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Adam L. Bartret led a radiological study testing whether variant sciatic nerve routes near the piriformis muscle were associated with piriformis syndrome. The researchers classified anatomy on 783 hip magnetic resonance imaging studies and compared recorded clinical diagnoses. Variants occurred in about 19% of hips, with no statistically significant diagnostic association in this cohort.^[ref]

The study illustrates the distinction between identifying an anatomical variant and showing that it causes pain. A visible difference can be incidental; conversely, this observational result does not establish that every possible compression mechanism is absent.

Alicia M. Maceira is a physician working in cardiology and cardiac imaging. Her hospital profile identifies cardiac diagnostic imaging as her specialization.^[ref] Her primary research includes establishing right ventricle reference measurements with magnetic resonance imaging.

In a 2006 paper, Maceira and colleagues studied 120 healthy adults, 60 men and 60 women aged 20–80 years, using cine images acquired by steady-state free-precession imaging and three-dimensional modelling. The study examined how age, sex and body surface area related to ventricular volumes and function.^[ref]

An original numerical example separates the measurements. If end-diastolic volume is 150 mL and end-systolic volume is 60 mL, the volume difference is 90 mL and right ventricular ejection fraction is $(150-60)/150=0.60$. Dividing the 150 mL end-diastolic volume by a body surface area of $1.8{\mathrm{m}}^2$ gives an indexed volume of approximately $83.3\mathrm{mL}{\mathrm{m}}^{-2}$. The fraction and the indexed volume describe different properties; neither numerical value alone specifies a universal reference interval.

The study found associations with age even for several size-normalized measurements. This motivates population conditioning of ventricular reference intervals: scaling by body surface area need not eliminate all dependence on age or sex.^[ref] Reference values also belong to an acquisition and analysis procedure. A numerical example explains the quantities; clinical interpretation requires the appropriate validated reference framework.

A cardiac long axis is a base-to-apex direction used to describe the heart or a specified ventricular chamber. In left-ventricular imaging it is commonly planned through the cardiac apex and the center of the mitral valve. It is a chamber-based anatomical reference, not necessarily the vertical direction of a patient's body or an image display.

The primary cardiovascular magnetic resonance imaging protocol specifies connected two-chamber, four-chamber and short-axis planning from anatomical landmarks.^[ref] A long-axis image plane contains the chosen cardiac long axis; the corresponding cardiac short axis describes a transverse direction or view. Different planes can contain the same long-axis line while displaying different walls and neighboring chambers.

An original vector construction makes the distinction precise. Let $a$ be the apex position and $b$ a chosen basal reference point. Thenis the axial unit vector. A displacement $r$ has axial component $(r\cdot \mathbf{u})\mathbf{u}$ and transverse component $r-(r\cdot \mathbf{u})\mathbf{u}$. The line alone does not determine how the transverse coordinates are rotated around it.

This geometry matters for cardiac image foreshortening. In a simple projection model, a length $L$ tilted by $\theta$ out of the display plane projects to $L\cos \theta$. A 10 cm length tilted by $30^{\circ }$ appears about 8.66 cm long. This is a geometrical illustration, not a correction formula for a tomographic slice: a slice may miss the true apex rather than project it. Consistent landmark selection is therefore part of meaningful comparisons of cavity shape, motion and volume.

A cardiac short axis is a transverse reference direction or imaging view relative to a specified cardiac long axis. For left-ventricular imaging, a short-axis plane is planned across the chamber rather than through its base-to-apex length. The chamber and anatomical landmarks must be specified; a patient's horizontal body plane is not automatically a cardiac short axis plane.

A primary cardiovascular magnetic resonance imaging protocol plans short-axis images using linked long-axis views and covers the ventricle from base to apex.^[ref] A cardiac short-axis stack turns successive cavity outlines into volumetric information.

For an original geometrical construction, let $\mathbf{u}$ be the unit vector along the chosen cardiac long axis. A transverse plane through $r_0$ satisfiesParallel planes at different axial positions sample different portions of the ventricle. With measured cavity areas $A_i$ and represented slice thicknesses $\Delta z_i$, a simple volume estimate is $V\simeq {\sum }_i{A}_i\Delta z_i$.

An oblique slice also illustrates a useful caution. An ideal circular cylinder cut at angle $\theta$ away from its perpendicular section has an elliptical cross-sectional area $A_0/\cos \theta$. At $30^{\circ }$ this is about $15.5\%$ larger. This does not prove that an entire consistently acquired oblique stack overestimates volume: integrating all areas with the correct normal spacing and complete coverage still recovers volume. Orientation, spacing and coverage must be treated together. The major practical question is whether the chosen stack and image segmentation represent the complete intended cavity, not whether one slice happens to look circular.

A cardiac short-axis stack is a series of images across a cardiac chamber at successive positions approximately transverse to its cardiac long axis. In ventricular volumetry, the series must cover the intended cavity from its basal boundary toward the cardiac apex. A primary cardiovascular magnetic resonance imaging protocol specifies linked long-axis planning and short-axis coverage.^[ref]

The stack supplies a spatial sum rather than a single diameter. Let $A_i(t)$ be the segmented cavity area in slice $i$ at phase $t$, and let $\Delta z_i$ be the represented distance along the stack normal. A basic approximation isAll areas in a given sum must refer to a compatible phase of the cardiac cycle. Image segmentation, slice coverage and phase matching are separate inputs to the volume estimate.

An original example uses four representative areas of 2, 6, 10 and 6 cm${}^2$, each assigned 1 cm of axial extent. Their represented volume is 24 cm${}^3$, or 24 mL. Omitting the basal 6 cm${}^2$ contribution reduces the result to 18 mL without changing the tracing quality of the other slices. If slice thickness is 0.8 cm but center spacing is 1 cm, the numerical integration convention must also account for the intervening extent; treating thickness and represented spacing as interchangeable changes the estimate.

Phase mixing causes a different error. An area from one slice near end-filling and another near end-ejection do not generally describe a cavity that existed at one time. A stack can therefore be complete spatially yet inconsistent temporally. With correctly matched phases, the derived end-diastolic volume and end-systolic volume can be used for stroke volume and ejection fraction; those formulas do not repair missing anatomy or mismatched acquisition phases.

Christopher M. Kramer is a cardiologist whose research uses cardiovascular magnetic resonance imaging to assess the heart. His University of Virginia profile identifies cardiovascular imaging as an area of expertise.^[ref] He is the first author of the 2020 primary protocol document specifying standardized cardiovascular magnetic resonance imaging acquisitions.^[ref]

One concrete contribution of such a protocol is to make image geometry reproducible. Its left-ventricular procedure links the cardiac apex, mitral valve center, cardiac long axis views and a cardiac short-axis stack.^[ref] The geometry determines which anatomy is acquired before an analyst draws a cavity boundary.

An original example explains the measurement consequence. A volume reconstructed as $V\simeq {\sum }_i{A}_i\Delta z_i$ depends on both the cavity areas and the represented slice thicknesses. If ten slices each have area 8 cm${}^2$ and represented thickness 0.8 cm, the estimate is 64 mL. Omitting one such slice loses 6.4 mL even if every retained boundary is traced perfectly. Standardized coverage and phase selection therefore address errors that cannot be removed merely by improving image segmentation on the available slices.

The documented protocol work connects acquisition choices to interpretable measurements of chamber structure and function. It provides technical procedures and reference geometry; the arithmetic example here illustrates their purpose rather than reporting a result from that document.

Derek Jones is a physicist at Cardiff University whose research develops quantitative magnetic resonance imaging, especially diffusion tensor imaging. He trained in physics at Nottingham, medical physics at Leeds and completed a Leicester doctorate on diffusion tensor imaging. His work asks how acquisition design changes what can be inferred from a measured signal.^[ref]

Jones investigated how diffusion MRI gradient sampling affects the measurement uncertainty of inferred diffusion tensors. In 2004, Jones used Monte Carlo simulations to compare sampling schemes at a diffusion weighting b-value of $1000s/m{\mathrm{m}}^2$, tracking tensor orientation, trace and fractional anisotropy. It showed why a minimal set of directions need not give robust estimates; its numerical findings belong to the tested models and noise conditions.^[ref]

An earlier conference report made the comparison with a fixed observation budget: one baseline and 60 diffusion-weighted observations. Six unique orientations repeated 10 times and 30 orientations repeated twice therefore used the same number of diffusion-weighted observations. Varying angular coverage while controlling that budget separates a direction-design question from simply acquiring more data.^[ref]

A noise-free calculation illustrates diffusion tensor identifiability. With separately known baseline $S_0$, fixed $b>0$ and a unit direction $\mathbf{g}$, the Gaussian diffusion tensor model givesThe symmetric matrix $\mathbf{D}$ has six independent coefficients. Its quadratic form produces a row $(g_x^2,g_y^2,g_z^2,2g_x{g}_y,2g_x{g}_z,2g_y{g}_z)$ in a linear least squares design. Directions $\pm {\mathbf{e}}_x,\pm {\mathbf{e}}_y,\pm {\mathbf{e}}_z$ give six observations but only matrix rank three: opposite directions repeat a row and the off-diagonal coefficients remain undetermined.

Adding the normalized mixed directions $({\mathbf{e}}_x+{\mathbf{e}}_y)/\sqrt{2}$, $({\mathbf{e}}_x+{\mathbf{e}}_z)/\sqrt{2}$ and $({\mathbf{e}}_y+{\mathbf{e}}_z)/\sqrt{2}$ to the three positive coordinate axes instead gives matrix rank six. For example,This establishes uniqueness in the stated noise-free model. It does not establish small measurement uncertainty or an optimal experimental design.

Jones also interviewed John E. Tanner about the physical origins of pulsed field gradient NMR. The interview preserved concrete details of the apparatus, including Tanner's carefully spaced mica stack and the practical difficulties of rapidly switching magnetic field gradients.^[ref]

Dilated cardiomyopathy is a form of cardiomyopathy involving enlargement of a ventricular chamber together with impaired pumping by the heart muscle. The left ventricle is a central site of the disorder, and other chambers can also be affected. Enlargement and pumping function are related but distinct observations; chamber size alone does not determine how much blood is expelled.^[ref]

A simple volume example makes that distinction quantitative. Let end-diastolic volume be $V_{\mathrm{ED}}$ and end-systolic volume be $V_{\mathrm{ES}}$. ThenHere SV is stroke volume and EF is ejection fraction. A stipulated chamber changing from $200$ to $150\mathrm{mL}$ ejects $50\mathrm{mL}$ with EF $25\%$. Another changing from $120$ to $60\mathrm{mL}$ ejects $60\mathrm{mL}$ with EF $50\%$. A larger filled volume need not produce a larger stroke volume. These are constructed mechanical examples, not diagnostic cutoffs or reference ranges.

Imaging can test several parts of this mechanism. Echocardiography follows chamber dimensions and contraction; cine magnetic resonance imaging can quantify volumes and longitudinal motion. In a primary study, Marcus Carlsson and colleagues compared twelve patients with dilated cardiomyopathy, twelve controls and twelve elite triathletes. Their analysis combined atrioventricular-plane displacement with anatomical area to investigate the longitudinal contribution to ventricular pumping.^[ref]

This experiment illustrates why the condition cannot be represented by one chamber diameter alone: geometry, motion and transported volume supply different information. Doppler echocardiography and its velocity-time integral provide complementary flow observations, while a clinical diagnosis also requires the surrounding evidence and cause of the myocardial abnormality.

D. R. Enzmann is the radiologist credited under that byline as first author of Normal flow patterns of intracranial and spinal cerebrospinal fluid defined with phase-contrast cine MR imaging by D. R. Enzmann and others. With N. J. Pelc, Enzmann reported measurements of moving cerebrospinal fluid, using magnetic resonance imaging to investigate physiology as well as anatomical appearance.^[ref]

The study examined ten healthy volunteers and four patients whose conventional MR images were normal. Peripheral gating produced sixteen quantitative flow-encoded images over the cardiac cycle. Measurements distinguished the timing of fluid motion in ventricular and subarachnoid spaces, demonstrating why static anatomy alone does not describe pulsatile movement.^[ref]

The methodological contribution is an example of turning image contrast into a physiological measurement. Direction-sensitive signals and repeated sampling across a heartbeat distinguish oscillatory motion from a compartment that simply looks fluid-filled. The reported display convention assigned opposite intensities to opposite craniocaudal directions; that convention belongs to the acquisition and is not a universal rule for brightness in every MR image.

The initials are retained as verified in the original research record. The paper establishes authorship and the reported results; it does not separately document which apparatus component or analysis step each coauthor personally performed.

Ejection fraction is the fraction of a ventricle's end-diastolic volume lost from its cavity during ejection:The numerator is volumetric stroke volume; $V_{\mathrm{ES}}$ is end-systolic volume. The chamber must be specified: right ventricular ejection fraction concerns the right ventricle, whereas a calculation for the left ventricle concerns its own pair of volumes.

Time-resolved magnetic resonance imaging can estimate the two volumes from a consistently defined cavity. A primary right-ventricular study used cine images and three-dimensional modelling in 120 subjects.^[ref] The ejection fraction is a derived quantity, not an additional independent volume observation.

An original example illustrates its scale dependence. Volumes of 120 and 60 mL give $\mathrm{EF}=50\%$ and stroke volume 60 mL. Volumes of 240 and 120 mL give the same ejection fraction but twice the stroke volume. Consequently, ejection fraction alone does not determine cardiac output; heart rate and an appropriate forward-flow interpretation are also needed.

Its response to shared measurement errors is instructive. Multiplying both measured volumes by the same positive scale $k$ leaves the ejection fraction unchanged. Adding the same offset $b$ does not:For the 120/60 mL example, $k=1$ and $b=20$ mL change the calculated fraction from $0.5$ to $60/140\approx 0.429$, even though the volume difference remains 60 mL. This is an error-model example, not a universal correction for image segmentation. Likewise, cavity volume loss can include backward flow through a heart valve; the formula alone does not establish net useful delivery.

End-diastolic volume is the volume of blood in a specified ventricle at the end of filling, before the subsequent ejection. It is the starting volume in the usual volumetric stroke volume calculation and the denominator of ejection fraction:The right ventricle and left ventricle each have their own end-diastolic volume. The chamber, phase and measurement convention must be identified before two values are compared.

For a constructed example, a chamber filling to 120 mL and ending ejection at 50 mL has a stroke volume of 70 mL and ejection fraction about $58.3\%$. Another chamber filling to 180 mL and ending at 110 mL has the same 70 mL stroke volume, but ejection fraction about $38.9\%$. Equal ejected volumes do not imply equal relative emptying.

The quantity can be obtained from time-resolved images by choosing the filling phase and identifying the complete cavity. A primary right-ventricular magnetic resonance imaging study generated volumes from cine images with three-dimensional modelling; its reference analysis also considered age, sex and body size.^[ref] These factors help explain why an isolated volume should not be treated as a universal reference value.

For a simple sum-of-slices model, $V_{\mathrm{ED}}\simeq {\sum }_i{A}_i\Delta z_i$, where $A_i$ is the measured cavity area in a slice and $\Delta z_i$ its represented thickness. Omitting a slice with area 10 cm${}^2$ and represented thickness 0.8 cm omits about 8 mL. This example connects image segmentation and coverage to a concrete volume error; it does not require a spherical ventricle.

End-systolic volume is the volume of blood remaining in a specified ventricle at the end of its ejection phase. It must be associated with a particular chamber and cardiac cycle. Subtracting it from the preceding end-diastolic volume gives the chamber's volumetric stroke volume:For example, $V_{\mathrm{ED}}=140$ mL and $V_{\mathrm{ES}}=60$ mL give $\mathrm{SV}=80$ mL. The residual 60 mL is not a separate compartment of permanently trapped blood; it is a chamber-volume measurement at one phase of a recurring cycle.

Measuring end-systolic volume requires both a phase choice and a cavity boundary. A primary magnetic resonance imaging study used cine images and three-dimensional modelling to measure right ventricular volumes and function in 120 healthy subjects.^[ref] An image's smallest-looking cavity in one view is not automatically the smallest three-dimensional volume.

An original sensitivity calculation makes the boundary issue tangible. If a selected cavity volume $V=60$ mL has surface area $S=100$ cm${}^2$, a hypothetical uniform outward boundary shift of $\delta =0.01$ cm gives a first-order volume error $\delta V\simeq S\delta =1$ mL. This geometrical approximation does not prescribe how a real image should be segmented, but shows how many small boundary displacements can accumulate into a volume error.

At fixed end-diastolic volume, increasing end-systolic volume reduces both stroke volume and ejection fraction. That algebra does not identify the physiological cause: changing contraction, loading and valve behavior can affect the observed volumes. A single residual-volume number is therefore a measurement of state, not a complete mechanism.

Magnetic resonance imaging with a prepared nuclear population imbalance exceeding ordinary thermal polarization under the imaging conditions. Dynamic nuclear polarization, optical spin transfer and spin-order transfer offer different preparation routes. Preparation and acquisition must account for spin-lattice relaxation, which erases the excess polarization.

Interventional radiology uses medical imaging to guide instruments into the body for diagnosis or treatment. A biopsy can obtain material for diagnosis; a catheter can provide access for a therapeutic procedure. Guidance may use fluoroscopy, ultrasound, computed tomography or magnetic resonance imaging, depending on the instrument, target and procedure.^[ref]

The central measurement problem is localization. In an image-guided biopsy, seeing a suspicious region and seeing a needle separately is insufficient: the operator needs evidence that the sampling part of the needle reaches the intended region. A single X-ray projection collapses depth, so two objects can overlap on the image while remaining separated in the body. Choosing imaging views and following instrument motion addresses that geometric uncertainty. This explains why image guidance is more than taking a picture before an intervention.

An early therapeutic motivation was to use the access already provided by arterial catheters to treat obstructed vessels. Charles T. Dotter and Melvin P. Judkins's 1965 report described a percutaneous transluminal approach to arterial obstruction. Its developmental discussion connected contrast examinations and observed catheter pathways with the possibility of opening a passage through an obstructed region.^[ref]

The example connects anatomical imaging to mechanical action: identifying a narrowed path and changing that path are different tasks, but the same image-guided access can support both. The historical report motivates the method; it is not a procedure-selection rule for an individual patient.

A researcher in magnetic resonance imaging instrumentation. His team’s 2001 comparison of head imaging at 7 T and 4 T examined signal-to-noise ratio, radio-frequency field uniformity and power requirements together. Increasing the main magnetic field can improve the measured signal while making the excitation field harder to control across the head. The comparison demonstrates why high-field imaging requires electromagnetic design and measurements of spatial uniformity in addition to a stronger magnet.^[ref]

Magnetic resonance cholangiopancreatography is a form of magnetic resonance imaging used to visualize the bile ducts and pancreatic duct. Its apparatus uses a magnetic field, radiofrequency excitation and spatially encoded magnetic-resonance signals to produce images of the ductal region. The image depends on the selected acquisition and reconstruction, so visible duct structure is an inference from that signal rather than a direct optical view.^[ref]

Spectroscopic measurement of tissue chemical signals, complementary to anatomical magnetic resonance imaging.

Marcus Carlsson investigates cardiac pumping using magnetic resonance imaging. His 2007 primary study measured longitudinal atrioventricular-plane displacement and related it to stroke volume in twelve controls, twelve elite triathletes and twelve patients with dilated cardiomyopathy.^[ref]

The study combined a longitudinal displacement with a short-axis area to estimate the longitudinal contribution to ejected volume.^[ref] A shorter displacement need not imply a proportionally smaller contribution when the chamber's transverse dimensions differ.

An original constant-area illustration givesWith stipulated $A=40\mathrm{c}{\mathrm{m}}^2$ and $s=1.0$ cm, the modeled contribution is 40 mL. Doubling area to $80\mathrm{c}{\mathrm{m}}^2$ while halving displacement to 0.5 cm gives the same 40 mL. If total stroke volume is 80 mL in both examples, both longitudinal fractions are one half. These are geometric examples, not group values from the study.

This explains why comparing displacement alone and comparing its contribution to stroke volume are different questions. The experimental paper supplies actual images and a specified geometric estimator, while the toy model isolates the multiplication responsible for that distinction. Neither a displacement nor its volume fraction alone determines every aspect of ventricular function; ejection fraction also requires the corresponding chamber volume.

Mitral annular excursion is displacement of the mitral annulus over a specified part of the cardiac cycle. A commonly used longitudinal observation follows an annular landmark along the cardiac long axis during ventricular systole. The reference position, direction and endpoints are part of the measurement; displacement is distinct from annular area or leaflet coaptation.

The measurement question can be written explicitly. For a fixed unit axis $\hat{\mathbf{e}}$ and landmark position $\mathbf{x}(t)$, defineAn original 10 mm displacement viewed along an axis tilted by $30^{\circ }$ projects to $10\cos 30^{\circ }\simeq 8.66$ mm. Thus changing the observation direction changes the reported excursion even for the same motion. A single landmark also need not represent every part of a deforming mitral annulus.

A primary human study used cine magnetic resonance imaging, measuring longitudinal displacement in long-axis views and stroke volume in short-axis views. Its model combined displacement with a ventricular short-axis area.^[ref] In an original rigid-piston approximation, area $A$ moving axially by $\Delta s$ sweeps volume $A\Delta s$. Areas 20 and 40 cm${}^2$ paired with displacements 1 and 0.5 cm both give 20 mL. Smaller excursion need not imply a smaller geometric swept volume when area differs; this model area is not automatically the mitral opening area.

A complementary experiment by C. Carlhäll and colleagues implanted markers around the mitral annulus and ventricular wall in six sheep. Biplane fluoroscopy reconstructed three-dimensional marker motion, and tetrahedron-based estimates assessed annular contributions to filling while loading and contraction were varied.^[ref] This connects a displacement measurement to moving-chamber geometry. The changing boundary, surrounding deformation and blood flow must be distinguished when relating mitral annular excursion to filling or ejection.

N. J. Pelc is a coauthor with D. R. Enzmann of a 1991 study that used phase-contrast magnetic resonance imaging to measure cerebrospinal fluid motion through the cardiac cycle. The work illustrates how magnetic resonance imaging can provide a time-dependent physiological measurement rather than only an anatomical picture.^[ref]

The investigators studied ten healthy volunteers and four patients whose conventional magnetic-resonance images were normal. Peripheral cardiac gating divided the measurement into 16 flow-encoded images per cycle. The flow encoding distinguished opposite directions of cerebrospinal fluid motion, and measurements at several locations showed that the timing of the motion differed between the ventricular system and surrounding spaces.^[ref]

For an illustrative one-second cycle, 16 equally spaced phases would separate samples by $1/16=0.0625$ seconds. The paper's number of cardiac phases therefore matters: an average over the entire cycle could hide changes of direction within it. Conversely, sixteen phases are a temporal sampling scheme, not evidence of sixteen independent subjects. This example explains the measurement design without assigning an unreported individual contribution to either coauthor.