Hyperthermia therapy

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Hyperthermia_therapy

 

Hyperthermia therapy
Whole-body suit used in hyperthermia therapy.
ICD-10-PCS	6A3
ICD-9-CM	93.35, 99.85
MeSH	D006979
OPS-301 code	8–60

Hyperthermia therapy (or hyperthermia, or thermotherapy) is a type of medical treatment in which body tissue is exposed to temperatures above body temperature, in the region of 40–45 °C (104–113 °F). Hyperthermia is usually applied as an adjuvant to radiotherapy or chemotherapy, to which it works as a sensitizer, in an effort to treat cancer.

Hyperthermia uses higher temperatures than diathermy and lower temperatures than ablation. When combined with radiation therapy, it can be called thermoradiotherapy.

Definition

Hyperthermia is defined as supra-normal body temperatures. There is no consensus as to what is the safest or most effective target temperature for the whole body. During treatment the body temperature reaches a level between 39.5 and 40.5 °C (103.1 and 104.9 °F). However, other researchers define hyperthermia between 41.8–42 °C (107.2–107.6 °F) (Europe, USA) to near 43–44 °C (109–111 °F) (Japan, Russia).

Types

Patient is undergoing local hyperthermia treatment for head and neck cancer.

• Local hyperthermia heats a very small area and is typically used for cancers near or on the skin or near natural openings in the body (e.g., the mouth). In some instances, the goal is to kill the tumor by heating it, without damaging anything else. The heat may be created with microwave, radiofrequency, ultrasound energy or using magnetic hyperthermia (also known as magnetic fluid hyperthermia). Depending on the location of the tumor, the heat may be applied to the surface of the body (superficial hyperthermia), inside normal body cavities (intraluminal hyperthermia), or deep in tissue through the use of needles or probes (interstitial hyperthermia). It should not be confused with ablation of small tumors, where higher temperatures (>55 °C) are applied with an aim to kill the tumor cells.
• Regional hyperthermia heats a larger part of the body, such as an entire organ or limb. Usually, the goal is to weaken cancer cells so that they are more likely to be killed by radiation and chemotherapeutic medications. This may use the same techniques as local hyperthermia treatment, or it may rely on blood perfusion. In blood perfusion, the patient's blood is removed from the body, heated up, and returned to blood vessels that lead directly through the desired body part. Normally, chemotherapy drugs are infused at the same time. One specialized type of this approach is continuous hyperthermic peritoneal perfusion (CHPP), which is used to treat difficult cancers within the peritoneal cavity (the abdomen), including primary peritoneal mesothelioma and stomach cancer. Hot chemotherapy drugs are pumped directly into the peritoneal cavity to kill the cancer cells.
• Whole-body hyperthermia heats the entire body to temperatures of about 39 to 43 °C (102 to 109 °F), with some advocating even higher temperatures. It is typically used to treat metastatic cancer (cancer that spread to many parts of the body). Techniques include infrared hyperthermia domes which include the whole body or the body apart from the head, putting the patient in a very hot room/chamber, or wrapping the patient in hot, wet blankets or a water tubing suit.

Treatment

Research has shown that hyperthermia is able to damage and kill cancer cells.

Localized hyperthermia treatment is a well-established cancer treatment method with a simple basic principle: If a temperature elevation to 40 °C (104 °F) can be maintained for one hour within a cancer tumor, the cancer cells will be destroyed.

The schedule for treatments has varied between study centers. After being heated, cells develop resistance to heat, which persists for about three days and reduces the likelihood that they will die from direct effects of the heat. Some even suggest maximum treatment schedule of twice a week. Japanese researchers treated people with "cycles" up to four times a week apart. Radiosensitivity may be achieved with hyperthermia, and using heat with every radiation treatment may drive the treatment schedule. Moderate hyperthermia treatments usually maintain the temperature for approximately an hour.

The St. George Klinik for hyperthermia in Germany is using it to kill Lyme disease bacteria that spread throughout the whole body. The entire body including blood is heated for approximately two hours.

Before the advent of modern antiretroviral therapy extracorporeal whole body hyperthermia was tried as a treatment for HIV/AIDS, with some positive outcomes.

Adverse effects

External application of heat may cause surface burns. Tissue damage to a target organ with a regional treatment will vary with what tissue is heated (e.g. brain treated directly may injure the brain, lung tissue treated directly may cause pulmonary problems) Whole body hyperthermia can cause swelling, blood clots, and bleeding. Systemic shock, may result, but is highly dependent upon method difference in achieving it. It may also cause cardiovascular toxicity. All techniques are often combined with radiation or chemotherapy, muddying how much toxicity is the result of those treatments versus the temperature elevation achieved.

Technique

Heat sources

There are many techniques by which heat may be delivered. Some of the most common involve the use of focused ultrasound (FUS or HIFU), RF sources, infrared sauna, microwave heating, induction heating, magnetic hyperthermia, infusion of warmed liquids, or direct application of heat such as through sitting in a hot room or wrapping a patient in hot blankets.

Controlling temperature

One of the challenges in thermal therapy is delivering the appropriate amount of heat to the correct part of the patient's body. For this technique to be effective, the temperatures must be high enough, and the temperatures must be sustained long enough, to damage or kill the cancer cells. However, if the temperatures are too high, or if they are kept elevated for too long, then serious side effects, including death, can result. The smaller the place that is heated, and the shorter the treatment time, the lower the side effects. Conversely, tumor treated too slowly or at too low a temperature will not achieve therapeutic goals. The human body is a collection of tissues with differing heat capacities, all connected by a dynamic circulatory system with variable relationship to skin or lung surfaces designed to shed heat energy. All methods of inducing higher temperature in the body are countered by the thermo-regulatory mechanisms of the body. The body as a whole relies mostly on simple radiation of energy to the surrounding air from the skin (50% of heat lost this way) which is augmented by convection (blood shunting) and vaporization through sweat and respiration. Regional methods of heating may be more or less difficult based on the anatomic relationships, and tissue components of the particular body part being treated. Measuring temperatures in various parts of the body may be very difficult, and temperatures may locally vary even within a region of the body.

To minimize damage to healthy tissue and other adverse effects, attempts are made to monitor temperatures. The goal is to keep local temperatures in tumor bearing tissue under 44 °C (111 °F) to avoid damage to surrounding tissues. These temperatures have been derived from cell culture and animal studies. The body keeps itself normal human body temperature, near 37.6 °C (99.7 °F). Unless a needle probe can be placed with accuracy in every tumor site amenable to measurement, there is an inherent technical difficulty in how to actually reach whatever a treating center defines as an "adequate" thermal dose. Since there is also no consensus as to what parts of the body need to be monitored (common clinically measured sites are ear drums, oral, skin, rectal, bladder, esophagus, blood probes, or even tissue needles). Clinicians have advocated various combinations for these measurements. These issues complicate the ability of comparing different studies and coming up with a definition of exactly what a thermal dose actually should be for tumor, and what dose is toxic to what tissues in human beings. Clinicians may be able to apply advanced imaging techniques, instead of probes, to monitor heat treatments in real time; heat-induced changes in tissue are sometimes perceptible using these imaging instruments.

There is the further difficulty inherent in the devices delivering energy. Regional devices may not uniformly heat a target area, even without taking into account compensatory mechanisms of the body. A great deal of current research focuses on how one might precisely position heat-delivery devices (catheters, microwave and ultrasound applicators, etc.) using ultrasound or magnetic resonance imaging, as well as developing new types of nanoparticles that can more evenly distribute heat within a target tissue.

Among hyperthermia therapy methods, magnetic hyperthermia is well known as the one that produce a controllable heat inside the body. Because of using magnetic fluid in this method, temperature distribution can be controlled by the velocity, size of nanoparticles and distribution of them inside the body. These materials upon application of external, alternating magnetic field convert electromagnetic energy into thermal energy and induce temperature rises.

Mechanism

Hyperthermia can kill cells directly, but its more important use is in combination with other treatments for cancer. Hyperthermia increases blood flow to the warmed area, perhaps doubling perfusion in tumors, while increasing perfusion in normal tissue by ten times or even more. This enhances the delivery of medications. Hyperthermia also increases oxygen delivery to the area, which may make radiation more likely to damage and kill cells, as well as preventing cells from repairing the damage induced during the radiation session.

Cancerous cells are not inherently more susceptible to the effects of heat. When compared in in vitro studies, normal cells and cancer cells show the same responses to heat. However, the vascular disorganization of a solid tumor results in an unfavorable microenvironment inside tumors. Consequently, the tumor cells are already stressed by low oxygen, higher than normal acid concentrations, and insufficient nutrients, and are thus significantly less able to tolerate the added stress of heat than a healthy cell in normal tissue.

Mild hyperthermia, which provides temperatures equal to that of a naturally high fever, may stimulate natural immunological attacks against the tumor. However it is also induces a natural physiological response called thermotolerance, which tends to protect the treated tumor.

Moderate hyperthermia, which heats cells in the range of 40 to 42 °C (104 to 108 °F), damages cells directly, in addition to making the cells radiosensitive and increasing the pore size to improve delivery of large-molecule chemotherapeutic and immunotherapeutic agents (molecular weight greater than 1,000 Daltons), such as monoclonal antibodies and liposome-encapsulated drugs. Cellular uptake of certain small molecule drugs is also increased.

Very high temperatures, above 50 °C (122 °F), are used for ablation (direct destruction) of some tumors. This generally involves inserting a metal tube directly into the tumor, and heating the tip until the tissue next to the tube has been killed.

History

The application of heat to treat certain conditions, including possible tumors, has a long history. Ancient Greeks, Romans, and Egyptians used heat to treat breast masses; this is still a recommended self-care treatment for breast engorgement. Medical practitioners in ancient India used regional and whole-body hyperthermia as treatments.

During the 19th century, tumor shrinkage after a high fever due to infection had been reported in a small number of cases. Typically, the reports documented the rare regression of a soft tissue sarcoma after erysipelas (an acute streptococcus bacterial infection of the skin; a different presentation of an infection by "flesh-eating bacteria") was noted. Efforts to deliberately recreate this effect led to the development of Coley's toxin. A sustained high fever after induction of illness was considered critical to treatment success. This treatment is generally considered both less effective than modern treatments and, when it includes live bacteria, inappropriately dangerous.

Around the same period Westermark used localized hyperthermia to produce tumor regression in patients. Encouraging results were also reported by Warren when he treated patients with advanced cancer of various types with a combination of heat, induced with pyrogenic substance, and x-ray therapy. Out of 32 patients, 29 improved for 1 to 6 months.

Properly controlled clinical trials on deliberately induced hyperthermia began in the 1970s.

Future directions

Hyperthermia may be combined with gene therapy, particularly using the heat shock protein 70 promoter.

Two major technological challenges make hyperthermia therapy complicated: the ability to achieve a uniform temperature in a tumor, and the ability to precisely monitor the temperatures of both the tumor and the surrounding tissue. Advances in devices to deliver uniform levels of the precise amount of heat desired, and devices to measure the total dose of heat received, are hoped for.

In locally advanced adenocarcinoma of middle and lower rectum, regional hyperthermia added to chemoradiotherapy achieved good results in terms of rate of sphincter sparing surgery.

Magnetic hyperthermia

Magnetic hyperthermia is an experimental treatment for cancer, based on the fact that magnetic nanoparticles can transform electromagnetic energy from an external high-frequency field to heat. This is due to the magnetic hysteresis of the material when it is subjected to an alternating magnetic field. The area enclosed by the hysteresis loop represents losses, which are commonly dissipated as thermal energy. In many industrial applications this heat is undesirable, however it is the basis for magnetic hyperthermia treatment.

As a result, if magnetic nanoparticles are put inside a tumor and the whole patient is placed in an alternating magnetic field, the temperature of the tumor will rise. This elevation of temperature may enhance tumor oxygenation and radio- and chemosensitivity, hopefully shrinking tumors. This experimental cancer treatment has also been investigated for the aid of other ailments, such as bacterial infections.

Magnetic hyperthermia is defined by specific absorption rate (SAR) and it is usually expressed in watts per gram of nanoparticles.

Relaxation (NMR)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Relaxation_(NMR) 

In MRI and NMR spectroscopy, an observable nuclear spin polarization (magnetization) is created by a homogeneous magnetic field. This field makes the magnetic dipole moments of the sample precess at the resonance (Larmor) frequency of the nuclei. At thermal equilibrium, nuclear spins precess randomly about the direction of the applied field. They become abruptly phase coherent when they are hit by radiofrequency (RF) pulses at the resonant frequency, created orthogonal to the field. The RF pulses cause the population of spin-states to be perturbed from their thermal equilibrium value. The generated transverse magnetization can then induce a signal in an RF coil that can be detected and amplified by an RF receiver. The return of the longitudinal component of the magnetization to its equilibrium value is termed spin-lattice relaxation while the loss of phase-coherence of the spins is termed spin-spin relaxation, which is manifest as an observed free induction decay (FID).

For spin=½ nuclei (such as ¹H), the polarization due to spins oriented with the field N₋ relative to the spins oriented against the field N₊ is given by the Boltzmann distribution:

${\displaystyle \frac{N_{+}}{N_{-}}=e^{-\frac{\mathrm{\Delta }E}{kT}}}$

where ΔE is the energy level difference between the two populations of spins, k is the Boltzmann constant, and T is the sample temperature. At room temperature, the number of spins in the lower energy level, N−, slightly outnumbers the number in the upper level, N+. The energy gap between the spin-up and spin-down states in NMR is minute by atomic emission standards at magnetic fields conventionally used in MRI and NMR spectroscopy. Energy emission in NMR must be induced through a direct interaction of a nucleus with its external environment rather than by spontaneous emission. This interaction may be through the electrical or magnetic fields generated by other nuclei, electrons, or molecules. Spontaneous emission of energy is a radiative process involving the release of a photon and typified by phenomena such as fluorescence and phosphorescence. As stated by Abragam, the probability per unit time of the nuclear spin-1/2 transition from the + into the - state through spontaneous emission of a photon is a negligible phenomenon. Rather, the return to equilibrium is a much slower thermal process induced by the fluctuating local magnetic fields due to molecular or electron (free radical) rotational motions that return the excess energy in the form of heat to the surroundings.

T₁ and T₂

The decay of RF-induced NMR spin polarization is characterized in terms of two separate processes, each with their own time constants. One process, called T₁, is responsible for the loss of resonance intensity following pulse excitation. The other process, called T₂, characterizes the width or broadness of resonances. Stated more formally, T₁ is the time constant for the physical processes responsible for the relaxation of the components of the nuclear spin magnetization vector M parallel to the external magnetic field, B₀ (which is conventionally designated as the z-axis). T₂ relaxation affects the coherent components of M perpendicular to B₀. In conventional NMR spectroscopy, T₁ limits the pulse repetition rate and affects the overall time an NMR spectrum can be acquired. Values of T₁ range from milliseconds to several seconds, depending on the size of the molecule, the viscosity of the solution, the temperature of the sample, and the possible presence of paramagnetic species (e.g., O₂ or metal ions).

T₁

Main article: Spin–lattice relaxation

The longitudinal (or spin-lattice) relaxation time T₁ is the decay constant for the recovery of the z component of the nuclear spin magnetization, M_z, towards its thermal equilibrium value, ${\displaystyle M_{z,\mathrm{e}\mathrm{q}}}$. In general,

${\displaystyle M_z(t)=M_{z,\mathrm{e}\mathrm{q}}-[M_{z,\mathrm{e}\mathrm{q}}-M_z(0)]e^{-t/T_1}}$

In specific cases:

• If M has been tilted into the xy plane, then ${\displaystyle M_z(0)=0}$ and the recovery is simply

${\displaystyle M_z(t)=M_{z,\mathrm{e}\mathrm{q}}\left(1-e^{-t/T_1}\right)}$

i.e. the magnetization recovers to 63% of its equilibrium value after one time constant T₁.

• In the inversion recovery experiment, commonly used to measure T₁ values, the initial magnetization is inverted, ${\displaystyle M_z(0)=-M_{z,\mathrm{e}\mathrm{q}}}$, and so the recovery follows

${\displaystyle M_z(t)=M_{z,\mathrm{e}\mathrm{q}}\left(1-2e^{-t/T_1}\right)}$

T₁ relaxation involves redistributing the populations of the nuclear spin states in order to reach the thermal equilibrium distribution. By definition, this is not energy conserving. Moreover, spontaneous emission is negligibly slow at NMR frequencies. Hence truly isolated nuclear spins would show negligible rates of T₁ relaxation. However, a variety of relaxation mechanisms allow nuclear spins to exchange energy with their surroundings, the lattice, allowing the spin populations to equilibrate. The fact that T₁ relaxation involves an interaction with the surroundings is the origin of the alternative description, spin-lattice relaxation.

Note that the rates of T₁ relaxation (i.e., 1/T₁) are generally strongly dependent on the NMR frequency and so vary considerably with magnetic field strength B. Small amounts of paramagnetic substances in a sample speed up relaxation very much. By degassing, and thereby removing dissolved oxygen, the T₁/T₂ of liquid samples easily go up to an order of ten seconds.

Spin saturation transfer

Especially for molecules exhibiting slowly relaxing (T₁) signals, the technique spin saturation transfer (SST) provides information on chemical exchange reactions. The method is widely applicable to fluxional molecules. This magnetization transfer technique provides rates, provided that they exceed 1/T₁.

T₂

Main article: Spin–spin relaxation

The transverse (or spin-spin) relaxation time T₂ is the decay constant for the component of M perpendicular to B₀, designated M_xy, M_T, or ${\displaystyle M_{\perp }}$. For instance, initial xy magnetization at time zero will decay to zero (i.e. equilibrium) as follows:

${\displaystyle M_{xy}(t)=M_{xy}(0)e^{-t/T_2}}$

i.e. the transverse magnetization vector drops to 37% of its original magnitude after one time constant T₂.

T₂ relaxation is a complex phenomenon, but at its most fundamental level, it corresponds to a decoherence of the transverse nuclear spin magnetization. Random fluctuations of the local magnetic field lead to random variations in the instantaneous NMR precession frequency of different spins. As a result, the initial phase coherence of the nuclear spins is lost, until eventually the phases are disordered and there is no net xy magnetization. Because T₂ relaxation involves only the phases of other nuclear spins it is often called "spin-spin" relaxation.

Spin echo pulse sequence and magnetization decay animation.

T₂ values are generally much less dependent on field strength, B, than T₁ values.

Hahn echo decay experiment can be used to measure the T₂ time, as shown in the animation below. The size of the echo is recorded for different spacings of the two applied pulses. This reveals the decoherence which is not refocused by the 180° pulse. In simple cases, an exponential decay is measured which is described by the ${\displaystyle T_2}$ time.

T₂* and magnetic field inhomogeneity

Further information: T2*-weighted imaging

In an idealized system, all nuclei in a given chemical environment, in a magnetic field, precess with the same frequency. However, in real systems, there are minor differences in chemical environment which can lead to a distribution of resonance frequencies around the ideal. Over time, this distribution can lead to a dispersion of the tight distribution of magnetic spin vectors, and loss of signal (free induction decay). In fact, for most magnetic resonance experiments, this "relaxation" dominates. This results in dephasing.

However, decoherence because of magnetic field inhomogeneity is not a true "relaxation" process; it is not random, but dependent on the location of the molecule in the magnet. For molecules that aren't moving, the deviation from ideal relaxation is consistent over time, and the signal can be recovered by performing a spin echo experiment.

The corresponding transverse relaxation time constant is thus T₂^*, which is usually much smaller than T₂. The relation between them is:

${\displaystyle \frac{1}{T_2^{\ast }}=\frac{1}{T_2}+\frac{1}{T_{inhom}}=\frac{1}{T_2}+\gamma \mathrm{\Delta }{B}_0}$

where γ represents gyromagnetic ratio, and ΔB₀ the difference in strength of the locally varying field.

Unlike T₂, T₂* is influenced by magnetic field gradient irregularities. The T₂* relaxation time is always shorter than the T₂ relaxation time and is typically milliseconds for water samples in imaging magnets.

Is T₁ always longer than T₂?

In NMR systems, the following relation holds absolute true ${\displaystyle T_2\le 2T_1}$. In most situations (but not in principle) ${\displaystyle T_1}$ is greater than ${\displaystyle T_2}$. The cases in which ${\displaystyle 2T_1>T_2>T_1}$ are rare, but not impossible.

Bloch equations

Main article: Bloch equations

Bloch equations are used to calculate the nuclear magnetization M = (M_x, M_y, M_z) as a function of time when relaxation times T₁ and T₂ are present. Bloch equations are phenomenological equations that were introduced by Felix Bloch in 1946.

${\displaystyle \frac{\mathrm{\partial }{M}_x(t)}{\mathrm{\partial }t}=\gamma (\mathbf{M}(t)\times \mathbf{B}(t){)}_x-\frac{M_x(t)}{T_2}}$

${\displaystyle \frac{\mathrm{\partial }{M}_y(t)}{\mathrm{\partial }t}=\gamma (\mathbf{M}(t)\times \mathbf{B}(t){)}_y-\frac{M_y(t)}{T_2}}$

${\displaystyle \frac{\mathrm{\partial }{M}_z(t)}{\mathrm{\partial }t}=\gamma (\mathbf{M}(t)\times \mathbf{B}(t){)}_z-\frac{M_z(t)-M_0}{T_1}}$

Where ${\displaystyle \times }$ is the cross-product, γ is the gyromagnetic ratio and B(t) = (B_x(t), B_y(t), B₀ + B_z(t)) is the magnetic flux density experienced by the nuclei. The z component of the magnetic flux density B is typically composed of two terms: one, B₀, is constant in time, the other one, B_z(t), is time dependent. It is present in magnetic resonance imaging and helps with the spatial decoding of the NMR signal.

The equation listed above in the section on T₁ and T₂ relaxation are those in the Bloch equations.

Solomon equations

Main article: Solomon equations

Solomon equations are used to calculate the transfer of magnetization as a result of relaxation in a dipolar system. They can be employed to explain the nuclear Overhauser effect, which is an important tool in determining molecular structure.

Common relaxation time constants in human tissues

Following is a table of the approximate values of the two relaxation time constants for hydrogen nuclear spins in nonpathological human tissues.

At a main field of 1.5 T

Tissue type	Approximate T1 value in ms	Approximate T2 value in ms
Adipose tissues	240-250	60-80
Whole blood (deoxygenated)	1350	50
Whole blood (oxygenated)	1350	200
Cerebrospinal fluid (similar to pure water)	4200 - 4500	2100-2300
Gray matter of cerebrum	920	100
White matter of cerebrum	780	90
Liver	490	40
Kidneys	650	60-75
Muscles	860-900	50

Following is a table of the approximate values of the two relaxation time constants for chemicals that commonly show up in human brain magnetic resonance spectroscopy (MRS) studies, physiologically or pathologically.

At a main field of 1.5 T

Signals of chemical groups	Relative resonance frequency	Approximate T1 value (ms)	Approximate T2 value (ms)
Creatine (Cr) and Phosphocreatine (PCr)	3.0 ppm	gray matter: 1150-1340, white matter: 1050-1360	gray matter: 198-207, white matter: 194-218
N-Acetyl group (NA), mainly from N-acetylaspartate (NAA)	2.0 ppm	gray matter: 1170-1370, white matter: 1220-1410	gray matter: 388-426, white matter: 436-519
—CH3 group of Lactate	1.33 ppm (doublet: 1.27 & 1.39 ppm)	(To be listed)	1040

Relaxation in the rotating frame, T_1ρ

The discussion above describes relaxation of nuclear magnetization in the presence of a constant magnetic field B₀. This is called relaxation in the laboratory frame. Another technique, called relaxation in the rotating frame, is the relaxation of nuclear magnetization in the presence of the field B₀ together with a time-dependent magnetic field B₁. The field B₁ rotates in the plane perpendicular to B₀ at the Larmor frequency of the nuclei in the B₀. The magnitude of B₁ is typically much smaller than the magnitude of B₀. Under these circumstances the relaxation of the magnetization is similar to laboratory frame relaxation in a field B₁. The decay constant for the recovery of the magnetization component along B₁ is called the spin-lattice relaxation time in the rotating frame and is denoted T_1ρ. Relaxation in the rotating frame is useful because it provides information on slow motions of nuclei.

Microscopic mechanisms

Relaxation of nuclear spins requires a microscopic mechanism for a nucleus to change orientation with respect to the applied magnetic field and/or interchange energy with the surroundings (called the lattice). The most common mechanism is the magnetic dipole-dipole interaction between the magnetic moment of a nucleus and the magnetic moment of another nucleus or other entity (electron, atom, ion, molecule). This interaction depends on the distance between the pair of dipoles (spins) but also on their orientation relative to the external magnetic field. Several other relaxation mechanisms also exist. The chemical shift anisotropy (CSA) relaxation mechanism arises whenever the electronic environment around the nucleus is non spherical, the magnitude of the electronic shielding of the nucleus will then be dependent on the molecular orientation relative to the (fixed) external magnetic field. The spin rotation (SR) relaxation mechanism arises from an interaction between the nuclear spin and a coupling to the overall molecular rotational angular momentum. Nuclei with spin I ≥ 1 will have not only a nuclear dipole but a quadrupole. The nuclear quadrupole has an interaction with the electric field gradient at the nucleus which is again orientation dependent as with the other mechanisms described above, leading to the so-called quadrupolar relaxation mechanism.

Molecular reorientation or tumbling can then modulate these orientation-dependent spin interaction energies. According to quantum mechanics, time-dependent interaction energies cause transitions between the nuclear spin states which result in nuclear spin relaxation. The application of time-dependent perturbation theory in quantum mechanics shows that the relaxation rates (and times) depend on spectral density functions that are the Fourier transforms of the autocorrelation function of the fluctuating magnetic dipole interactions. The form of the spectral density functions depend on the physical system, but a simple approximation called the BPP theory is widely used.

Another relaxation mechanism is the electrostatic interaction between a nucleus with an electric quadrupole moment and the electric field gradient that exists at the nuclear site due to surrounding charges. Thermal motion of a nucleus can result in fluctuating electrostatic interaction energies. These fluctuations produce transitions between the nuclear spin states in a similar manner to the magnetic dipole-dipole interaction.

BPP theory

In 1948, Nicolaas Bloembergen, Edward Mills Purcell, and Robert Pound proposed the so-called Bloembergen-Purcell-Pound theory (BPP theory) to explain the relaxation constant of a pure substance in correspondence with its state, taking into account the effect of tumbling motion of molecules on the local magnetic field disturbance. The theory agrees well with experiments on pure substances, but not for complicated environments such as the human body.

This theory makes the assumption that the autocorrelation function of the microscopic fluctuations causing the relaxation is proportional to ${\displaystyle e^{-t/{\tau }_c}}$, where ${\displaystyle {\tau }_c}$ is called the correlation time. From this theory, one can get T₁ > T₂ for magnetic dipolar relaxation:

${\displaystyle \frac{1}{T_1}=K\left[\frac{{\tau }_c}{1+{\omega }_0^2{\tau }_c^2}+\frac{4{\tau }_c}{1+4{\omega }_0^2{\tau }_c^2}\right]}$

${\displaystyle \frac{1}{T_2}=\frac{K}{2}\left[3{\tau }_c+\frac{5{\tau }_c}{1+{\omega }_0^2{\tau }_c^2}+\frac{2{\tau }_c}{1+4{\omega }_0^2{\tau }_c^2}\right]}$,

where ${\displaystyle {\omega }_0}$ is the Larmor frequency in correspondence with the strength of the main magnetic field ${\displaystyle B_0}$. ${\displaystyle {\tau }_c}$ is the correlation time of the molecular tumbling motion. ${\displaystyle K=\frac{3{\mu }_0^2}{160{\pi }^2}\frac{{\hslash }^2{\gamma }^4}{r^6}}$ is defined for spin-1/2 nuclei and is a constant with ${\displaystyle {\mu }_0}$ being the magnetic permeability of free space of the ${\displaystyle \hslash =\frac{h}{2\pi }}$ the reduced Planck constant, γ the gyromagnetic ratio of such species of nuclei, and r the distance between the two nuclei carrying magnetic dipole moment.

Taking for example the H₂O molecules in liquid phase without the contamination of oxygen-17, the value of K is 1.02×10¹⁰ s⁻² and the correlation time ${\displaystyle {\tau }_c}$ is on the order of picoseconds = ${\displaystyle {10}^{-12}}$ s, while hydrogen nuclei ¹H (protons) at 1.5 tesla precess at a Larmor frequency of approximately 64 MHz (Simplified. BPP theory uses angular frequency indeed). We can then estimate using τ_c = 5×10⁻¹² s:

${\displaystyle {\omega }_0{\tau }_c=3.2\times {10}^{-5}}$(dimensionless)

${\displaystyle T_1={\left(1.02\times {10}^{10}\left[\frac{5\times {10}^{-12}}{1+(3.2\times {10}^{-5}{)}^2}+\frac{4\cdot 5\times {10}^{-12}}{1+4\cdot (3.2\times {10}^{-5}{)}^2}\right]\right)}^{-1}}$= 3.92 s

${\displaystyle T_2={\left(\frac{1.02\times {10}^{10}}{2}\left[3\cdot 5\times {10}^{-12}+\frac{5\cdot 5\times {10}^{-12}}{1+{\left(3.2\times {10}^{-5}\right)}^2}+\frac{2\cdot 5\times {10}^{-12}}{1+4\cdot (3.2\times {10}^{-5}{)}^2}\right]\right)}^{-1}}$= 3.92 s,

which is close to the experimental value, 3.6 s. Meanwhile, we can see that at this extreme case, T₁ equals T₂. As follows from the BPP theory, measuring the T₁ times leads to internuclear distances r. One of the examples is accurate determinations of the metal – hydride (M-H) bond lengths in solutions by measurements of ¹H selective and non-selective T₁ times in variable-temperature relaxation experiments via the equation:

${\displaystyle r(M-H)=C{\left(\frac{(1.4k+4.47)T_{1min}}{\nu }\right)}^{1/6}}$

${\displaystyle k=(f-1)/(0.5-f/3)}$, with ${\displaystyle f=T_{1s}/T_1}$

${\displaystyle C={10}^7{\left(\frac{{\gamma }_H^2{\gamma }_M^2{\hslash }^2{I}_M(I_M+1)}{15}\right)}^{1/6}}$

where r, frequency and T₁ are measured in Å, MHz and s, respectively, and I_M is the spin of M.