Dermal Lymphatic Capillaries Do Not Obey Murray's Law.

Lymphatic vessels serve as a major conduit for the transport of interstitial fluid, immune cells, lipids and drugs. Therefore, increased knowledge about their development and function is relevant to clinical issues ranging from chronic inflammation and edema, to cancer metastasis to targeted drug delivery. Murray's Law is a widely-applied branching rule upheld in diverse circulatory systems including leaf venation, sponge canals, and various human organs for optimal fluid transport. Considering the unique and diverse functions of lymphatic fluid transport, we specifically address the branching of developing lymphatic capillaries, and the flow of lymph through these vessels. Using an empirically-generated dataset from wild type and genetic lymphatic insufficiency mouse models we confirmed that branching blood capillaries consistently follow Murray's Law. However surprisingly, we found that the optimization law for lymphatic vessels follows a different pattern, namely a Murray's Law exponent of ~1.45. In this case, the daughter vessels are smaller relative to the parent than would be predicted by the hypothesized radius-cubed law for impermeable vessels. By implementing a computational fluid dynamics model, we further examined the extent to which the assumptions of Murray's Law were violated. We found that the flow profiles were predominantly parabolic and reasonably followed the assumptions of Murray's Law. These data suggest an alternate hypothesis for optimization of the branching structure of the lymphatic system, which may have bearing on the unique physiological functions of lymphatics compared to the blood vascular system. Thus, it may be the case that the lymphatic branching structure is optimized to enhance lymph mixing, particle exchange, or immune cell transport, which are particularly germane to the use of lymphatics as drug delivery routes.

Author Correction: Notch signaling pathway is a potential therapeutic target for extracranial vascular malformations.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Notch signaling pathway is a potential therapeutic target for extracranial vascular malformations.

Notch expression has been shown to be aberrant in brain arteriovenous malformations (AVM), and targeting Notch has been suggested as an approach to their treatment. It is unclear whether extracranial vascular malformations follow the same patterning and Notch pathway defects. In this study, we examined human extracranial venous (VM) (n = 3), lymphatic (LM) (n = 10), and AV (n = 6) malformations, as well as sporadic brain AVMs (n = 3). In addition to showing that extracranial AVMs demonstrate interrupted elastin and that AVMs and LMs demonstrate abnormal α-smooth muscle actin just as brain AVMS do, our results demonstrate that NOTCH1, 2, 3 and 4 proteins are overexpressed to varying degrees in both the endothelial and mural lining of the malformed vessels in all types of malformations. We further show that two gamma secretase inhibitors (GSIs), DAPT (GSI-IX) and RO4929097, cause dose-dependent inhibition of Notch target gene expression (Hey1) and rate of migration of monolayer cultures of lymphatic endothelial cells (hLECs) and blood endothelial cells (HUVEC). GSIs also inhibit HUVEC network formation. hLECs are more sensitive to GSIs compared to HUVEC. GSIs have been found to be safe in clinical trials in patients with Alzheimer's disease or cancer. Our results provide further rationale to support testing of Notch inhibitors in patients with extracranial vascular malformations.