1：Experimental Design and Method Selection:

The study involved synthesizing amphiphilic gadolinium(III)-DOTA and europium(III)-DTPA complexes, incorporating a folate-targeting molecule, and forming mixed micelles. Methods included synthesis of ligands and complexes, micelle formation, and evaluation of photophysical and relaxometric properties using theoretical models like Solomon-Bloembergen-Morgan theory.

2：Sample Selection and Data Sources:

Samples included synthesized complexes and micelles, with characterization using mass spectrometry, NMR, FT-IR, and dynamic light scattering. Data were obtained from in vitro experiments with HeLa cells for imaging and viability assays.

3：List of Experimental Equipment and Materials:

Instruments included Bruker Avance spectrometers, Thermo Finnigan LCQ Advantage mass spectrometer, Bruker S2 Picofox TXRF, Stelar Spinmaster FFC NMR relaxometer, Minispec mq20 and mq60, Bruker Avance spectrometers, BIC multiangle laser light scattering system, Olympus FV1000 confocal microscope, and Tecan Safire2 plate reader. Materials included chemicals from Acros Organics, Matrix Scientific, ChemLab, Sigma-Aldrich, BDH Prolabo, DPPC, Tween 80?, and modified folic acid.

4：Experimental Procedures and Operational Workflow:

Synthesis of ligands and complexes was performed using reported procedures. Micelles were prepared by mixing complexes with DPPC and Tween 80?. Photophysical properties were measured with absorption and emission spectroscopy. Relaxometric studies involved NMRD profile measurements at various magnetic fields. Cell culture imaging used confocal microscopy with 405 nm excitation, and viability was assessed via MTT assay.

5：0?. Photophysical properties were measured with absorption and emission spectroscopy. Relaxometric studies involved NMRD profile measurements at various magnetic fields. Cell culture imaging used confocal microscopy with 405 nm excitation, and viability was assessed via MTT assay. Data Analysis Methods:

5. Data Analysis Methods: Data were analyzed using theoretical fitting of NMRD profiles, luminescence decay fitting for water coordination number calculation, and statistical analysis of MTT assay results.