Comment calculer la fréquence de Larmor: fréquence precession spins nucleaires champ magnétique, base physique NMR MRI. ω_L = γ × B, f_L = γ × B / (2π). ¹H proton γ=42.577 MHz/T. 1.5T MRI f_L=63.87 MHz, 3T=127.74 MHz, 7T=298 MHz. Joseph Larmor (Ireland-UK 1857-1942) Cambridge 1897. Felix Bloch + Edward Purcell Nobel 1952. Paul Lauterbur Peter Mansfield Nobel 2003. France: SFR Societe Francaise Radiologie Paris; CEA Saclay. Hopitaux 7T NeuroSpin CEA Saclay.

Formule Larmor

Équation fondamentale: ω_L = γ × B, f_L = γB/(2π).

γ gyromagnetique: ¹H 42.577 MHz/T, ¹³C 10.708, ³¹P 17.251.

B champ clinical: 1.5T standard, 3T research, 7T brain.

NMR vs MRI: NMR laboratoire chimie, MRI clinical imaging.

RF excitation: 90° pulse rotates magnetization.

Histoire et contexte

Joseph Larmor Cambridge 1897 Philosophical Magazine 44:503. Felix Bloch Stanford 1946 Physical Review 70:460. Edward Purcell Harvard 1946. Nobel Physics 1952. Richard Ernst Switzerland Nobel Chemistry 1991. Paul Lauterbur SUNY Stony Brook + Peter Mansfield Nottingham UK Nobel Medicine 2003 MRI. France recherche NMR-MRI: NeuroSpin CEA Saclay 7T 11.7T MRI brain research center France first 11.7T preclinical 2010 first 7T human; CHU CHU France hopitaux Pitie-Salpetriere Paris, Bichat Paris, Necker Paris, Toulouse, Marseille, Lyon Hospices Civils. Industries France: Siemens Healthineers France subsidiary Saint-Denis Paris; GE Healthcare France Buc Paris; Philips Healthcare France Suresnes Paris; Bruker France Wissembourg Strasbourg subsidiary; Bayer Pharma France Loos Lille contrast media. Universites France: Sorbonne Universite Paris; Paris-Saclay 60000 etudiants; ENS Paris-Lyon-Cachan; Polytechnique Palaiseau X; Centrale Paris-Saclay; Mines Paris; INSA Lyon Toulouse. CNRS Paris 32000 chercheurs federe 1100 laboratoires; INSERM Paris 1964 14000 employes biomedical research; Institut Pasteur Paris 1887 6000 employes vaccins virologia immunologia.

Table Larmor fréquences

• 1H 1.5T: 63.87 MHz clinical
• 1H 3T: 127.74 MHz research
• 1H 7T: 298 MHz brain
• 1H 11.7T NeuroSpin: 500 MHz France
• 13C 9.4T: 100.7 MHz organic
• 31P 3T: 51.7 MHz ATP
• γ 1H: 42.577 MHz/T

Exemples numériques detailles

Exemple 1 - 1.5T MRI. f=63.87 MHz France 60% hopitaux.

Exemple 2 - 3T MRI. f=127.74 MHz SNR 2x.

Exemple 3 - 7T brain. f=298 MHz NeuroSpin CEA Saclay.

Exemple 4 - 11.7T NeuroSpin. f=500 MHz France first 11.7T human Iseult 2024.

Exemple 5 - 3T 31P MRS. f=51.7 MHz ATP metabolism.

Limites et considerations

1. B uniform shimming.
2. Larmor classical.
3. SAR safety.
4. Susceptibility artifacts.
5. Gradient linearity.
6. T1 T2 relaxation.
7. RF penetration.
8. Cost scanners.
9. Scan time.
10. γ précision.

Erreurs communes

1. ω vs f.
2. γ nucleo.
3. Tesla vs Gauss.
4. γ signs.
5. B0 vs B1.
6. Math.PI.
7. Susceptibility.
8. Classical.
9. Larmor vs cyclotron.
10. Resonance.

Applications numerotees

1. France NeuroSpin CEA Saclay: 7T 11.7T MRI brain research center France first 11.7T human 2024 Iseult preclinical 2010.
2. Industries France: Siemens Healthineers Saint-Denis, GE Healthcare Buc, Philips Healthcare Suresnes, Bruker France Wissembourg, Bayer France Loos Lille.
3. CNRS INSERM Pasteur: CNRS Paris 32000 chercheurs, INSERM Paris 1964 14000 employes, Institut Pasteur Paris 1887 6000 employes.
4. Universites France: Sorbonne Paris, Paris-Saclay, ENS Paris-Lyon, Polytechnique Palaiseau, Strasbourg.
5. SFR France: Societe Francaise Radiologie Paris standards.
6. USA MRI scanners: 12000+ installed, 80+ 7T NIH UCSF Stanford Penn.
7. NIH research: NIBIB Bethesda MD biomedical imaging.
8. Famous NMR USA: Bloch Stanford 1946 Nobel 1952; Purcell Harvard Nobel 1952; Lauterbur Nobel 2003 MRI.
9. Industry USA: GE Healthcare Chicago, Siemens Malvern PA, Philips Andover MA.
10. Italian CERM: Firenze 1995 1200 MHz NMR Bruker world-class.

Pour support

Pour questions techniques: info@calcoi.com. Outil educatif physique resonance magnétique. Références Larmor 1897, Bloch Purcell 1946 Nobel 1952.

Mis à jour en juillet 2026