## Abstract

Significant differences exist among textbook definitions for the terms preload and afterload, leading to confusion and frustration among students and faculty alike. Many faculty also chose to use in their teaching simple terms such as “end-diastolic volume” or “aortic pressure” as common-usage approximations of preload and afterload, respectively, but these are only partial representations of these important concepts. Straightforward definitions both of preload and afterload that are concise yet still comprehensive can be developed using the Law of LaPlace to describe the relationships among chamber pressure, chamber radius, and wall thickness. Within this context, the term “preload” can be defined as all of the factors that contribute to passive ventricular wall stress (or tension) at the end of diastole, and the term “afterload” can be defined as all of the factors that contribute to total myocardial wall stress (or tension) during systolic ejection. The inclusion of “wall stress” in both definitions helps the student appreciate both the complexities of cardiac pathophysiology and the rationale for therapeutic intervention.

- Law of LaPlace
- wall tension
- wall stress
- cardiac remodeling
- hypertrophy

Recent changes in the basic science curriculum at the University of New England College of Osteopathic Medicine have included a reduction in the number of classroom contact hours devoted to the traditional lecture format. These reductions have prompted (i.e., required) faculty to be more creative and productive in their use of their formal classroom time with students, with much more attention being paid to outlining major concepts, establishing linkages among topics, utilizing classroom case presentations and breakout groups–a variety of techniques intended to foster student understanding. One outcome of this approach is that students, in turn, are more clearly required to master much of the basic knowledge (facts, definitions, etc.) on their own, with guidance from the faculty in the form of recommended and required readings in texts, review articles, and current literature.

This seemingly rational use of published written materials by students to obtain the factual underpinnings for the concepts and relationships developed in class has one consequence that is very troublesome: published sources often have very different and sometimes conflicting definitions for important physiological terms. Because medical students generally dislike ambiguity and because faculty generally strive for accuracy, such discrepancies are annoying to both groups. But if conflicts among definitions of important terms and concepts remain unresolved, students may carry into their clinical training incomplete or inaccurate working definitions of these terms that may be adequate most of the time but may fail the students in novel or complicated clinical situations.

Such is the case with the concepts of preload and afterload, major determinants of cardiac function along with heart rate and myocardial contractility. Each year, after the completion of the pathophysiology segment of our second-year Cardiovascular System course, students begin turning up at my office door claiming that some of the clinical faculty defined preload and afterload much differently, and more simply, than I had. As I routinely do when students bring to my attention evidence of differing opinions or contrary definitions provided by faculty, I suggested that they check the textbooks and the biomedical literature to resolve the differences. This year, because of an inordinate number of complaints and confusion about the definition of afterload, in particular, I decided to follow my own advice.

#### Compilations of textbook definitions of preload and afterload.

To assess the extent of variability in the definitions of preload and afterload, I decided simply to compile a list of definitions for these two terms from all of the comprehensive physiology texts, cardiovascular physiology monographs, and physiology review books in a representative faculty collection (namely, the books sitting on my office shelves) as well as from two selected websites. Most, but not all, of the 29 texts I surveyed were the current editions, but for such basic concepts as preload and afterload, I did not feel that an edition or two would make much of a difference. With the use of the index, I searched in each text for the clearest statement that defined either term and generated a table summarizing my findings (Table 1). In the quotes provided in this table, words in *italics* or **bold** print appeared as such in the original text.

The variability among the textbook definitions was surprising. For example, preload is variously defined as: muscle fiber tension (7, 9, 20, 22), muscle fiber stretch (1, 6, 25), muscle fiber length (3, 18), end-diastolic volume (2, 5, 12, 19, 24, 27–29), end-diastolic filling pressure (7, 9, 12, 14, 17, 21, 26, 28, 29, 31), force (3), or, as part of a description of basic muscle mechanics, weight (15). A number of texts describe preload as *either* volume or pressure (24, 29), and some distinguish between a strict physiological definition and what might serve as an approximation of preload clinically according to common usage (9, 16).

A similar degree of variability was observed among the textbook definitions of afterload. This term was defined as the load against which a muscle exerts force (9), the pressure in the arteries leading from the ventricles (1, 4, 8, 9, 14, 16, 17, 21, 22, 24, 25, 27–29), aortic and ventricular pressures (assumed to be identical) (15, 16, 31), myocardial wall tension or stress (15, 16, 31), peripheral resistance (6, 11, 12, 16), force needed to overcome opposition to ejection (18), output impedance (19, 20), and diastolic aortic pressure (26). As was the case for preload, some texts gave multiple definitions (16, 19) and some gave specific definitions but allowed for afterload to be approximated as aortic pressure according to common clinical usage (16, 18, 20, 27). This is where I first encountered the discrepancy between my own physiological approach to defining afterload and the choice by some clinical faculty during their lectures to use simpler terms such as “arterial pressure” or “peripheral resistance” to define afterload, terms that are only indirect and incomplete representations of the real concept.

#### Definitions of preload and afterload.

The basis for the definitions of both preload and afterload is the Law of LaPlace (also known as the surface tension law or the Law of Young-LaPlace), stated as follows for a thin-walled spherical structure: *T* = P*R*/2, where *T* is wall tension, P is chamber pressure, and *R* is chamber radius. For a thick-walled structure such as the left ventricle, a more appropriate form of the equation would be ς = P*R*/2*w*, where wall stress (ς) is related to *T* and wall thickness (*w*) as follows: *T* = ς*w*.

With the use of the format of LaPlace’s equation, preload for the left ventricle can be best described as the left ventricular ς or *T* at the end of diastolic filling, as follows: preload_{LV} = (EDP_{LV})(ED*R*_{LV})/2*w*_{LV}, where EDP_{LV} is left ventricular end-diastolic filling pressure, ED*R*_{LV} is left ventricular end-diastolic radius, and *w*_{LV} is left ventricular *w*. The preload for the right ventricle would be described mathematically in an analogous fashion. Defined in words, therefore,** preload represents all the factors that contribute to passive ventricular wall stress (or tension) at the end of diastole**. From this expression, one can see that end-diastolic filling pressure or end-diastolic volume (manifested in the equation above as radius) *contribute *to preload, but should not be *equated* with preload. A summary flow chart of factors contributing to preload is provided in Fig. 1.

Similarly, with the use of LaPlace’s equation again, left ventricular afterload can be best described as the left ventricular ς or *T* during systolic ejection: afterload_{LV} = (SP_{LV})(S*R*_{LV})/2*w*_{LV}, where SP_{LV} is left ventricular systolic pressure and S*R*_{LV} is left ventricular systolic radius. The afterload for the right ventricle would be described mathematically in an analogous fashion. Defined in words, therefore, **afterload represents all the factors that contribute to total myocardial wall stress (or tension) during systolic ejection**. (In vivo, both systolic pressure and systolic volume are changing constantly during the ejection phase of the cardiac cycle, and, therefore, so is afterload; but this variability during systole doesn’t significantly affect the basic arguments presented here.) From the expression above, it is clear that anything that increases left ventricular output impedance and therefore requires a greater ventricular pressure during systole (aortic stenosis, hypertension, increased total peripheral resistance, hypertrophic cardiomyopathy, etc.) will cause an increase in afterload. Also, if the chamber radius is increased as the result of increased filling during diastole or ventricular remodeling in response to chronic increases in filling pressures, afterload will be increased even if arterial pressure is normal. Arterial pressure and total peripheral resistance *contribute *to afterload but should not be *equated* with afterload. A summary flow chart of factors contributing to afterload is provided in Fig. 2.

These definitions for preload and afterload fit the psychological need for conciseness and brevity, yet by their mention of wall stress, these definitions force a consideration of the Law of LaPlace and of the complex relationships among pressure, volume, and wall tension in the beating heart. The importance of focusing on wall stress in the definitions of preload and afterload (afterload, in particular) relates to the metabolic costs associated with the development of myocardial wall tension and, therefore, chamber pressure. The greater the tension requirement during systole, the greater the demand for oxygen and metabolic substrate by the myocardium. In the presence of cardiac disease, both physiological compensatory mechanisms and therapeutic regimens have as their goals the reduction of myocardial wall tension (and, therefore, myocardial oxygen consumption) and the restoration of a balance between oxygen supply and demand, especially important in patients with impaired coronary blood flow. A comprehensive definition of afterload, such as that provided here, would help students appreciate this therapeutic rationale.

The relationships among pressure, radius, and wall thickness described above provide a clear physiological explanation for the different patterns of hypertrophy and remodeling seen in response to increased preload and increased afterload. If filling pressures, output pressures, and stretch (factors in the numerators of the equations described above) are loads imposed on the heart by conditions within the circulatory system, then a change in myocardial wall thickness (in the denominator) can be considered as a major myocardial response to these externally imposed perturbations. For increased preload, the additional wall stress caused by a larger chamber radius is normalized by increasing the wall thickness enough to restore the ratio ED*R*_{ LV}/*w*_{LV} in the equation above for preload. Likewise, for an increased afterload generated by a greater output impedance requiring higher ventricular pressures during systole, the systolic wall stress is normalized by hypertrophy that restores the ratio SP_{LV}/*w*_{LV}.

In conclusion, the tendency clearly exists in texts, in conversation, and even in formal lectures to use short, simple definitions of preload and afterload. Preload is defined variously as “filling pressure” or end-diastolic volume; afterload is often simplified as “total peripheral resistance” or arterial pressure. According to the above analysis, these are only *components* of preload and afterload and don’t tell the whole story. If, in the mind of a student, afterload is defined only as aortic pressure, then that student will not be able to appreciate fully the increases in afterload (left ventricular wall stress) and, therefore, oxygen consumption that would accompany aortic stenosis, obstructive cardiomyopathy, or ventricular remodeling associated with increased chamber radius.

It is my contention that preload and afterload should be consistently defined in terms of myocardial wall stress (or tension) and that the definitions should always include the major factors affecting wall tension for each, namely, chamber pressure, chamber radius, and wall thickness. If you keep wall stress or “wall tension” built into your definitions of preload and afterload, you will be better able, in my opinion, to help your students understand cardiovascular pathophysiology and the therapeutic approaches to heart disease.

## Acknowledgments

The author acknowledges the students in the College of Osteopathic Medicine and in Physician Assistant and Nurse Anesthesia programs of the University of New England for many constructive criticisms and comments regarding what really works in the classroom.

## Footnotes

Address for reprint requests and other correspondence: J. M. Norton, Dept. of Physiology and Pharmacology, Univ. of New England College of Osteopathic Medicine, 11 Hill’s Beach Rd., Biddeford, ME 04005 (E-mail: jnorton{at}mailbox.une.edu).

- © 2001 American Physiological Society