Medical physics

Medical physics applies physics to quantitative problems in medical imaging, nuclear medicine and radiation therapy. It connects an instrument's signal to a physical quantity, tests the model behind that inference, and establishes its measurement uncertainty. Examples include reconstructing an image from radiation or acoustic measurements and determining the absorbed dose delivered by an ionizing radiation beam.

The sealed-water calorimeter of Steve R. Domen gives a concrete measurement example. Domen's 1994 study placed sealed water in a glass cylinder, 110 mm long and 33 mm in diameter, inside a 30 cm water-filled acrylic cube. Two calibrated thermistors formed opposite arms of a Wheatstone bridge; their change in electrical resistance measured the small temperature rise. The glass also limited convection.^[ref]

In the ideal water calorimetry balance, deposited energy becomes heat, givingwhere $D$ is absorbed dose and $c_p$ specific heat capacity. Using a rounded illustrative $c_p=4180\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$, depositing $1\mathrm{J}$ in $1\mathrm{kg}$ corresponds to one gray and onlyThis small signal makes thermal control and measurement calibration central to the experiment.

Domen also investigated the heat defect: radiation-induced chemistry can release or store energy, changing the heat readout. Approximately 3700 measurements varied dissolved-gas conditions and compared the response with other calorimeters. The test examined whether a measured temperature rise represented the intended absorbed dose, rather than assuming the equivalence.^[ref]

Metrological traceability connects such measurements through documented calibrations and their measurement uncertainties. In the IAEA/WHO network, national laboratories and secondary-standard laboratories link reference dosimeters to the instruments used in practice. A primary measurement standard supplies the reference realization; the calibration chain transfers it to other instruments.^[ref]

A water phantom is a water-filled reference object used to measure how a radiation field deposits energy under specified, reproducible conditions. In radiation dosimetry, a detector can be positioned at controlled depths and lateral locations inside the water. The measured quantity is related to absorbed dose in that reference medium; the tank is not a complete anatomical model of a patient.^[ref]

The surrounding medium matters physically. Photons and charged particles can scatter, attenuate and transfer energy before it is collected locally. An empty holder, a small isolated water sample and a large water tank need not produce identical fields at a detector. The named IAEA edition treats both water as reference material and the margins of scattering material around a measurement region. A water-equivalent material must be compared in relevant absorption and scattering properties, not identified by similar bulk density alone.^[ref]

A practical apparatus combines a tank, a positionable ionization chamber or another characterized detector, a readout and a way to define the water surface. For example, PTW's MP1 description specifies one-dimensional detector travel, levelling supports and fill marks. Its depth-positioning mechanism supports a depth-dose curve; one mechanical coordinate is not itself a full three-dimensional scan.^[ref]

An original position-error model shows why the reference coordinates matter. At a fixed depth, stipulate a lateral absorbed dose profileA $1\mathrm{mm}$ displacement from $x=20\mathrm{mm}$ changes the dose ratio toThe same displacement from the centre gives $D(1)/D(0)\simeq 0.99875$. Thus the same absolute positioning error can produce about $5\%$ variation on a gradient and only $0.125\%$ at the centre of this stipulated profile. These are mathematical examples, not measured beam characteristics or equipment accuracy claims.

An ionization chamber also samples a finite sensitive volume, so detector volume averaging can differ from a point value of $D(x)$. Converting its collected electric charge to absorbed dose requires the applicable measurement calibration and measurement model, as described in medical physicist. Changing the tank position does not remove a detector's intrinsic spatial response.

Comparisons should therefore identify the water surface, detector reference point, irradiation geometry, water conditions and background treatment. The IAEA discussion of waterproof sleeves and chamber positioning illustrates why the detector and its surrounding hardware are part of the measurement configuration.^[ref]

A water-equivalent material is a material whose relevant interaction with ionizing radiation approximates that of water under specified conditions. For a water phantom, the comparison concerns energy absorption and scattering in the measurement geometry. It is not a statement that the material merely has a density near that of water, or that equivalence at one energy applies at every other energy.^[ref]

For a narrow monoenergetic photon beam, the linear attenuation coefficient satisfieswhere $\rho$ is the mass density and $\mu /\rho$ the mass attenuation coefficient. Equal densities leave the mass interaction coefficients unconstrained. Predicting absorbed dose also involves how transferred energy is deposited, for which the mass energy-absorption coefficient is relevant; the attenuation of primary photons alone is not the complete scattering and deposition problem. For charged particles, the corresponding comparison also involves stopping power.

For an original toy calculation, stipulate equal densities but linear attenuation coefficients ${\mu }_w=0.05\mathrm{c}{\mathrm{m}}^{-1}$ and ${\mu }_m=0.08\mathrm{c}{\mathrm{m}}^{-1}$ at one chosen photon energy. For $t=10\mathrm{cm}$, the unscattered fractions in the Beer-Lambert law areThe substitute transmits only $e^{-0.3}\approx 0.74082$ times the unscattered intensity of the reference, despite identical density. These coefficients are stipulated model inputs, not tabulated data for real water or a named plastic. Matching even this transmission at one energy would not establish equal absorbed dose throughout a larger scattering object. Energy dependence of water equivalence is therefore part of any meaningful equivalence specification.

A focused physical comparison places the same characterized detector in reference water and in a candidate slab assembly, with controlled material thickness, irradiation geometry and detector position. Record density and composition as well as detector response over the intended radiation conditions. Slab gaps and changes in surrounding scattering material can confound the comparison; the primary IAEA discussion explicitly treats material variability and the approximate nature of plastic-to-water scaling.^[ref]

Energy dependence of water equivalence means that a material can approximate water for one radiation energy or spectrum yet differ for another. A water-equivalent material must therefore be characterized for the interaction and radiation conditions of interest, rather than by one density or one transmission comparison.

For primary photon attenuation, defineusing the material and water mass attenuation coefficients. Equal surface mass densities give equal primary transmission only when this coefficient ratio is one. Changing slab thickness can match one selected energy, but cannot generally make $Q_{\mu }(E)$ constant at all energies.

A concrete example uses the primary NIST tables for liquid water and PMMA. Their mass attenuation coefficients, in $\mathrm{c}{\mathrm{m}}^2/g$, areso the PMMA-to-water ratios are about $0.80724$ at $30\mathrm{keV}$ and $0.96134$ at $100\mathrm{keV}$. These are material data at specified photon energies, not an assertion that PMMA is a universally equivalent substitute.^[ref]

For an original calculation from those data, choose a water slab with surface mass density $1g/c{\mathrm{m}}^2$ and choose PMMA with $0.1707/0.1641\approx 1.04022$ times that value. Their Beer-Lambert law optical depths then agree at $100\mathrm{keV}$. At $30\mathrm{keV}$, however, the PMMA optical depth is only about $0.83971$ of the water value. The primary transmitted fractions become $e^{-0.3756}\approx 0.68688$ for water and $e^{-0.31539}\approx 0.72950$ for the adjusted PMMA slab. Matching one row of the table did not match another.

The interaction being matched also matters. A mass energy-absorption coefficient concerns retained energy, while a mass attenuation coefficient concerns removal of primary photons from a beam. Matching the latter does not by itself match absorbed dose. A beam containing several photon energies introduces a spectrum-weighted water-equivalence ratio, which can change when those contributions change.

A proposed physical comparison uses the same characterized detector and irradiation geometry while varying the incident photon energy or filtration. Measure slab density and thickness, and compare both primary transmission and the relevant energy-deposition response. The NIST coefficients provide interaction data; scattering from the surrounding apparatus and the detector's own energy response remain separate parts of that experiment.

A spectrum-weighted water-equivalence ratio compares a specified material response with the corresponding water response after accounting for the radiation's energy distribution. Its definition must identify the interaction coefficient and the spectral weighting. An attenuation comparison and an energy-absorption comparison are different quantities.

For an energy-absorption comparison, let ${\Psi }_E(E)dE$ be the photon energy fluence in an energy interval, and write $a_j(E)=({\mu }_{\mathrm{en}}/\rho {)}_j(E)$ for material $j$. Define the coefficient-weighted response and its ratio bywith $A_w>0$. The same prescribed local photon energy fluence is used for both materials in this comparison. NIST distinguishes the mass energy-absorption coefficient from the mass attenuation coefficient and relates energy fluence to photon fluence through the additional photon-energy factor.^[ref]

The ratio is a weighted mean of the monoenergetic ratios $q(E)=a_m(E)/a_w(E)$, but its normalized weights areThus the weights depend on the water response as well as the incident spectrum. Averaging the ratios with energy-fluence weights alone generally gives a different result.

For an original two-line calculation, use the NIST water and PMMA energy-absorption data: at $30\mathrm{keV}$ the coefficients are $0.1557$ and $0.09645\mathrm{c}{\mathrm{m}}^2/g$ respectively; at $100\mathrm{keV}$ they are $0.02546$ and $0.02368\mathrm{c}{\mathrm{m}}^2/g$.^[ref] Equal energy fluences in the two lines giveEqual photon counts instead give energy-fluence weights proportional to $30$ and $100$, producing $Q_{\Psi }\approx 0.72904$. The different answers reflect different physical spectra, not a discrepancy in the tabulated coefficients.

An absorbed dose interpretation needs additional conditions such as charged-particle equilibrium. A finite object can also change the local spectrum through beam hardening and scattering. The ratio above therefore specifies a local coefficient-weighted comparison; it is not a universal conversion factor for every phantom size or irradiation geometry. A physical validation should characterize the local spectrum and detector energy response rather than assume that equal total fluence means equal spectral weighting.

A medical physicist applies physics to measurement, modeling and instrumentation in medicine. Typical scientific work concerns radiation therapy, medical imaging and nuclear medicine, together with research and teaching. A medical physicist connects an instrument's readout with a defined physical quantity, tests the assumptions behind that conversion and evaluates its measurement uncertainty. The professional role includes investigating equipment performance and consulting on the physical basis of diagnosis and treatment.^[ref]

An ionization chamber illustrates the reasoning. Ionizing radiation generates mobile charges in a chamber; the collected electric charge is an instrument reading, not already an absorbed dose. In a stipulated reference setup, let $Q$ be the measured charge, $Q_0$ a matched background reading and $N$ a calibrated conversion coefficient. A simple measurement model isThe coefficient is valid only for the conditions covered by its measurement calibration. The IAEA describes the documented chain linking reference laboratories, calibrated instruments and their users; moving a coefficient into a different beam or geometry requires an appropriate justification.^[ref]

For an original arithmetic example choose $Q=101\mathrm{nC}$, $Q_0=1\mathrm{nC}$ and $N=0.050Gy/nC$. The model gives $D=5.00\mathrm{Gy}$. Ignoring that background gives $5.05\mathrm{Gy}$. These stipulated detector values illustrate background subtraction and dimensional conversion; they do not specify a treatment or a clinical beam-calibration protocol.

Suppose the corrected charge $q=Q-Q_0$ has standard uncertainty $u(q)=1\mathrm{nC}$, and independently $u(N)=0.0005Gy/nC$. First-order uncertainty propagation givesA covariance term must be included if the input estimates are correlated. The medical physicist's task includes establishing whether that model describes the actual readout, rather than just multiplying a displayed number by a remembered constant.

A water phantom provides a reproducible medium for measurement comparisons; measurements at specified positions can test a beam model without equating the test object with every patient's anatomy. In medical imaging, analogous comparisons use known geometry or material properties to assess image formation and instrument response. Repeated equipment checks test constancy, while comparison against calibrated references tests accuracy. Research, reference measurements and clinical implementation therefore involve connected scientific questions with distinct evidence.

Brian Diffey, credited as B. L. Diffey in the primary byline, coauthored the 1983 study of optical transmission through human toenails with S. G. Parker. The paper measured thirteen autopsy toenails at fifteen wavelengths between 300 and 600 nm using a monochromator, integrating sphere and photodiode; its analysis included a correction for nail fluorescence.^[ref]

Newcastle University's named profile identifies Brian Diffey as a photobiology researcher, lists work under the initials B. L. Diffey and records his medical-physics work at Dryburn Hospital, the affiliation given for the nail paper. His research interests include measuring human exposure to ultraviolet radiation.^[ref] The research attribution here is collective; a joint byline does not establish which author performed a particular apparatus task.

The nail experiment illustrates fluorescence contamination in nail-transmission measurements. A light detector can register both incident-wavelength light transmitted through a sample and light emitted at other wavelengths. In an original linear detector model,where $s$ is spectral responsivity and $P_{\lambda }$ is spectral radiant power. Converting the total detector current into transmittance requires separating those contributions or specifying a valid correction. The detector's response at the emitted wavelengths need not equal its response at the illumination wavelength.

For an illustrative already power-calibrated signal, suppose incident power is 1.00 mW and the collected signal contains 0.08 mW of transmitted illumination plus 0.02 mW of fluorescence. Treating all detected power as transmitted illumination gives 10% instead of 8%, a 25% relative overestimate. These are invented values explaining the measurement issue, not data reported by the authors. Their explicit fluorescence correction shows why a detector reading alone does not define the desired optical quantity.

Methods that infer internal biological structure or function from measured signals. Computed tomography, positron emission tomography and single-photon emission computed tomography use different signal-generation and reconstruction physics.

Pelvic ultrasonography uses ultrasonography to image structures in the pelvis, including the reproductive organs and urinary bladder. The probe's position determines the acoustic path and which structures lie in view: transabdominal and transvaginal ultrasound approaches observe the region from different geometries. Returning echoes provide information about interfaces and motion, with the usual limitations of acoustic access through gas and bone.^[ref]

Endoscopic ultrasonography combines an endoscope with an acoustic transducer to obtain ultrasonography images from within the gastrointestinal tract. Positioning the source and receiver near a target shortens the intervening acoustic path and can reveal the wall and nearby structures. A probe integrated into the endoscope tip and a probe passed through its working channel are different apparatus arrangements.^[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]

Transillumination examines internal structure using light transmitted through a body region or specimen. The source illuminates one side and the observer or detector records light emerging after propagation through the material. Different optical absorption and scattering properties can create image contrast.^[ref]

A simple physical demonstration illuminates a fingertip from behind and observes the diffuse transmitted glow. Its appearance depends on wavelength, path length and the tissue's optical properties. Strong scattering redistributes the paths, so a brightness difference cannot generally be interpreted as a sharply localized anatomical boundary without an additional model.

Ultrasonography forms medical images using ultrasound. In pulse-echo imaging, a piezoelectric transducer emits a short acoustic pulse and receives echoes from changes in acoustic impedance. If an echo returns after time $\Delta t$ from a reflector at distance $d$ in a uniform medium with sound speed $c$, the round trip gives $d=c\Delta t/2$. Scanning the beam assembles spatial information from many such measurements.^[ref]

A water-tank experiment with two reflectors at known separations tests the depth calculation without biological interpretation. An incorrect assumed sound speed changes the inferred depths; overlapping pulses limit the separation of nearby reflectors. In tissue, acoustic attenuation, scattering and the geometry of the beam further affect the image. These mechanisms explain why the displayed anatomy depends on both physical propagation and the acquisition model.

Pulse-echo imaging sends a short acoustic pulse and records echoes returning from interfaces or scatterers. If sound speed is approximately constant and the path is straight, an echo delay $t$ corresponds to range $r=ct/2$, because sound travels to the scatterer and back.

Scanning beam direction and measuring echo strength produces an image. Pulse duration and bandwidth affect axial resolution, while beam width affects transverse resolution. Incorrect sound-speed assumptions distort inferred positions, and multiple reflections can create echoes that do not correspond to a single direct round trip.

Use of ultrasonography to examine the urinary bladder, including assessment of its distension in suspected urinary retention.

Transvaginal ultrasound is pelvic ultrasonography with an internal probe positioned in the vagina, close to pelvic structures such as the uterus and ovaries. This changes the imaging geometry and the intervening acoustic path. The measured signal is still an ultrasound echo; the probe's position supplies access to structures that can be harder to view along an external abdominal path.^[ref]

Doppler ultrasonography applies Doppler ultrasound to motion within the body, especially flowing blood. Moving scatterers change the returned frequency or phase; the shift measures a component of velocity along the acoustic geometry. Combining that information with ultrasonography locates motion relative to the imaged structures.^[ref]

A color map assigns a display color to a measured flow quantity under a chosen sign convention. It therefore represents an inferred motion, rather than the literal optical color of the blood. Estimating a speed requires the beam-to-flow angle and the assumptions behind the Doppler ultrasound measurement; a small shift can reflect a nearly transverse flow as well as a small speed.

Compression ultrasonography combines ultrasonography with observation of how a structure deforms under an applied load. For a vein, the image records whether the opposing walls approach each other during compression. A segment that fails to compress can provide evidence of an obstructing thrombus; the useful measurement is the dynamic mechanical response as well as its visual appearance.^[ref]

Interpretation depends on adequate visualization and loading: an incomplete view or ineffective compression does not establish the same physical observation as a properly imaged noncompressible segment. This illustrates a general measurement principle: the input perturbation and the object's response both belong to the experiment.

Compensation for photons lost along an emission-imaging path. In PET/CT or SPECT/CT, a registered computed tomography attenuation map supplies information for this correction.

Imaging or therapy using administered radiopharmaceuticals. The distribution of the labelled compound selects biological function or tissue, while emitted radiation provides a measurement or deposited energy.

Functional imaging of bone-seeking tracer uptake with a gamma camera or single-photon emission computed tomography. Uptake patterns can reveal abnormal bone turnover.

A position-sensitive detector, usually using a collimator, scintillator and light sensors, that forms a projection image of a gamma-emitting tracer. Energy selection reduces scattered-photon contamination.

A pharmaceutical containing a radionuclide, with uptake and clearance chosen for imaging or treatment. Biological targeting and radioactive decay jointly determine its useful signal and tissue dose.

An iodine radionuclide with approximately eight-day half-life, emitting beta particles and gamma rays. Its uptake and retention depend strongly on the carrier and tissue physiology.

Radioiodide used in selected thyroid treatments because iodine uptake localizes activity in thyroid tissue. Iodine-131 supplies local beta radiation and imageable gamma emission.

A diagnostic bone tracer combining technetium-99m with a diphosphonate carrier. Uptake reflects bone turnover and delivery, rather than a unique disease diagnosis.

A metastable nuclear isomer used in diagnostic tracers, with approximately six-hour half-life and $140\mathrm{keV}$ imageable gamma rays. Its chemical carrier determines biological uptake.

Treatment through controlled deposition of ionizing absorbed dose. External beams and internal radiopharmaceuticals require different delivery and radiation dosimetry models.

An effect-equivalent dose derived from the linear-quadratic radiobiology model, with a subscript often indicating the tissue's assumed $\alpha /\beta$ in gray. It is distinct from the physical total absorbed dose $Nd$. Increasing fraction size at fixed tumour BED can increase the normal-tissue BED when the latter has smaller $\alpha /\beta$.

A model for surviving fraction $S$ after radiation dose $d$. Independent fully repaired fractions add their logarithmic effects. For $N$ equal fractions and no repopulation, dividing the total log kill by $\alpha$ gives the biologically effective dose $Nd(1+d/(\alpha /\beta ))$. Comparing tissue types requires their own parameters and the same stated repair assumptions.

The variation of absorbed dose with depth for a specified beam, geometry and medium. A megavoltage photon beam has a secondary-electron buildup region followed by gradual dose reduction. A nearly monoenergetic proton beam instead exhibits a Bragg peak near the end of its range.

A specified geometry, beam configuration and dose prescription intended to cover a target while limiting normal-tissue dose. Robustness to setup, motion and anatomy changes is part of assessing a plan.

Treatment using proton beams with controllable finite range and a Bragg peak. Potential normal-tissue sparing must be assessed against range uncertainty, motion and biological-effect uncertainties.

Uncertainty in where a charged-particle beam stops because of material conversion, anatomy, motion or delivery errors. A steep distal dose gradient makes it particularly consequential for target coverage and nearby tissue.

External-beam treatment using photons that create secondary charged particles in tissue. Megavoltage depth-dose curves usually show build-up followed by an extended fall-off and exit dose.

Treatment using spatially varying beam fluence to shape the combined three-dimensional dose distribution. Improved target conformity may come with dose distributed through a larger volume at lower levels.