{"artifact_id":"L1-506","layer":"L1","title":"Hyperpolarized 13C Metabolic MRI","domain":"Medical Imaging","sub_domain":"Real-time metabolic kinetic imaging via dynamic nuclear polarization (multi-physics joint inverse)","physics_fingerprint":{"L_DAG":10.4,"title":"Hyperpolarized 13C Metabolic MRI","domain":"Medical Imaging","carrier":"spin_13C_hyperpolarized","primitives":["L.dnp_polarization","L.injection_bolus","L.chemical_exchange_ode","L.bloch_dynamics","L.rf_excitation","L.spectral_spatial_encoding","L.gradient_readout","int.spectral","int.temporal"],"sub_domain":"Real-time metabolic kinetic imaging via dynamic nuclear polarization (multi-physics joint inverse)","noise_model":"gaussian","problem_class":"nonlinear_inverse_4d","solution_space":"4D_metabolic_rate_constant_map","difficulty_delta":5,"integration_axis":"spectral_temporal_spatial","sensing_mechanism":"dnp_with_chemical_exchange_and_chemical_shift_mri"},"observable_profile":{"metric":"PSNR_dB","regime":"Existence of recovered metabolic rate-constant maps (k_PL, k_PA, k_PB)(r) and per-pool T1 maps is guaranteed within the declared Omega bounds. Uniqueness holds when at least 3 metabolite pools are sampled with sufficient temporal resolution (frame duration <= 5 s) and SNR per metabolite > 10 dB; degenerate cases (all rate constants near zero, or T1 << acquisition window) require regularization. Stability is moderately conditioned (kappa_eff ~ 50 after rate-constant-aware spatiotemporal regularization) — dnp_polarization_loss dominates absolute rate-constant scaling; injection_bolus_uncertainty dominates K_1-equivalent bias; t1_uncertainty contributes a per-pool scaling factor; partial_volume_effect dominates small-structure quantitation. Joint Hadamard well-posedness for the coupled DNP-chemical-exchange-MR forward is established by Bahrami et al. (2014), Larson et al. (2018), Maidens-Gordon-Arcak (2016 control-theoretic identifiability), and Brindle (2015 review on hyperpolarized MR imaging principles).","secondary":"RMSE_per_rate_constant"},"size_tiers":{"center_spec":{"omega":{"H":64,"W":64,"Z":16,"P_DNP":0.3,"SNR_dB":18,"N_frames":20,"B0_field_T":3.0,"N_metabolites":3,"voxel_size_mm":5.0,"t1_uncertainty":0.0,"b1_inhomogeneity":0.0,"frame_duration_s":3.0,"dnp_polarization_loss":0.0,"partial_volume_effect":0.0,"susceptibility_artifact":0.0,"injection_bolus_uncertainty":0.0},"input_format":"chemical_shift_resolved_dynamic_kspace","problem_class":"hp13c_pyruvate_3pool","forward_operator":"hp13c_joint_forward","epsilon_fn_center":"22.0"},"omega_bounds":{"H":[32,256],"W":[32,256],"Z":[8,64],"P_DNP":[0.05,0.5],"SNR_dB":[5.0,35.0],"N_frames":[5,60],"B0_field_T":[1.5,7.0],"N_metabolites":[2,6],"voxel_size_mm":[2.0,15.0],"t1_uncertainty":[0.0,0.3],"b1_inhomogeneity":[0.0,0.3],"frame_duration_s":[1.0,10.0],"dnp_polarization_loss":[0.0,0.4],"partial_volume_effect":[0.0,0.4],"susceptibility_artifact":[0.0,0.3],"injection_bolus_uncertainty":[0.0,0.3]},"epsilon_bounds":{"psnr_db":[5.0,40.0]},"allowed_problem_classes":["hp13c_pyruvate_3pool","hp13c_pyruvate_4pool","hp13c_alpha_kg_glutamate","hp13c_acetate_metabolism","hp13c_fumarate_apoptosis"],"allowed_omega_dimensions":["H","W","Z","N_frames","frame_duration_s","B0_field_T","voxel_size_mm","N_metabolites","P_DNP","SNR_dB","dnp_polarization_loss","b1_inhomogeneity","t1_uncertainty","injection_bolus_uncertainty","partial_volume_effect","susceptibility_artifact"],"allowed_forward_operators":["hp13c_joint_forward","hp13c_two_step_forward","hp13c_direct_kinetic_forward","hp13c_spectral_spatial_forward","hp13c_balanced_ssfp_forward"]},"hardness_fn":{"type":"epsilon_fn","delta":5,"kappa":280,"metric":"PSNR_dB"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0x97ad824ebd08b02b8f9189ec95f881e277530e6417b27853ca4157303a266ce8","chain_tx_hash":"0xdb7bb7e798e0ff9cffb9dd27b33714c756c74b69b9a179180d86a48f7a70a4a6","chain_block":41552304}