{"artifact_id":"L1-505","layer":"L1","title":"Pharmacokinetic Dynamic PET (PK-PET)","domain":"Medical Imaging","sub_domain":"Quantitative tracer kinetic imaging (multi-physics joint inverse)","physics_fingerprint":{"L_DAG":8.3,"title":"Pharmacokinetic Dynamic PET (PK-PET)","domain":"Medical Imaging","carrier":"photon_511keV","primitives":["L.tracer_injection","L.compartmental_ode","L.activity_distribution","L.attenuation_correction","L.scatter_correction","L.lor_projection","int.temporal","int.spatial"],"sub_domain":"Quantitative tracer kinetic imaging (multi-physics joint inverse)","noise_model":"poisson","problem_class":"linear_inverse_4d","solution_space":"4D_kinetic_parameter_map","difficulty_delta":5,"integration_axis":"spatial_temporal","sensing_mechanism":"annihilation_with_compartmental_kinetics"},"observable_profile":{"metric":"PSNR_dB","regime":"Existence of recovered 4D kinetic parameter maps (K_1, k_2, k_3, k_4)(r) is guaranteed within the declared Omega bounds. Uniqueness holds for irreversible 2-tissue compartmental models (FDG-like, k_4 = 0) with sufficient temporal sampling and known C_p(t); reversible 2-tissue models (4 free parameters) require either reference-region constraint or sufficient SNR for full identifiability. Stability is moderately conditioned (kappa_eff ~ 25 after 4D-EM-ML or direct kinetic reconstruction) — input_function_uncertainty dominates K_1 bias; partial_volume_effect dominates small-structure quantitation; count_statistics_dropoff dominates late-frame variance. Joint Hadamard well-posedness for the coupled compartmental-PET forward is established by Carson (1996, 2003), Gunn-Gunn-Cunningham (2001), Patlak-Blasberg-Fenstermacher (1983 Patlak plot), Logan et al. (1990 Logan plot), Wang-Qi (2013 direct kinetic estimation), and Reader-Verhaeghe (2014 4D image reconstruction).","secondary":"RMSE_per_kinetic_parameter"},"size_tiers":{"center_spec":{"omega":{"H":256,"W":256,"Z":64,"N_frames":28,"tracer_class":"FDG","voxel_size_mm":2.0,"compartment_count":2,"scan_duration_min":60,"motion_during_scan":0.0,"partial_volume_effect":0.0,"count_statistics_dropoff":0.0,"scatter_correction_error":0.0,"input_function_uncertainty":0.0,"noise_equivalent_count_rate":100000,"attenuation_correction_error":0.0},"input_format":"dynamic_sinogram_with_input_function","problem_class":"pkpet_2tissue_irreversible","forward_operator":"pkpet_joint_forward","epsilon_fn_center":"24.0"},"omega_bounds":{"H":[128,512],"W":[128,512],"Z":[32,256],"N_frames":[12,60],"voxel_size_mm":[1.0,4.0],"compartment_count":[1,4],"scan_duration_min":[20,180],"motion_during_scan":[0.0,0.3],"partial_volume_effect":[0.0,0.4],"count_statistics_dropoff":[0.0,0.5],"scatter_correction_error":[0.0,0.2],"input_function_uncertainty":[0.0,0.3],"noise_equivalent_count_rate":[10000,1000000],"attenuation_correction_error":[0.0,0.2]},"epsilon_bounds":{"psnr_db":[8.0,42.0]},"allowed_problem_classes":["pkpet_2tissue_irreversible","pkpet_2tissue_reversible","pkpet_3tissue_metabolite","pkpet_reference_tissue","pkpet_graphical_irreversible","pkpet_graphical_reversible"],"allowed_omega_dimensions":["H","W","Z","N_frames","scan_duration_min","voxel_size_mm","tracer_class","compartment_count","noise_equivalent_count_rate","input_function_uncertainty","attenuation_correction_error","scatter_correction_error","motion_during_scan","partial_volume_effect","count_statistics_dropoff"],"allowed_forward_operators":["pkpet_joint_forward","pkpet_two_step_forward","pkpet_direct_kinetic_forward","pkpet_patlak_forward","pkpet_logan_forward"]},"hardness_fn":{"type":"epsilon_fn","delta":5,"kappa":200,"metric":"PSNR_dB"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0xe345d09b0e6f005469ab139b4deb1ae1ee8eccfac92ca8f8a188aec92f139809","chain_tx_hash":"0x2739c91ad7312bf16f884dc0b15f996df74fce8a13ed24bddd0871fcccca8779","chain_block":41553386}