John Fiske Brown Associates, Inc.

 by L.L. Wickham, Ph.D.
                                                                                                                                  What do blood, traffic and rheology all have in common?  They all involve flow.  Rheology is the study of flow.   Rheological applications include flow analyses of water in pipes or air around airplanes.  Bioengineers often study flowing blood, body fluids, cells and tissues. What does this have to do with Traffic?  Skimming through the Journal of Rheology one finds articles on mathematical modeling of car flow on roads as well as blood flow inside organisms.  There are even models of clothes tumbling in washers and dryers.  Driving on highways at night, the flow behavior of those red taillights ahead seems similar to red blood cells.  Both those who study blood flow behavior (hemorheologists) and traffic engineering modelers use the terms arterial flow and collateral flow.  Sometimes there are perturbations in both systems causing slow flow, "sludging" or "traffic jams".  In both fields, optimization involves enhancement of  fluidity and/or reduction of  interactions between the particles [cells or vehicles].  Deformability and elasticity are quite different between cells and cars.  Cells are usually deformable and elastic while cars rarely assume their original shape after a collision.  Accident reconstructionists measure the "crush" of vehicles after an accident in order to determine the "flow" in terms of  speed at impact.  Calculations of the forces during impact can be used to study the effects to both vehicles and occupants after a crash.  A traffic jam or clog can exhibit "elasticity" changing from completely stalled to “stop and go” or “high flow”.  Stalled jams are similar to blood “sludging” where cells contact each other and become transiently attached in loose formations resulting in three dimensional networks with a great deal of elasticity. These cell aggregations can require high forces to re-establish flow during peripheral vascular disease, deep vein thrombosis and intermittent claudication.  The latter pathology is common to diabetic and geriatric patients when cell aggregation causes poor circulation in the extremities. Unfortunately, over time, these aggregations may irreversibly clot causing the death of surrounding or downstream  tissue.  Myocardial infarction or "heart attack" happens when coronary vessels feeding the heart are compromised. 

Similarly, vehicle collisions often happen during traffic “jams” contributing to stagnation.  Congested flow also occurs in areas of merging particles in both systems.  Those who travel from San Diego to North County are familiar with this concept at the I-805 to I-5 junction.  Bifurcations (“Y’s”) where one flow path separates into two can split aggregations apart but may cause collisions at the apex of the split [e.g. the I-5/I-805 split southbound from North County to San Diego].  Proper infrastructure is essential in both systems. Collateral flow, the development of parallel or intersecting flow paths, can be effective in both systems. Collateral vessel recruitment increases during atherosclerosis when fatty deposits harden and narrow blood vessels making them prone to clots.  When collateral flow is insufficient, a surgical bypass can meet flow demands. The same term is used for roads routing traffic around an area where municipal growth or redevelopment exceeds original carrying capacity and infrastructure.  Rheologists trying to destroy cancer cells surrounded by myriad interconnecting blood vessels in a tortuous geometry analyze tumor microcirculation.  Traffic engineers meet similar problems  regulating flow in complex combinations of intersections, bypasses and cloverleaf  geometries. Traffic "roundabouts" can be effective alternatives to intersections and bifurcations,  sites of collisions and disturbed flow in both systems. 
Throughput during congested flow can be maintained by a velocity profile that is uneven across lanes so that slower vehicles or cells do not “line up” reducing flow.  In blood vessels, the optimum velocity profile is parabolic with cells in the center of the vessel traveling faster than those near the 'wall'.  A layer of plasma, the suspending fluid, next to the walls causes a lubrication effect.    Models of the separation of blood at branch points and the effects on downstream flow are applicable to traffic flow. "Plasma skimming" lowers the numbers of cells in a side branch at vessel bifurcations. Highway off-ramps are similar in architecture but not in effect since they are skimming off vehicles thereby enhancing flow in the main thoroughfare. When cars block access ramps, decreased flow, collisions, and stagnation may occur.  Current highway flow design indicates that cars in the left [#1] lane should travel faster than the other lanes. Slow vehicles in the left lane can cause “plug flow” where vehicles in adjacent lanes travel closely at similar speeds reducing throughput and making ramp access difficult. Faster drivers may then try to squeeze between slower cars increasing the probability for collisions that can cause stagnation.  Proposed freeway "tracking" lanes that automatically control vehicles could prevent driver behaviors that reduce traffic flow.  Carpool lanes and high-speed trains built over freeways are designed to accomplish the same goal. 

 The generalizations and oversimplifications presented here are meant to emphasize rheological similarities rather than the many differences in these systems.  Forensic consultants in engineering and accident reconstruction are often called upon to analyze road architecture and flow patterns in assessment of motor vehicle accidents while biomedical consultants may be more concerned with body fluids, tissues, and mechanical properties of the occupants.  Effective communication among these scientists can provide synergistic collaborations using tools for prediction and problem solving from seemingly disparate fields resulting in novel approaches and solutions.