Bjarke Jensen

Transition Densities of Diffusion Processes: Numerical Comparison of Approximation Techniques

Trying to build option models with price dynamics that better match empirical price behavior, we run into the problem that only a few returns processes, like the standard Black-Scholes lognormal diffusion, lead to closed form solutions for the transition densities. Generally these must be approximated numerically, using one of a variety of approaches. The Euler approximation is probably the most common technique of discretizing the process, but others are also in use, including the Milshtein scheme. Monte Carlo simulation is another approach. Simulation methods may make use of (pseudo-) random numbers, or deterministic quasi-random sequences that may be more efficient. Alternatives include the binomial model, Hermite expansions, and more. In this article, Jensen and Poulsen examine the comparative performance of a large number of approximation techniques in terms of accuracy and execution time. The winner in their tests, by a surprisingly large margin, is the Hermite expansion approach.

How the python heart separates pulmonary and systemic blood pressures and blood flows

Summary The multiple convergent evolution of high systemic blood pressure among terrestrial vertebrates has always been accompanied by lowered pulmonary pressure. In mammals, birds and crocodilians, this cardiac separation of pressures relies on the complete division of the right and left ventricles by a complete ventricular septum. However, the anatomy of the ventricle of most reptiles does not allow for complete anatomical division, but the hearts of pythons and varanid lizards can produce high systemic blood pressure while keeping the pulmonary blood pressure low. It is also known that these two groups of reptiles are characterised by low magnitudes of cardiac shunts. Little, however, is known about the mechanisms that allow for this pressure separation. Here we provide a description of cardiac structures and intracardiac events that have been revealed by ultrasonic measurements and angioscopy. Echocardiography revealed that the atrioventricular valves descend deep into the ventricle during ventricular filling and thereby greatly reduce the communication between the systemic (cavum arteriosum) and pulmonary (cavum pulmonale) ventricular chambers during diastole. Angioscopy and echocardiography showed how the two incomplete septa, the muscular ridge and the bulbuslamelle – ventricular structures common to all squamates – contract against each other in systole and provide functional division of the anatomically subdivided ventricle. Washout shunts are inevitable in the subdivided snake ventricle, but we show that the site of shunting, the cavum venosum, is very small throughout the cardiac cycle. It is concluded that the python ventricle is incapable of the pronounced and variable shunts of other snakes, because of its architecture and valvular mechanics.

Change of cardiac function, but not form, in postprandial pythons.

Pythons are renowned for a rapid and pronounced postprandial growth of the heart that coincides with a several-fold elevation of cardiac output that lasts for several days. Here we investigate whether ventricular morphology is affected by digestive state in two species of pythons (Python regius and Python molurus) and we determine the cardiac right-to-left shunt during the postprandial period in P. regius. Both species experienced several-fold increases in metabolism and mass of the digestive organs by 24 and 48 h after ingestion of meals equivalent to 25% of body mass. Surprisingly there were no changes in ventricular mass or dimensions as we used a meal size and husbandry conditions similar to studies finding rapid and significant growth. Based on these data and literature we therefore suggest that postprandial cardiac growth should be regarded as a facultative rather than obligatory component of the renowned postprandial response. The cardiac right-to-left shunt, calculated on the basis of oxygen concentrations in the left and right atria and the dorsal aorta, was negligible in fasting P. regius, but increased to 10-15% during digestion. Such shunt levels are very low compared to other reptiles and does not support a recent proposal that shunts may facilitate digestion in reptiles.

Anatomy of the python heart.

The hearts of all snakes and lizards consist of two atria and a single incompletely divided ventricle. In general, the squamate ventricle is subdivided into three chambers: cavum arteriosum (left), cavum venosum (medial) and cavum pulmonale (right). Although a similar division also applies to the heart of pythons, this family of snakes is unique amongst snakes in having intracardiac pressure separation. Here we provide a detailed anatomical description of the cardiac structures that confer this functional division. We measured the masses and volumes of the ventricular chambers, and we describe the gross morphology based on dissections of the heart from 13 ball pythons (Python regius) and one Burmese python (P. molurus). The cavum venosum is much reduced in pythons and constitutes approximately 10% of the cavum arteriosum. We suggest that shunts will always be less than 20%, while other studies conclude up to 50%. The high-pressure cavum arteriosum accounted for approximately 75% of the total ventricular mass, and was twice as dense as the low-pressure cavum pulmonale. The reptile ventricle has a core of spongious myocardium, but the three ventricular septa that separate the pulmonary and systemic chambers—the muscular ridge, the bulbuslamelle and the vertical septum—all had layers of compact myocardium. Pythons, however, have unique pads of connective tissue on the site of pressure separation. Because the hearts of varanid lizards, which also are endowed with pressure separation, share many of these morphological specializations, we propose that intraventricular compact myocardium is an indicator of high-pressure systems and possibly pressure separation.

Evolution and development of ventricular septation in the amniote heart.

During cardiogenesis the epicardium, covering the surface of the myocardial tube, has been ascribed several functions essential for normal heart development of vertebrates from lampreys to mammals. We investigated a novel function of the epicardium in ventricular development in species with partial and complete septation. These species include reptiles, birds and mammals. Adult turtles, lizards and snakes have a complex ventricle with three cava, partially separated by the horizontal and vertical septa. The crocodilians, birds and mammals with origins some 100 million years apart, however, have a left and right ventricle that are completely separated, being a clear example of convergent evolution. In specific embryonic stages these species show similarities in development, prompting us to investigate the mechanisms underlying epicardial involvement. The primitive ventricle of early embryos becomes septated by folding and fusion of the anterior ventricular wall, trapping epicardium in its core. This folding septum develops as the horizontal septum in reptiles and the anterior part of the interventricular septum in the other taxa. The mechanism of folding is confirmed using DiI tattoos of the ventricular surface. Trapping of epicardium-derived cells is studied by transplanting embryonic quail pro-epicardial organ into chicken hosts. The effect of decreased epicardium involvement is studied in knock-out mice, and pro-epicardium ablated chicken, resulting in diminished and even absent septum formation. Proper folding followed by diminished ventricular fusion may explain the deep interventricular cleft observed in elephants. The vertical septum, although indistinct in most reptiles except in crocodilians and pythonidsis apparently homologous to the inlet septum. Eventually the various septal components merge to form the completely septated heart. In our attempt to discover homologies between the various septum components we aim to elucidate the evolution and development of this part of the vertebrate heart as well as understand the etiology of septal defects in human congenital heart malformations.

The Heart of the South American Rattlesnake, Crotalus durissus

Most anatomical and physiological studies of the sauropsid heart have focused on species with extraordinary physiologies, and detailed anatomical descriptions of hearts from sauropsids with more common physiologies are therefore warranted. Here, we present a comprehensive study of the cardiac anatomy of the South American rattlesnake (Crotalus durissus). The cardiovascular physiology of this species has been investigated in a number of studies, whereas only a few cursory studies exist on the cardiac anatomy of viperid snakes. The heart of C. durissus is typically squamate in many regards. Both atria are thin‐walled sacs, and the right atrium is the most voluminous. The single ventricle contains three major septa; the vertical septum, the muscular ridge (MR), and the bulbuslamelle. These partially divide the ventricle into three chambers; the systemic and left‐sided cavum arteriosum (CA), the pulmonary and right‐sided cavum pulmonale, and the medial cavum venosum (CV). The MR is the most developed septum, and several additional and minor septa are found within the CA and CV. An extraordinary thin cortical layer encloses the ventricle, and it is irrigated by a remarkably rich arborization of coronary arteries. Previous studies show high degrees of blood flow separation in the Crotalus heart, and this can only be explained by the coordinated actions of the septa and the prominent atrioventricular valves. J. Morphol. 271:1066‐1077, 2010.

Hemodynamic Consequences of Cardiac Malformations in Two Juvenile Ball Pythons (Python regius)

Abstract Two cases of bifid ventricles and cardiac malformations in juvenile ball python (Python regius) were investigated by blood pressure measurements and macro- and microscopic sectioning. A study of a normal ball python was included for reference. In both cases, all cardiac chambers were enlarged and abnormally shaped. Internal assessment of the ventricles revealed a pronounced defect of the muscular ridge, which normally is responsible for separating the systemic and pulmonary circuits. Consistent with the small muscular ridge, systolic pressures were identical in the pulmonary and systemic arteries, but, the snakes, nevertheless, lived to reach body weights severalfold of their hatchling weight.

Controlled Electrochemical Carboxylation of Graphene To Create a Versatile Chemical Platform for Further Functionalization

An electrochemical approach is introduced for the versatile carboxylation of multi-layered graphene in 0.1 M Bu4NBF4/MeCN. First, the graphene substrate (i.e., graphene chemically vapor-deposited on Ni) is negatively charged at -1.9 V versus Ag/AgI in a degassed solution to allow for intercalation of Bu4N(+) and, thereby, separation of the individual graphene sheets. In the next step, the strongly activated and nucleophilic graphene is allowed to react with added carbon dioxide in an addition reaction, introducing carboxylate groups stabilized by Bu4N(+) already present. This procedure may be carried out repetitively to further enhance the carboxylation degree under controlled conditions. Encouragingly, the same degree of control is even attainable, if the intercalation and carboxylation is carried out simultaneously in a one-step procedure, consisting of simply electrolyzing in a CO2-saturated solution at the graphene electrode for a given time. The same functionalization degree is obtained for all multi-layered regions, independent of the number of graphene sheets, which is due to the fact that the entire graphene structure is opened in response to the intercalation of Bu4N(+). Hence, this electrochemical method offers a versatile procedure to make all graphene sheets in a multi-layered but expanded structure accessible for functionalization. On a more general level, this approach will provide a versatile way of forming new hybrid materials based on intimate bond coupling to graphene via carboxylate groups.

Examples of Weak, If Not Absent, Form-Function Relations in the Vertebrate Heart

That form and function are related is a maxim of anatomy and physiology. Yet, form-function relations can be difficult to prove. Human subjects with excessive trabeculated myocardium in the left ventricle, for example, are diagnosed with non-compaction cardiomyopathy, but the extent of trabeculations may be without relation to ejection fraction. Rather than rejecting a relation between form and function, we may ask whether the salient function is assessed. Is there a relation to electrical propagation, mean arterial blood pressure, or propensity to form blood clots? In addition, how should the extent of trabeculated muscle be assessed? While reviewing literature on trabeculated muscle, we applied Tinbergen’s four types of causation—how does it work, why does it work, how is it made, and why did it evolve—to better parse what is meant by form and function. The paper is structured around cases that highlight advantages and pitfalls of applying Tinbergen’s questions. It further uses the evolution of lunglessness in amphibians to argue that lung reduction impacts on chamber septation and it considers the evolution of an arterial outflow in fishes to argue that reductions in energy consumption may drive structural changes with little consequences to function. Concerning trabeculations, we argue they relate to pumping function in the embryo in the few weeks before the onset of coronary circulation. In human fetal and postnatal stages, a spectrum of trabeculated-to-compact myocardium makes no difference to cardiac function and in this period, form and function may appear unrelated.

The Anatomy, Development, and Evolution of the Atrioventricular Conduction Axis

It is now well over 100 years since Sunao Tawara clarified the location of the axis of the specialised myocardium responsible for producing coordinated ventricular activation. Prior to that stellar publication, controversies had raged as to how many bundles crossed the place of the atrioventricular insulation as found in mammalian hearts, as well as the very existence of the bundle initially described by Wilhelm His Junior. It is, perhaps surprising that controversies continue, despite the multiple investigations that have taken place since the publication of Tawara’s monograph. For example, we are still unsure as to the precise substrates for the so-called slow and fast pathways into the atrioventricular node. Much has been done, nonetheless, to characterise the molecular make-up of the specialised pathways, and to clarify their mechanisms of development. Of this work itself, a significant part has emanated from the laboratory coordinated for a quarter of a century by Antoon FM Moorman. In this review, which joins the others in recognising the value of his contributions and collaborations, we review our current understanding of the anatomy, development, and evolution of the atrioventricular conduction axis.