{"artifact_id":"L1-510","layer":"L1","title":"Cardiac 4D-flow MRI with Hemodynamic Biomechanics","domain":"Medical Imaging","sub_domain":"Cardiovascular blood-flow and pressure recovery via MR phase-contrast + Navier-Stokes coupling (multi-physics joint inverse)","physics_fingerprint":{"L_DAG":8.3,"title":"Cardiac 4D-flow MRI with Hemodynamic Biomechanics","domain":"Medical Imaging","carrier":"radio_wave_with_blood_flow","primitives":["L.rf_excitation","L.flow_encoding_gradient","L.gradient_echo","L.larmor_precession","L.phase_extract","L.navier_stokes_constraint","L.boundary_conditions","int.spatial_temporal"],"sub_domain":"Cardiovascular blood-flow and pressure recovery via MR phase-contrast + Navier-Stokes coupling (multi-physics joint inverse)","noise_model":"gaussian","problem_class":"nonlinear_inverse","solution_space":"4D_velocity_pressure_joint","difficulty_delta":5,"integration_axis":"spatial_temporal","sensing_mechanism":"phase_contrast_mri_with_navier_stokes"},"observable_profile":{"metric":"PSNR_dB","regime":"Existence of joint (v(r, t), p(r, t)) is guaranteed within the declared Omega bounds and chamber geometry. Uniqueness holds under physiologically-consistent boundary conditions (no-slip walls, prescribed inflow/outflow, periodic-cardiac-cycle) and adequate venc/SNR; pressure recovery is conditionally unique up to a constant (Helmholtz-Hodge decomposition) — typical practice fixes pressure at one anatomical reference. Stability is moderately conditioned (kappa_eff ~ 30 after NS-regularized variational reconstruction) — venc_aliasing dominates aliasing-induced velocity errors; partial_volume_at_walls dominates wall-shear-stress bias; eddy_current_offset contributes a systematic background-velocity bias; viscosity_uncertainty contributes a scaling factor for shear-related quantities. Joint Hadamard well-posedness for the coupled MR-PC + NS forward is established by Markl et al. 2012 (foundational 4D-flow review), Stankovic et al. 2014 (clinical 4D-flow), Bertoglio-Caiazzo 2015 (NS-regularized 4D-flow inverse), Pereira et al. 2016 (assimilation), Garcia et al. 2018 (NS-regularized clinical 4D-flow), and Soulat et al. 2020 (4D-flow benchmarking).","secondary":"RMSE_per_velocity_component"},"size_tiers":{"center_spec":{"omega":{"H":192,"W":192,"Z":64,"TE_ms":2.5,"TR_ms":5.0,"SNR_dB":24,"venc_mps":1.5,"B0_field_T":3.0,"venc_aliasing":0.0,"voxel_size_mm":2.5,"N_cardiac_phases":25,"breath_hold_motion":0.0,"eddy_current_offset":0.0,"viscosity_uncertainty":0.0,"partial_volume_at_walls":0.0,"segmentation_error_at_chambers":0.0},"input_format":"phase_contrast_3component_4d","problem_class":"cardiac_4dflow_ns_regularized","forward_operator":"cardiac_4dflow_joint_forward","epsilon_fn_center":"26.0"},"omega_bounds":{"H":[128,512],"W":[128,512],"Z":[32,256],"TE_ms":[1.5,5.0],"TR_ms":[3.0,10.0],"SNR_dB":[5.0,38.0],"venc_mps":[0.5,6.0],"B0_field_T":[1.5,7.0],"venc_aliasing":[0.0,0.3],"voxel_size_mm":[1.0,4.0],"N_cardiac_phases":[10,50],"breath_hold_motion":[0.0,0.3],"eddy_current_offset":[0.0,0.2],"viscosity_uncertainty":[0.0,0.3],"partial_volume_at_walls":[0.0,0.4],"segmentation_error_at_chambers":[0.0,0.3]},"epsilon_bounds":{"psnr_db":[10.0,42.0]},"allowed_problem_classes":["cardiac_4dflow_ns_regularized","cardiac_4dflow_aortic","cardiac_4dflow_pulmonary","cardiac_4dflow_intracardiac","cardiac_4dflow_with_wall_shear_stress","cardiac_4dflow_with_pressure_drop"],"allowed_omega_dimensions":["H","W","Z","N_cardiac_phases","venc_mps","B0_field_T","voxel_size_mm","TR_ms","TE_ms","SNR_dB","venc_aliasing","partial_volume_at_walls","breath_hold_motion","eddy_current_offset","segmentation_error_at_chambers","viscosity_uncertainty"],"allowed_forward_operators":["cardiac_4dflow_joint_forward","cardiac_4dflow_two_step_forward","cardiac_4dflow_pinn_forward","cardiac_4dflow_with_pressure_recovery"]},"hardness_fn":{"type":"epsilon_fn","delta":5,"kappa":220,"metric":"PSNR_dB"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0xb25b2551bc781001bdbc0c456066a6dbda2ec0862615e8c6d13eaccd12c31009","chain_tx_hash":"0x6eef5f3c58e7f98baff189b5095bd56113d47f055cf3e3ebc3265addd1b22f58","chain_block":41552305}