Networks embedded in three dimensional matrices are beneficial to delivering physical flows to the matrices. Leaf architectures, pervasive natural network-matrix architectures, endow leaves with high transpiration rates and low water pressure drops, providing inspiration for efficient network-matrix architectures. In this study, the network-matrix model for general flow transport inspired by natural pinnate leaves is investigated analytically. The results indicate that the optimal network

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... ure inspired by natural pinnate leaves can greatly reduce the maximum potential drop and the total potential drop caused by the flow through the network while maximizing the total flow rate through the matrix. These results can be used to design efficient networks in network-matrix architectures for a variety of practical applications, such as tissue engineering, cell culture, photovoltaic devices and heat transfer.