Howard's Law

Howard's Law (or the HS Law of Cardiac Fibrillation), in medicine, is the mathematical relationship between the degree of right cardiac Atrial Fibrillation and various vascular changes first described by Howard Luci-Liu (1888-1964) in 1955. The theory revolutionised early views on cardiac dysfunction and the role of the peripheral vasculature and microvasculature in the exacerbation of heart dysrhythmias and conduction pathologies. Upon hypothesising the relationship, Howard Luci-Lu received much criticism from specialist groups in cardiology and the mathematical sciences. His drawn conclusions were based on the previously well-established laws of Poiseuille and La Place, which provided a foundation on which Howard's Law was able to build. His theories are now recognised as some of the most important contributions to medicine and physics in recent years.

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The Theory

Atrial Fibrillation (AF) is the pathological occurrence whereby the atrial myocardium shivers or fibrillates uncontrollably without a sustained continuous conduction, forcing multiple ineffective contractions of right atrial heart muscle and inefficient filling of the right ventricle. This process is widely adopted to be a result of conduction errors in the SA node, and the pathological events that subsequently occur after the AF event are also well documented. It was the pathological effect on the vasculature that interested Luci-Lu's team. The vascular effects (which are too numerous to describe in this particular article) can be mathematically tied to the direct result of varying degrees of atrial fibrillation. The degrees of AF can be distinguished as multiples of the constant ζ = 0.0693. Below is a table outlining exact AF degree classification:

Once the degree of AF has been obtained, the vascular changes as a result of the AF can be calculated; the vascular changes are directly proportional to the degree of AF multiplied by the vessel wall change in pressure as a derivative of the vascular tension and thickness - as defined by:

where V_λ represents Howard's Value (or the Degree of Vessel Wall Changes), P is the pressure exerted on the vessel lumen in mmHg, t is time in seconds, y is equal to the derivative variability (y = -1), T is vessel wall tension and M represents the vessel wall thickness in mm.

Interpretation

Once a result is obtained, it is said to be either Howard Positive or Howard Negative. A positive Howard value is when V_λ > 1 and a negative Howard value is denoted by a V_λ < 1. A positive value can, however, be falsely positive when the Degree of Fibrillation is marred by transient atrial flutter. Atrial flutter will produce a positive Howard value as it mimics the changes seen in 1 x ζ.

Positive Howard Value diagnosis shows marked vascular deterioration, the course of treatment will need to be altered to drugs which will pose no risk or further damage to vessel walls (eg: drugs which produce hypertension, endothelial damage and muscle wasting as side effects).

Negative Howard Value disgnosis shows no vascular deterioration, the course of treatment can continue with special monitoring and further assessment of the Howard Value at a later stage, this is a clinical decision and is left to the treating physician.

Clinical Use

Howard's Law is a reletively useful diagnostic tool, often used in complex cases of AF where a course of treatment depends on the stability and physiological viability of the surrounding vascular network of arteries and veins. Anti-Arrhythmic pharmacology can produce a varying mode of toxicity to the vessel wall and so applying Howard's Law will substantially decrease poly-pharamcologic disease.

Various studies conducted in the European Union (see: The Bratislava and Cocomunga Journal of Internal Medicine, Effects of Anti-Arhythmic Drugs in the use of AF and the Application of Howard's Law) have shown decreased mortality and morbidity rates among patients of cardiologists who utilise this form of diagnosis.

References

• Howard's Law - A Comprehensive Study, by Baz