: wall t...

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