Non-invasive assessment of the hemodynamic changes of cirrhosis might help guide management of patients with liver disease but are currently limited. To determine whether free-breathing 4D flow MRI can be used to quantify the hemodynamic effects of cirrhosis and introduce hydraulic circuit indexes of severity. Retrospective. Forty-seven patients including 26 with cirrhosis. 3 T/free-breathing 4D flow MRI with soft gating and golden-angle view ordering. Measurements of the supra-celiac abdominal aorta, supra-renal abdominal aorta (SRA), celiac trunk (CeT), superior mesenteric artery (SMA), splenic artery (SpA), common hepatic artery (CHA), portal vein (PV), and supra-renal inferior vena cava (IVC) were made by two radiologists. Measures of hepatic vascular resistance (hepatic arterial relative resistance [HARR]; portal resistive index [PRI]) were proposed and calculated. Bland-Altman, Pearson's correlation, Tukey's multiple comparison, and Cohen's kappa. P < 0.05 was considered significant. Forty-four of 47 studies yielded adequate image quality for flow quantification (94%). Arterial structures showed high inter-reader concordance (range; ρ = 0.948-0.987) and the IVC (ρ = 0.972), with moderate concordance in the PV (ρ = 0.866). Conservation of mass analysis showed concordance between large vessels (SRA vs. IVC; ρ = 0.806), small vessels (celiac vs. CHA + SpA; ρ = 0.939), and across capillary beds (CeT + SMA vs. PV; ρ = 0.862). Splanchnic flow was increased in patients with portosystemic shunting (PSS) relative to control patients and patients with cirrhosis without PSS (P < 0.05, difference range 0.11-0.68 liter/m). HARR was elevated and PRI was decreased in patients with PSS (3.55 and 1.49, respectively) compared to both the control (2.11/3.18) and non-PSS (2.11/2.35) cohorts. 4D flow MRI with self-navigation was technically feasible, showing promise in quantifying the hemodynamic effects of cirrhosis. Proposed quantitative metrics of hepatic vascular resistance correlated with PSS. 3 TECHNICAL EFFICACY STAGE: 2.