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Furthermore, Guyton\u2019s graphical analysis does not predict pulmonary venous pressure, which is a critical variable for evaluating heart failure patients\u2019 risk of pulmonary edema. Therefore, the purpose of the present work was to use a minimal closed-loop mathematical model to develop an alternative to Guyton\u2019s analysis. Limitations inherent in Guyton\u2019s model were addressed by 1) partitioning the cardiovascular system differently to isolate left ventricular function and lump all blood volumes together, 2) linearizing end-diastolic pressure-volume relationships to obtain algebraic solutions, and 3) treating arterial pressures as constants. This approach yielded three advances. First, variables related to morbidities associated with left ventricular failure were predicted. Second, an algebraic formula predicting left ventricular function was derived in terms of ventricular properties. Third, an algebraic formula predicting flow through the portion of the system isolated from the left ventricle was derived in terms of mechanical properties without neglecting redistribution of blood between systemic and pulmonary circulations. Although complexities were neglected, approximations necessary to obtain algebraic formulas resulted in minimal error, and predicted variables were consistent with reported values. <\/jats:p>","DOI":"10.1152\/ajpregu.00260.2019","type":"journal-article","created":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T01:02:41Z","timestamp":1613610161000},"page":"R851-R870","update-policy":"https:\/\/doi.org\/10.1152\/aps-crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Algebraic formulas characterizing an alternative to Guyton\u2019s graphical analysis relevant for heart failure"],"prefix":"10.1152","volume":"320","author":[{"given":"Thomas W.","family":"Stiles","sequence":"first","affiliation":[{"name":"Michael E. 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