Testing Foundations of Biological Scaling Theory Using Automated Measurements of Vascular Networks

Abstract

Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to capillaries and uses scaling exponents to quantify these changes. Prominent scaling theories predict that combinations of these exponents explain how metabolic, growth, and other biological rates vary with body size. Nevertheless, direct measurements of individual vessel segments have been limited because existing techniques for measuring vasculature are invasive, time consuming, and technically difficult. We developed software that extracts the length, radius, and connectivity of in vivo vessels from contrast-enhanced 3D Magnetic Resonance Angiography. Using data from 20 human subjects, we calculated scaling exponents by four methods—two derived from local properties of branching junctions and two from whole-network properties. Although these methods are often used interchangeably in the literature, we do not find general agreement between these methods, particularly for vessel lengths. Measurements for length of vessels also diverge from theoretical values, but those for radius show stronger agreement. Our results demonstrate that vascular network models cannot ignore certain complexities of real vascular systems and indicate the need to discover new principles regarding vessel lengths.

Energy and time determine scaling in biological and computer designs

“…This is not surprising given that different tissues and organs have different metabolic requirements. D r may vary within the vascular network with area-preserving branching closer to the heart and area-increasing branching slowing blood velocity in smaller vessels, but Newberry et al [22] find values for D r consistent with our predictions. Similarly, there is evidence that D w varies across hierarchical levels in computer chips [32].…”

“…The predicted value of D r between 2 and 3 is also consistent with the idea that the upper region of the network is area preserving with D r ¼ 2, while D r ¼ 3 in the lower region as proposed by West et al [5], and it is consistent with the empirical radius scaling reported in [22].…”

“…In reality, each of these may vary. For example, Newberry et al [22] did not find evidence for a constant D l ¼ 3 in mouse vasculature, suggesting that the network does not deliver resources uniformly throughout the body volume. This is not surprising given that different tissues and organs have different metabolic requirements.…”

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

“…Because vessel radii exhibit relatively little asymmetry and are consistent with existing models [29], we focus on asymmetries in vessel lengths and branching angles. Through the identification and investigation of these new, systematic patterns, an explanation might eventually be obtained for the mismatch between theoretical predictions from scaling theory and empirical data [9].…”

Rediscovering and Reviving Old Observations and Explanations of Metabolic Scaling in Living Systems

“…New RTN-based models (e.g., [84,[173][174][175][176]) or applications (e.g., [22,172,177]) continue to appear that have not sufficiently heeded the history of accumulating negative evidence against the assumptions, logic and predictions of previous RTN models.…”