MR ANGIOGRAPHY

Combining a perfectly timed gadolinium contrast agent injection with three-dimensional (3D) spoiled gradient-echo (SPGR) magnetic resonance (MR) imaging produces high signal-to-noise ratio (S/N) MR angiograms covering extensive regions of vascular anatomy within a breath hold (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). This article provides information for radiologists on

1. Principles of 3D gadolinium-enhanced MR angiography.
2. Patient set-up and positioning.
3. Selection of optimal imaging parameters.
4. Timing of the gadolinium bolus.
5. Reconstruction of images on a computer workstation.
6. Identification of normal variants, postoperative cases, and common pathologic entities.


Principles of 3D Gadolinium-enhanced MR Angiography

Gadolinium is one of the rare earth elements in the transition group IIIb of the periodic table. Actually, it is not rare at all, but a rather common element found throughout the earth's crust. It has eight unpaired electrons in its outer shell, which causes its paramagnetic effects. Gadolinium by itself can cause heavy metal poisoning. However, when bound to a chelator, it is safe for intravenous injection, yet remains paramagnetic. It shortens the T1 of blood in the region of the gadolinium molecule according to the following equation (1):

1/T1=1/1,200 + (R1 × [Gd]),

where R1 is the T1 relaxivity of the gadolinium chelate, [Gd] is the gadolinium concentration in the blood, and 1,200 is the blood T1 (in msec) without gadolinium.


Figure 1. Effect of gadolinium concentration on blood T1. (The graph was calculated with Microsoft Excel 97 [Microsoft, Redmond, Wash] by using the above formula.)

The blood [Gd] must be greater than 1.0 mmol/L for T1 to be less than 270 msec, which is the T1 of fat at 1.5 T (1, 5). This is the property which is important for increasing the MR signal intensity of blood on contrast-enhanced SPGR images. Note that this T1 shortening effect is maximized by using gadolinium chelates with the highest relaxivity and by having a high gadolinium concentration in the blood.

Gadolinium Safety

Gadolinium contrast agents have an extraordinarily favorable safety profile. There is no clinically detectable nephrotoxicity for gadopentetate dimeglumine (Magnevist; Berlex Imaging, Wayne, NJ), gadoteridol (ProHance; Bracco Diagnostics, Princeton, NJ), or gadodiamide (Omniscan; Nycomed Amersham, Princeton, NJ) even at high doses (11). In addition, they have a very low frequency of adverse events. Idiosyncratic reactions are rare, and serious adverse events are extremely rare (1 in 20,000) (12). Note that important contraindications to gadolinium include pregnancy and a history of a life-threatening reaction to gadolinium itself. In patients with poor renal function, there may be delayed excretion of gadolinium contrast agents.

Gadolinium Dose

With intravenous injection, gadolinium is initially in the arm vein, then the pulmonary circulation, then the arteries; eventually it is distributed throughout the circulatory system. Within a few minutes, there is redistribution into the extracellular fluid space. To make blood bright compared with all background tissues, it is necessary to give a sufficient dose of gadolinium. Two or three bottles (20 mL each) of the gadolinium contrast agent (about 0.3 mmol/kg gadolinium) is usually sufficient for an average or heavy person when imaging in the equilibrium phase. However, arteries are best imaged during the arterial phase of gadolinium infusion. This gives a higher arterial S/N and eliminates the confusion caused by overlapping venous enhancement. It may seem that a fast acquisition is necessary to capture the contrast agent bolus during the brief moment when the agent is present in the arteries but not yet in the veins. However, it is possible to take advantage of three important effects that allow the relatively slow MR acquisition to capture an arterial-phase image without having to use large amounts of gadolinium.

K Space

The most important effect is related to how MR data are mapped in k space. K space, or Fourier space, does not map to the image pixel by pixel. Rather, the information within k space determines spatial frequency features of the image. The low spatial frequency information, in the center of k space, dominates image contrast, while the higher spatial frequency data, at the periphery of k space, determines image detail. To obtain an arterial-phase image in which arteries are bright and veins are dark, it is essential that the central k-space data (ie, the low spatial frequency data) are acquired while the gadolinium concentration in the arteries is high but relatively lower in the veins. The presence of contrast agent is not as important for acquisition of peripheral k-space data. This trick allows a relatively long MR acquisition to achieve the image contrast associated with a brief window of time. That brief window of time is the instant when central k-space data are acquired. Therefore, it is critical to time the bolus for maximum arterial [Gd] during acquisition of central k-space data. With perfect bolus timing, high S/N arterial-phase images are possible with smaller doses of gadolinium.

Gadolinium Extraction

A second important effect is the extraction of gadolinium in the systemic capillary beds. This extraction results in venous blood tending to have a lower concentration of gadolinium relative to arterial blood, even for relatively long, sustained infusions lasting several minutes. This effect is not present in the cerebrovascular circulation because of the blood-brain barrier. Consequently, arterial-phase imaging in the central nervous system is more difficult.

Infusion Rate and Cardiac Output

A third effect is the relationship between arterial gadolinium concentration, the infusion rate, and cardiac output as follows:

[Gd]Arterial=Injection Rate/Cardiac Output



Figure 2. T1 versus injection rate at differing cardiac outputs.


This graph is a computer model generated for different cardiac outputs. Note that this graph is for static, nonmoving blood. The actual T1 of moving blood is even less than in the above graph. Notice that an injection rate of 0.2-0.3 mL/sec is required to decrease the blood T1 value to less than 150 msec in a patient with a cardiac output of 5 L/min. This is sufficiently below the T1 of fat (270 msec at 1.5 T) so that only the gadolinium in blood produces high signal intensity on T1-weighted SPGR images.

Arterial [Gd] is maximized by relaxing the patient to reduce cardiac output and by using a high infusion rate. However, fast infusion rates lasting for at least half of the acquisition time require large doses of gadolinium. The dose can be kept to a reasonable level by scanning rapidly. Fast acquisitions (<45 seconds) are possible with high performance gradient systems that allow short repetition and echo times, without having to make the bandwidth too wide. Fast acquisition has the additional benefit of making it possible for the cooperative patient to suspend breathing and to hold perfectly still.

Saline Flush and Intravenous Tubing

It is important to use intravenous (IV) line tubing that allows simultaneous attachment of separate syringes for the contrast agent and saline flush. The SmartSet (TopSpins, Ann Arbor, Mich), developed at the University of Michigan, has one-way valves that allow automatic switching between the contrast agent injection and saline flush so that there will be one continuous bolus with no gaps. By using the same tubing set for all patients receiving dynamic contrast agent injection, the operator becomes familiar with performing the injections and especially with the resistance to injection. It is then easier to concentrate on correctly timing the bolus and instructing the patient to suspend breathing.
Click here to view IV setup and use of SmartSet.



At least 20 mL of saline is recommended to adequately flush the contrast agent through the IV tubing and arm vein. By starting with a 30-mL saline-filled syringe, it is possible to initially prime the SmartSet with 8 mL of saline, test the IV once or twice with a 1-mL saline injection, and still have 20 mL left for the dynamic flush.

Gadolinium Dose

When beginning, we recommend use of two bottles (42 mL) for the average-size patient and three bottles (63 mL) for patients weighing more than 100 kg. Once you learn how to time the contrast agent injections perfectly, you will find it is possible to reduce the dose and still obtain diagnostic images.

Contrast Agent Bolus Timing

Perfect contrast agent bolus timing is crucial to ensure that the maximum arterial [Gd] occurs during the middle of the acquisition, when central k-space data are acquired. It is also essential that [Gd] not change too rapidly, as this will create a "ringing" artifact (13) (click here for example). Minimizing the ringing artifact requires that the contrast agent infusion last for at least half the duration of the 3D image acquisition. Bolus timing is difficult because the time required for the contrast agent bolus to travel from the injection site (typically an antecubital vein) to the artery being imaged is highly variable. For renal arteries, it may be only 10 seconds in a young, healthy person with a central intravenous line, or it may be as long as 50 seconds in an older patient with congestive heart failure and an intravenous line in the hand or wrist.

Timing for Long Acquisitions

For long acquisitions, lasting more than 100 seconds, timing is easy because errors of 10-15 seconds are small relative to the total scan duration. Use sequential ordering of k space, so that the center of k space is collected during the middle of the acquisition. Sequential ordering tends to result in fewer artifacts. Begin injecting the gadolinium just after initiating imaging. Finish the injection just after the midpoint of the acquisition, being careful to maintain the maximum injection rate for the approximately 10-30 seconds prior to the middle of the acquisition. This will ensure a maximum arterial [Gd] during the middle of the acquisition, when central k-space data are collected. To ensure full use of the entire dose of contrast agent, it is useful to flush the IV tubing with 20 mL of normal saline. This can be facilitated by using the SmartSet, which has ports for simultaneous attachment of contrast agent and saline syringes and valves for automatic switching between syringes. In this way, there is no delay between finishing the contrast agent injection and beginning the saline flush.

Timing for Fast (Breath-hold) Scans

For fast scans, less than 45 seconds in duration, contrast agent bolus timing is more critical and challenging. This is because bolus timing errors of 15 seconds can ruin a fast breath-hold scan. There are several approaches to determining the optimal bolus timing for these fast scans. The simplest, although least successful approach, is to guess on the basis of patient age, cardiac status, presence of aortic aneurysmal disease, and IV location. For a typical breath-hold scan duration of 35-45 seconds in a reasonably healthy patient with an IV site in the antecubital vein, a delay of approximately 10-12 seconds is appropriate. Therefore, in this scenario, begin the injection, and then 10 seconds later start imaging while the patient suspends breathing. If there is no convenient clock available to time this delay, take advantage of the natural rhythm of the patient's respiration. One deep breath in followed by a deep breath out takes approximately 4 seconds. Two breaths are eight seconds, followed by a deep breath in, 10 seconds, which represents the optimum delay between start of injection and beginning of scanning. If a patient is older and has a history of cardiac or aortic aneurysmal disease, add one or two extra breaths to the delay. Also, if the IV site is in the wrist, add an extra breath to the delay. Alternatively, if the patient is a marathon runner or you are injecting via a central line, it may be suitable to use only 1½ breaths of delay, or 6 seconds. A firm injection is necessary to keep the contrast agent bolus together. However, if the injection is too vigorous, it may cause rupture of the vein, with resulting extravasation of the contrast agent.

More reliable and precise techniques for determining the contrast travel time are also available. These include using a test bolus (14) to precisely measure the contrast travel time, using an automatic pulse sequence that monitors signal in the aorta and then initiates imaging after contrast is detected arriving in the aorta (Fluoroscopic triggering or MR SmartPrep) (15, 16), or imaging so rapidly that bolus timing is unimportant (10). A typical monitor signal graph is shown below.




Figure 3. Tracking signal versus time.
Blue line - MR signal intensity in volume of interest.
Green line - Level at which signal is 100% above baseline.
Red arrows - Time of injection and optimal time for imaging.


Note that the centric ordering of k space for the triggered acquisitions may create artifacts if the contrast agent bolus is still arriving when the scan is started. Sometimes this artifact may be reduced with sequential ordering. This artifact may also be reduced by delaying 5-8 seconds after detecting the leading edge of the bolus to give the contrast agent time to flow in completely and reach the plateau phase of the bolus.

Postprocessing of MR Data

Substantial improvement in image quality, and especially image contrast, can be attained through postprocessing techniques.

* Zero Padding
Image resolution can be increased with interpolation. One particularly useful interpolation scheme is known as zero padding. This involves filling out peripheral lines of k-space data with zeroes prior to performing the Fourier transform. Although no additional time is required for data collection, the Fourier transform will reconstruct more images with a smaller spacing. For example, with two-fold zero padding, if the partition thickness is 3 mm, the Fourier transform will reconstruct additional images that also have a 3-mm slice thickness but at 1.5-mm spacing with 50% overlap. This helps eliminate volume averaging and creates smooth visualization of small vessels on the reformatted maximum intensity projection (MIP) images. If available, two-fold zero padding in the slice direction is recommended.
* MR Digital Subtraction Angiography (DSA)
Image contrast can be improved by digital subtraction of precontrast image data from dynamic, arterial, or venous phase image data. This subtraction can be performed either slice-by-slice or prior to the Fourier transform by using a complex subtraction method. The improvement in contrast achieved with DSA may reduce the gadolinium dose required. However, there must be no change in the patient position between the precontrast and dynamic contrast-enhanced imaging. This requirement for no motion is easily met in the pelvis and legs, which can be sandbagged and strapped down. It is more difficult to achieve in the chest and abdomen, where respiratory, cardiac, and peristaltic motions are more difficult to avoid. Note that complex subtraction is generally performed automatically by the scanner before creating any of the images.


Multiplanar Reconstructions

Reformations and MIPs are essential for optimal assessment of vascular anatomy. Single-voxel-thick reformations and narrow subvolume MIPs show bifurcations and branch vessels in profile. This is important because atherosclerotic disease tends to be most severe at branch points. By creating subvolume MIPs of the 3D image data, these techniques help unfold tortuous vessels and eliminate the confusing overlap of vascular anatomy.

Creating an MIP Image

One approach to performing a subvolume MIP is to first load the entire 3D volume of arterial phase image data into the computer workstation 3D analysis program. Display a coronal MIP of the entire volume, an axial reformation, and an oblique view. On the coronal view, move the dot (which tracks the location) cranially and caudally while watching the axial reconstruction window to find the renal arteries. Display this subvolume of sagittal data as an MIP. Make this oblique MIP thick enough to encompass most of the aorta. Be certain to align the axis of the subvolume MIP so that it is parallel to the origin of the vessel. Although the entire length of the vessel may not be seen on this image, it will be an accurate representation of the vessel's origin, with no overlap from the aorta. This may then be repeated by moving the tracker dot on the axial image and watching the oblique view to create a sagittal view of the celiac and superior mesenteric arteries. This will show the celiac and superior and inferior mesenteric arteries, as well as the anterior and posterior margins of the aorta to best advantage.

Renal Artery Stenosis

Renal artery stenosis is an important cause of hypertension and renal failure (17, 18, 19, 20). This should be imaged with a comprehensive approach (11) that includes both morphologic and functional assessment of the renal vasculature.Many sequences are available which provide important information (21, 10, 22, 23, 24). We have chosen to do 3D phase contrast because of its simplicity and reliability (2).

AN INTRODUCTION TO PET

1. Introduction
   

   

   Diagnosing, staging, and re-staging of cancer, as well as the planning and monitoring of cancer treatment, have traditionally relied heavily on anatomic imaging with computed tomography (CT) or magnetic resonance imaging (MRI). These anatomic imaging modalities provide exquisite anatomic detail and are invaluable, especially for guiding surgical intervention and radiotherapy. However, they do have limitations in their ability to characterize tissue reliably as malignant or benign. Anatomic imaging generally has a high sensitivity for the detection of obvious structural alterations (e.g. enlarged structures, abnormal imaging characteristics) but a low specificity for further characterizing these abnormalities as malignant or benign. Necrotic tissue, scar tissue, and inflammatory changes often cannot be differentiated from malignancy based on anatomic imaging alone. In addition, lymph nodes which are not pathologically enlarged by size criteria alone but are harboring malignant cells pose a special diagnostic problem when using traditional cross-sectional imaging.

   Therefore, much effort has been forth in the research and development of molecular imaging techniques to detect abnormal behavior of tissues. The nuclear medicine community has developed positron emission tomography (PET) for imaging the activity of an injected radionuclide labeled glucose analogue, Fluorine-18-deoxyglucose (FDG), as a means to discriminate benign from malignant tissues accurately in many clinical settings. This technique is based on the fact that malignant tissue typically exhibits markedly increased rates of glucose metabolism.

   Just like glucose, FDG is actively transported into cells mediated by a group of structurally related glucose transport proteins. Once intracellular, glucose (and therefore also FDG) are phosphorylated by hexokinase as the first step in the glycolytic metabolism pathway. Normally, after being phosphorylated glucose continues along the glycolytic pathway for energy production. FDG, on the other hand, cannot enter the glycolytic pathway and becomes effectively trapped intracellularly as FDG-6-phosphate. Tumor cells display increased numbers of glucose transporters as well as higher levels of hexokinase. Most tumor cells are highly metabolically active with high mitotic rates that favor the more inefficient anaerobic metabolic pathway which adds to the already increased glucose demands. These combined mechanisms allow tumor cells to take up and retain higher levels of FDG when compared to normal tissues.

   PET provides imaging of the whole body distribution of FDG, thus highlighting the markedly increased metabolic activity of tumor cells. Sites of tumor involvement not obvious from cross-sectional images alone are often found, such as lymph nodes involved by tumor which are not pathologically enlarged by size criterion.
2. 

An important concept regarding PET imaging is that FDG is not cancer specific and will accumulate in any areas of high rates of metabolism and glycolysis. Therefore, increased uptake can be expected in all sites of hyperactivity at the time of FDG administration (e.g. muscles and nervous system tissues); at sites of active inflammation or infection (e.g. sarcoidosis, arthritis, pneumonia, etc.); and at sites of active tissue repair (e.g. surgical or traumatic wounds, healing fractures, etc.).

Taking the molecular imaging concept of PET one step further is the combined imaging modality positron emission tomography/computed tomography (PET/CT). PET/CT fuses functional information in the form of PET data and anatomic information in the form of CT data acquired almost simultaneously so that these information sets can be viewed and interpreted together. In PET/CT, both the multidetector CT apparatus and the PET detectors are mounted in the same gantry, one immediately behind the other. Both PET and CT scanning are performed with the patient lying in the same position on the imaging table resulting in optimal correlation of anatomic and metabolic information. For interpretation, the PET data is actually superimposed upon the CT data (co-registration) resulting in improved anatomic localization of normal and abnormal FDG activity. This fusion process has proven beneficial in more exactly localizing tissues involved by tumor. Better co-registration is especially significant in regions of complex anatomy, such as in the abdomen and in the head and neck. More exact localization of the involved tissues results in more accurate staging and more appropriate treatment planning including surgical therapy, radiotherapy, and medical therapy.

GLIOBLASTOMA MULTIFORME

Axial Gd enhanced T1W Image

Axial T2 W Image

WHO Grade IV

Cell of Origin: ASTROCYTE

Synonyms: GBM, glioblastoma multiforme, spongioblastoma multiforme

Common Locations: cerebral hemispheres, occasionally elsewhere (brainstem, cerebellum, cord)

Demographics: peak from 45-60 years

Histology: grossly heterogeneous, degeneration, necrosis and hemorrhage are common

Special Stains: GFAP varies, often present in areas of better differentiation

Progression : Can't get any worse.

Radiology: Glioblastoma is usually seen as a grossly heterogeneous mass. Ring enhancement surrounding a necrotic center is the most common presentation, but there may be multiple rings. Surrounding vasogenic edema can be impressive, and adds significantly to the mass effect. Signs of recent (methemoglobin) and remote (hemosiderin) hemorrhage are common. Despite it’s apparent demarcation on enhanced scans, the lesion may diffusely infiltrate into the brain, crossing the corpus callosum in 50-75% of cases.

INTRACEREBRAL HEMORRHAGE ON MRI

Hemorrhage T1 T2

Hyperacute hemorrhage(0-1 day) Isointense Hyperintense

Acute hemorrhage (1-3 days) Isointense Hypointense

Early subacute hemorrhage(4-7 days) Hyperintense Hypointense

Late subacute (7-14 days) Hyperintense Hyperintense

Chronic (> 2 weeks) Hypointense Hypointense

BASIC PRINCIPLES OF MRI

In the absence of a strong magnetic field, hydrogen nuclei are randomly aligned as in (a). When the strong magnetic field, Bo , is applied, the hydrogen nuclei precess about the direction of the field as in (b).

The basis of MRI is the directional magnetic field, or moment, associated with charged particles in motion. Nuclei containing an odd number of protons and/or neutrons have a characteristic motion or precession. Because nuclei are charged particles, this precession produces a small magnetic moment.
When a human body is placed in a large magnetic field, many of the free hydrogen nuclei align themselves with the direction of the magnetic field,as shown in the figure above... The nuclei precess about the magnetic field direction like gyroscopes. This behavior is termed Larmor precession.
The frequency of Larmor precession is proportional to the applied magnetic field strength as defined by the Larmor frequency, Wo
Wo = Y x Bo
where Y is the gyromagnetic ratio and Bo is the strength of the applied magnetic field. The gyromagnetic ratio is a nuclei specific constant. For hydrogen, Y =46.2 MHz/ Tesla.
To obtain an MR image of an object, the object is placed in a uniform magnetic field, Bo, of between 0.5 to 1.5 Tesla. As a result, the object's hydrogen nuclei align with the magnetic field and create a net magnetic moment, M , parallel to Bo. This behavior is illustrated in Figure Below

Figure (a) The RF pulse, Brf, causes the net magnetic moment of the nuclei, M, to tilt away from Bo. (b) When the RF pulse stops, the nuclei return to equilibrium such that M is again parallel to Bo. During realignment, the nuclei lose energy and a measurable RF signal

Once the RF signal is removed, the nuclei realign themselves such that their net magnetic moment, M , is again parallel with Bo. This return to equilibrium is referred to as relaxation. During relaxation, the nuclei lose energy by emitting their own RF signal (see Figure 2.2b). This signal is referred to as the free-induction decay (FID) response signal. The FID response signal is measured by a conductive field coil placed around the object being imaged. This measurement is processed or reconstructed to obtain 3D grey-scale MR images.

To produce a 3D image, the FID resonance signal must be encoded for each dimension. The encoding in the axial direction, the direction of Bo, is accomplished by adding a gradient magnetic field to Bo. This gradient causes the Larmor frequency to change linearly in the axial direction. Thus, an axial slice can be selected by choosing the frequency of Brf to correspond to the Larmor frequency of that slice. The 2D spatial reconstruction in each axial slice is accomplished using frequency and phase encoding. A ``preparation'' gradient, Gy , is applied causing the resonant frequencies of the nuclei to vary according to their position in the y-direction. Gy is then removed and another gradient, Gx , is applied perpendicular to Gy . As a result, the resonant frequencies of the nuclei vary in the x-direction due to Gx and have a phase variation in the y-direction due to the previously applied Gy. Thus, x-direction samples are encoded by frequency and y-direction samples are encoded by phase. A 2D Fourier Transform is then used to transform the encoded image to the spatial domain.
The voxel intensity of a given tissue type (i.e. white matter vs grey matter) depends on the proton density of the tissue; the higher the proton density, the stronger the FID response signal. MR image contrast also depends on two other tissue-specific parameters:
The longitudinal relaxation time, T1 , and
the transverse relaxation time, T2
T1 measures the time required for the magnetic moment of the displaced nuclei to return to equilibrium (ie. realign itself with Bo). T2 indicates the time required for the FID response signal from a given tissue type to decay.
When MR images are acquired, the RF pulse, Brf , is repeated at a predetermined rate. The period of the RF pulse sequence is the repetition time, TR. The FID response signals can be measured at various times within the TR interval. The time between which the RF pulse is applied and the response signal is measured is the echo delay time, TE. By adjusting TR and TE the acquired MR image can be made to contrast different tissue types.

The MR images used in this article were all acquired using a Multiple Echo Spin Echo pulse sequence in which two images are acquired simultaneously. TR and TE are adjusted such that tissues with a high proton density appear bright in the first image and tissues with a long T2 appear bright in the second image. The two images are said to be proton density-weighted (PD-weighted) and T2-weighted respectively. Figure 2.3 shows 2D slices from the weighted MRI volumes.

Figure (a) A proton density (PD) weighted MR image slice. (b) The same T2-weighted slice.

Spin-spin relaxation or T2 Relaxation

Immediately after a 90 degree RF pulse, the individual magnetic moments are all located in the transverse plane ; more important. However , they are coherent ( pointig in the same direction at nearly the same frequency). In other words , all protons have the same rotating phase.
Because the FID (free induction decay) is the sum of voltage from many protons at each spatial location,the protons must precess at the sane frequency and with the same alignment so that their magnetization work together. As the time goes on ,following the RF excitation pulse the individual magnetic moments begin to become spread out in the transverse plane. One cause of this spread is due to small local variation in the otherwise static magnetic field resulting out of random interaction from the magnetic moments of nearby protons. It is the spreading out that causes the vector sum to decrease. With time ,therefore, the individual spins

Spin-lattice relaxation or T1 Relaxation

When a 90 degree RF pulse is applied, it rotates
net magnetization vector M into the x-y or transverse plane , entire vector is located in that plane and its value along the z-axis is zero. Following cessation of the RF pulse , the nuclei returns towards their equilibrium magnetization. M rotates back from the x-y plane to the z-axis and M returns to to the initial magnetization at some finite time latter. The process of returning towards the equilibrium magnetization costitutes T1 rlaxation or longitudinal relaxation. The process is cused by release of energy into the surrounding tissue ( i.e., into the molecular environment or lattice around the proton ). Hence this relaxation is also known as spin-lattice relaxation.