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Heart failure is a co-morbidity for critical illness at both the beginning and end of the critically ill process. At the beginning it limits the ability of the host to sustain an adequate DO necessary to prevent the initial ischemia-induced organ injury, while at the end, it limits the host’s ability to wean successfully from mechanical ventilatory support. When treating critically ill patients, one must remember that failure to achieve an adequate DO may reflect occult heart failure. Since the treatment for heart failure is often the opposite to the treatment of hypovolemia, which itself is the other major cause of cardiovascular insufficiency, this consideration is of profound practical importance in the management of the critically ill.

The hypermetabolic response that follows a severe burn cannot be halted or reversed, however with the use of prompt surgical intervention to remove the burn eschar, aggressive treatment of developing sepsis, early enteral feeding of high carbohydrate high protein diet together with a program of resistance exercises there are several ways that its effects can be limited. Adding to this an anabolic agent with or without an anticatabolic catecholamine antagonist we will be able to ameliorate the difficult sequelae to an already tragic event. Looking to the future with gene profiling, our understanding of this complex process can only increase and with it better treatment and care for our patients.

The interplay between cardiac function and general systemic disturbances is at the core of intensive care practice. Echocardiography is becoming ‘mainstream’, in that many ICUs now have their own machine and the objective is to utilize it during, as well as outside, regular working hours. Clinical urgency demands application at any time. Echocardiography frequently yields important diagnostic information, non-invasively, usually rapidly, and it can be readily reapplied as the situation demands. It has evolved from being a useful adjunct in the past to what is now an indispensable tool in the management of the critically ill patient.

The state of the art of the preload condition, volemia and cardiac performance in critically ill patients is still under investigation. After several years of ‘filling pressures’, PAOP and CVP values should be limited only in well known clinical conditions. The ITBV, correlates well with the cardiac output and with the stroke volume, and provides the opportunity to evaluate the central blood volume. The integration of ITBV together with other hemodynamic data and organ perfusion parameters today offers a chance to better understand the volemic condition. This has been studied and demonstrated in cardiac surgical patients, in sepsis, in solid organ transplantation, in positioning changes, and in children. In all other fields more investigations should be done.

The esophageal Doppler technique has progressively emerged as a minimally invasive and reliable tool for measuring aortic blood flow and estimating cardiac output. Numerous studies have emphasized its clinical utility by showing improved outcome in surgical patients when hemodynamic therapy was driven by algorithms based on esophageal Doppler data. In the setting of the ICU, the ability of esophageal Doppler to track the changes in aortic blood flow in a beat-to-beat manner makes it particularly suitable for predicting fluid responsiveness, either by the measurement of the aortic blood flow respiratory variation or by testing the effects of passive leg raising.

ANP and BNP are secreted from cardiac myocytes in response to atrial or ventricular wall stretch. The physiologic effects of both cardiac natriuretic peptides include natriuresis, diuresis, and inhibition of the activities of several neuroendocrine systems, including the renin-angiotensin-aldosterone system, endothelins, cytokines, and the sympathetic nervous system. Single and serial plasma measurement of BNP is a promising tool for diagnosis and risk stratification of patients with heart failure and acute coronary syndromes. Levels of BNP could also be used to guide drug therapy in these patients. Finally, the administration of nesiritide, a synthetic recombinant human BNP, appears to offer a novel approach in the management of acute heart failure.

Pulse pressure analysis has an important role in the management of critically ill patients. There are currently several devices available that are less invasive and serve to provide continuous and accurate measurements of cardiac output. PiCCO is the oldest device and has been validated in several clinical situations. LiDCO is more recent and has also been validated, with more studies to follow. PRAM and FloTrac are very new devices that have the advantage of not requiring calibration and being quick and easy to use. There is evidence validating PRAM and results on the use of FloTrac are expected in the near future. There has been much criticism about the use of the PAC recently. It is our vision that pulse pressure analysis will be implemented in clinical protocols to change management and outcome in critically ill patients.

Variation in pulse pressure is probably a good parameter for management of fluid requirement in patients with circulatory failure. Its measurement is less invasive than that of other parameters, and several studies have reported its value in clinical practice. However, reliable use of this parameter is dependent on awareness that there are pitfalls with a strong underlying physiological rationale, especially in an unselected population.

In Section 6.1 we sum up with brief indications of the proofs some facts on the open sets in where a differential equation () = with constant coefficients can always be solved. Depending on whether is allowed to be an arbitrary distribution or a function (or a distribution of finite order), we get two classes of admissible open sets depending on . Those which are admissible for every are precisely the genuinely convex sets. However, more general domains are admissible for individual operators . In Section 6.2 we prove by methods close to those used in Section 4.2 that in a pseudo-convex open set in C all equations of the form can be solved. In fact, we prove more general results for operators in a product space × which have this structure with respect to the complex variables. In Section 6.3 we pass to the existence of analytic solutions of equations of the form (,..., ) = in a pseudo-convex open set ⊂ where is analytic. We show that it is precisely in the C convex sets that a solution exists for arbitrary and .

Major studies designed to improve our understanding of the pathophysiology of TMA have been conducted over recent years. This improved knowledge opens up new perspectives for more targeted treatment. However, until these innovative treatments become available, early diagnosis of these diseases is essential in order to rapidly initiate specific treatment, as the interval between diagnosis and initiation of plasma exchange is a decisive element in the prognosis of TTP. Treatment must not be stopped too early or too rapidly and must take into account the various associated factors, especially the presence of infection.