Bloch–Torrey equation
E645943
The Bloch–Torrey equation is an extension of the Bloch equations that incorporates diffusion effects to describe the evolution of nuclear magnetization in magnetic resonance imaging and NMR.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bloch–Torrey equation canonical | 1 |
| Bloch–Torrey equations | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7145247 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bloch–Torrey equation Context triple: [Bloch equations, relatedTo, Bloch–Torrey equation]
-
A.
Bloch equations
The Bloch equations are a set of differential equations in nuclear magnetic resonance and quantum mechanics that describe the time evolution of nuclear magnetization in an external magnetic field.
-
B.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
C.
MRI
MRI (Matz's Ruby Interpreter) is the standard reference implementation of the Ruby programming language, written in C and known for prioritizing simplicity and developer happiness.
-
D.
Cahn–Hilliard equation
The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.
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E.
Fick's first law of diffusion
Fick's first law of diffusion is a fundamental physical law that relates the diffusive flux of particles to the spatial gradient of their concentration, describing how substances move from regions of high to low concentration.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bloch–Torrey equation Target entity description: The Bloch–Torrey equation is an extension of the Bloch equations that incorporates diffusion effects to describe the evolution of nuclear magnetization in magnetic resonance imaging and NMR.
-
A.
Bloch equations
The Bloch equations are a set of differential equations in nuclear magnetic resonance and quantum mechanics that describe the time evolution of nuclear magnetization in an external magnetic field.
-
B.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
C.
MRI
MRI (Matz's Ruby Interpreter) is the standard reference implementation of the Ruby programming language, written in C and known for prioritizing simplicity and developer happiness.
-
D.
Cahn–Hilliard equation
The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.
-
E.
Fick's first law of diffusion
Fick's first law of diffusion is a fundamental physical law that relates the diffusive flux of particles to the spatial gradient of their concentration, describing how substances move from regions of high to low concentration.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
extension of Bloch equations
ⓘ
mathematical model ⓘ partial differential equation ⓘ physical law ⓘ |
| appliesTo |
MR diffusion experiments
ⓘ
diffusing spin ensembles ⓘ diffusion tensor imaging ⓘ diffusion-weighted MRI ⓘ nuclear spins in a magnetic field ⓘ |
| assumes | classical continuum description of magnetization ⓘ |
| describes |
effects of diffusion on nuclear magnetization
ⓘ
evolution of nuclear magnetization ⓘ magnetization dynamics in inhomogeneous media ⓘ signal attenuation due to diffusion ⓘ time evolution of longitudinal magnetization ⓘ time evolution of transverse magnetization ⓘ |
| domain |
NMR spectroscopy
ⓘ
biomedical imaging ⓘ theoretical MRI ⓘ |
| extends | Bloch equations by adding diffusion ⓘ |
| field |
diffusion NMR
ⓘ
magnetic resonance imaging ⓘ magnetic resonance physics ⓘ medical imaging ⓘ nuclear magnetic resonance ⓘ spin dynamics ⓘ |
| generalizes | Bloch equations ⓘ |
| hasComponent |
Bloch equation terms
ⓘ
Laplacian of magnetization ⓘ diffusion term ⓘ precession term ⓘ relaxation terms ⓘ |
| includes |
T1 relaxation
ⓘ
T2 relaxation ⓘ diffusion coefficient ⓘ |
| includesOperator | Laplacian operator ⓘ |
| mathematicalForm | time derivative of magnetization equals Bloch terms plus diffusion term ⓘ |
| parameter |
diffusion coefficient tensor
ⓘ
gyromagnetic ratio ⓘ longitudinal relaxation time T1 ⓘ magnetic field ⓘ transverse relaxation time T2 ⓘ |
| relatedTo |
Bloch–McConnell equations
ⓘ
Fick's law of diffusion ⓘ
linked to:
Fick's first law of diffusion
spin-echo experiments ⓘ |
| usedFor |
analyzing diffusion-weighted NMR experiments
ⓘ
modeling diffusion effects in MRI ⓘ modeling diffusion in porous media ⓘ modeling restricted diffusion ⓘ quantitative diffusion parameter estimation ⓘ simulating MR signal formation in diffusing media ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bloch–Torrey equation Description of subject: The Bloch–Torrey equation is an extension of the Bloch equations that incorporates diffusion effects to describe the evolution of nuclear magnetization in magnetic resonance imaging and NMR.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Bloch–Torrey equation