A microfluidic device comprising: a manifold having a first manifold channel, a second manifold channel, and a third manifold channel, coupled to a substrate defining an artificial vasculature, wherein: the first manifold channel is configured to carry blood in a first direction; each of the second and third manifold channels couples to the first manifold channel at a first junction and is configured to receive blood from the first manifold channel such that a total blood flow rate through the second and third manifold channels is substantially the same as a blood flow rate through the first manifold channel; the second manifold channel is configured to carry blood in a second direction away from the first direction; the third manifold channel is configured to carry blood in a third direction away from the first direction; and the first, second, and third manifold channels are non-coplanar, wherein: at least one of the first manifold channel, the second manifold channel and the third manifold channel further comprises a transition region, the cross-sectional area of the at least one manifold channel upstream from the transition region is larger than the cross-sectional area of the at least one manifold channel downstream from the transition region, and the transition region comprises sidewalls defined by one of a Hicks-Henne bump function, a non- uniform rational basis spline, a cubic spline, a T spline, a point cloud, and a polynomial function. the first manifold channel is configured to carry blood in a first direction; each of the second and third manifold channels couples to the first manifold channel at a first junction and is configured to receive blood from the first manifold channel such that a total blood flow rate through the second and third manifold channels is substantially the same as a blood flow rate through the first manifold channel; the second manifold channel is configured to carry blood in a second direction away from the first direction; the third manifold channel is configured to carry blood in a third direction away from the first direction; and the first, second, and third manifold channels are non-coplanar, wherein: at least one of the first manifold channel, the second manifold channel and the third manifold channel further comprises a transition region, the cross-sectional area of the at least one manifold channel upstream from the transition region is larger than the cross-sectional area of the at least one manifold channel downstream from the transition region, and the transition region comprises sidewalls defined by one of a Hicks-Henne bump function, a non- uniform rational basis spline, a cubic spline, a T spline, a point cloud, and a polynomial function. at least one of the first manifold channel, the second manifold channel and the third manifold channel further comprises a transition region, the cross-sectional area of the at least one manifold channel upstream from the transition region is larger than the cross-sectional area of the at least one manifold channel downstream from the transition region, and the transition region comprises sidewalls defined by one of a Hicks-Henne bump function, a non- uniform rational basis spline, a cubic spline, a T spline, a point cloud, and a polynomial function.