Fractional Powers of Non-Negative Operators in Fréchet Spaces

[EN] In the present paper the theory of fractional powers, which has been restricted to date to certain operators on Banach spaces, is generalized to certain particular operators in Frchet spaces. The main difficulty consists in the fact that neither the holomorphlc functional calculus nor the results on Banach algebras are available for bounded operators on Frchet spaces. All the basic properties which a good theory of fractional powers must fulfill are proved, except for the spectral relation,Martinez, C.; Sanz, M.; Calvo Roselló, V. (1989). Fractional Powers of Non-Negative Operators in Fréchet Spaces. International Journal of Mathematics and Mathematical Sciences. 12(2):309-320. http://hdl.handle.net/10251/19145630932012

Fractional Powers of Non-Negative Operators in Fréchet Spaces

[EN] In the present paper the theory of fractional powers, which has been restricted to date to certain operators on Banach spaces, is generalized to certain particular operators in Frchet spaces. The main difficulty consists in the fact that neither the holomorphlc functional calculus nor the results on Banach algebras are available for bounded operators on Frchet spaces. All the basic properties which a good theory of fractional powers must fulfill are proved, except for the spectral relation,Martinez, C.; Sanz, M.; Calvo Roselló, V. (1989). Fractional Powers of Non-Negative Operators in Fréchet Spaces. International Journal of Mathematics and Mathematical Sciences. 12(2):309-320. http://hdl.handle.net/10251/19145630932012

El espectador desorientado: luz, espacio y percepción en las instalaciones de James Turrell

Las instalaciones de James Turrell son producto de una técnica precisa basada en sus conocimientos de ingeniería aeronáutica, física, astronomía, geología y psicología de la percepción. Y su complejidad es fruto de la voluntad del artista de proponer un nuevo vocabulario de la luz que modifica la relación del espectador con el espacio de la obra. El espectador desorientado trata de enfrentarse a la ambigüedad generada por la incapacidad de distinguir entre su propio espacio y el de la obra. Este artículo pretende reflexionar sobre las implicaciones del giro hacia el arte ambiental, el énfasis en el espacio real, y el papel del espectador como un colaborador y un elemento fundamental de la obra.Palabras Clave: cuerpo, desmaterialización, arte vaporoso, percepción, experiencia, espacio, instalación.AbstractJames Turrell’s light installations are the result of his accurate technique –based on his knowledge of aeronautical engineering, physics, astronomy, geology and psychology of perception. Their complexity is the result of the artist’s yearning to put forward a new vocabulary of light that modifies the viewer’s relationship to the space. The disoriented viewer deals with the ambiguity generated by the inability to distinguish between their own space and the work. This article intends to reflect on the implication of the turn to environmental art, the emphasis on real space, and the role of the viewer as a participant and a key element of the work.Keywords: body, dematerialization, vaporous art, perception, experience, space, installation.</p

Losartan activates sirtuin 1 in rat reduced-size orthotopic liver transplantation

© 2015 Baishideng Publishing Group Inc. All rights reserved. Aim: To investigate a possible association between losartan and sirtuin 1 (SIRT1) in reduced-size orthotopic liver transplantation (ROLT) in rats. Methods: Livers of male Sprague-Dawley rats (200-250 g) were preserved in University of Wisconsin preservation solution for 1 h at 4°C prior to ROLT. In an additional group, an antagonist of angiotensin II type 1 receptor (AT1R), losartan, was orally administered (5 mg/kg) 24 h and 1 h before the surgical procedure to both the donors and the recipients. Transaminase (as an indicator of liver injury), SIRT1 activity, and nicotinamide adenine dinucleotide (NAD+, a co-factor necessary for SIRT1 activity) levels were determined by biochemical methods. Protein expression of SIRT1, acetylated FoxO1 (ac-FoxO1), NAMPT (the precursor of NAD+), heat shock proteins (HSP70, HO-1) expression, endoplasmic reticulum stress (GRP78, IRE1α, p-eIF2) and apoptosis (caspase 12 and caspase 3) parameters were determined by Western blot. Possible alterations in protein expression of mitogen activated protein kinases (MAPK), such as p-p38 and p-ERK, were also evaluated. Furthermore, the SIRT3 protein expression and mRNA levels were examined. Results: The present study demonstrated that losartan administration led to diminished liver injury when compared to ROLT group, as evidenced by the significant decreases in alanine aminotransferase (358.3 133.44 vs 206 33.61, P + (0.87 0.22 vs 1.195 0.144, P < 0.05) the co-factor necessary for SIRT1 activity, as well as with decreases in ac-FoxO1 expression. Losartan treatment also provoked significant attenuation of endoplasmic reticulum stress parameters (GRP78, IRE1α, p-eIF2) which was consistent with reduced levels of both caspase 12 and caspase 3. Furthermore, losartan administration stimulated HSP70 protein expression and attenuated HO-1 expression. However, no changes were observed in protein or mRNA expression of SIRT3. Finally, the protein expression pattern of p-ERK and p-p38 were not altered upon losartan administration. Conclusion: The present study reports that losartan induces SIRT1 expression and activity, and that it reduces hepatic injury in a ROLT model.Supported by Grants from Fondo de Investigaciones Sanitarias, No. FIS PI12/00519; fellowship from Agència de Gestió d’Ajuts Universitaris i de Recerca, No. 2012FI_B00382; Generalitat de Catalunya, Barcelona, Catalonia, Spain (to Pantazi E)Peer Reviewe

Computing option pricing models under transaction costs

AbstractThis paper deals with the Barles–Soner model arising in the hedging of portfolios for option pricing with transaction costs. This model is based on a correction volatility function Ψ solution of a nonlinear ordinary differential equation. In this paper we obtain relevant properties of the function Ψ which are crucial in the numerical analysis and computing of the underlying nonlinear Black–Scholes equation. Consistency and stability of the proposed numerical method are detailed and illustrative examples are given

Losartan activates sirtuin 1 in rat reduced-size orthotopic liver transplantation

© 2015 Baishideng Publishing Group Inc. All rights reserved. Aim: To investigate a possible association between losartan and sirtuin 1 (SIRT1) in reduced-size orthotopic liver transplantation (ROLT) in rats. Methods: Livers of male Sprague-Dawley rats (200-250 g) were preserved in University of Wisconsin preservation solution for 1 h at 4°C prior to ROLT. In an additional group, an antagonist of angiotensin II type 1 receptor (AT1R), losartan, was orally administered (5 mg/kg) 24 h and 1 h before the surgical procedure to both the donors and the recipients. Transaminase (as an indicator of liver injury), SIRT1 activity, and nicotinamide adenine dinucleotide (NAD+, a co-factor necessary for SIRT1 activity) levels were determined by biochemical methods. Protein expression of SIRT1, acetylated FoxO1 (ac-FoxO1), NAMPT (the precursor of NAD+), heat shock proteins (HSP70, HO-1) expression, endoplasmic reticulum stress (GRP78, IRE1α, p-eIF2) and apoptosis (caspase 12 and caspase 3) parameters were determined by Western blot. Possible alterations in protein expression of mitogen activated protein kinases (MAPK), such as p-p38 and p-ERK, were also evaluated. Furthermore, the SIRT3 protein expression and mRNA levels were examined. Results: The present study demonstrated that losartan administration led to diminished liver injury when compared to ROLT group, as evidenced by the significant decreases in alanine aminotransferase (358.3 133.44 vs 206 33.61, P + (0.87 0.22 vs 1.195 0.144, P < 0.05) the co-factor necessary for SIRT1 activity, as well as with decreases in ac-FoxO1 expression. Losartan treatment also provoked significant attenuation of endoplasmic reticulum stress parameters (GRP78, IRE1α, p-eIF2) which was consistent with reduced levels of both caspase 12 and caspase 3. Furthermore, losartan administration stimulated HSP70 protein expression and attenuated HO-1 expression. However, no changes were observed in protein or mRNA expression of SIRT3. Finally, the protein expression pattern of p-ERK and p-p38 were not altered upon losartan administration. Conclusion: The present study reports that losartan induces SIRT1 expression and activity, and that it reduces hepatic injury in a ROLT model.Supported by Grants from Fondo de Investigaciones Sanitarias, No. FIS PI12/00519; fellowship from Agència de Gestió d’Ajuts Universitaris i de Recerca, No. 2012FI_B00382; Generalitat de Catalunya, Barcelona, Catalonia, Spain (to Pantazi E)Peer Reviewe

pH intramucoso gástrico (pHi) y gradiente sistémico-regional de CO2 en el paciente pediátrico crítico. Monitorización contínua de la perfusión tisular esplácnica.

INTRODUCCIÓN Las situaciones de shock compensado identificadas por la presencia de acidosis en la mucosa intestinal mediante la monitorización del pHi (pH intramucoso), son extremadamente frecuentes en el paciente crítico. Estos episodios de isquemia intestinal se relacionan con el síndrome de disfunción multiorgánica (SDMO). El pHi puede medirse de forma indirecta utilizando una modificación de la fórmula de Henderson-Hasselbach, mediante tonometría. Esta técnica se fundamenta en 2 asunciones: 1. La PCO2, medida tonométricamente se aproxima a la de la mucosa intestinal, 2. La concentración de bicarbonato en la mucosa intestinal está en equilibrio con la del lecho capilar intestinal, y ésta a su vez, con la de la sangre arterial. La utilidad del pHi como indicador pronóstico en el paciente crítico ha sido demostrado en numerosas publicaciones: un pHi disminuido al ingreso en UCI es signo de mal pronóstico. No obstante, existía controversia sobre su utilidad para guiar la terapia en el paciente crítico, probablemente relacionadas con sus limitaciones tecnológicas (mediciones intermitentes, laboriosas e invasivas). Además, surgieron dudas metodológicas sobre el uso del pHi, proponiéndose el uso de otro parámetro relacionado, el gradiente de CO2 gastro-arterial (CO2gap = PgCO2 - PaCO2 ) y, en un intento de medición continua y no invasiva, la sustitución del CO2 arterial por el CO2et (CO2 end tidal). Estas aportaciones no fueron útiles con lo que la técnica entró en desuso y el sistema dejó de comercializarse en 2010. El interés por la técnica tonométrica resurge en 2015 con la publicación de un metaanálisis que concluye: “en pacientes de cuidados intensivos la terapia guiada por tonometría gástrica puede reducir la mortalidad total”. Pese a este resultado, reconocen inconvenientes metodológicos: “es necesario aclarar el significado exacto de la fisiología de pHi y PCO2gap”. La superación de estas dificultades técnicas y metodológicas podría tener gran interés clínico. OBJETIVOS. 1. Dilucidar las dudas metodológicas de la monitorización de la perfusión tisular esplácnica por tonometría. 2. Aportar mejoras tecnológicas que simplifiquen el cálculo de sus parámetros de monitorización, disminuyan su invasividad y permitan disponer de información continua, según la patente ES 2 379 817 B1 MATERIAL Y MÉTODOS. Estudio clínico prospectivo observacional en niños críticos ingresados en la Sección de CIP (Cuidados Intensivos Pediátricos) del Hospital Clínico Universitario de Valencia, desde octubre del 2005 hasta abril 2008. Tras la estabilización inicial, se colocó en el paciente una sonda de tonometría (Tonometrics TM Catheter) de 8 F. que permite determinar de forma automatizada la PgCO2, para el cálculo del pHi y otros parámetros derivados. Se conecta al monitor de tonometría, Módulo M-Tono de la Casa Datex-Ohmeda Instrumentarium Corp. (Helsinki. Finland) (actual General Electric), desechando las mediciones de la primera hora tras su colocación. Se midió también la: - PtCO2 (Presión transcutánea de CO2) con monitor transcutáneo Tosca 500. Radiometer (Copenhague, Denmark) - EtCO2 (CO2 al final de la espiración) con módulo metabólico M-COVX - Muestras sangre arterial: pHa, PaCO2, PaO2, bicarbonato y lactato. Se recogieron una serie de variables respiratorias y hemodinámicas. Todos los datos clínicos y analíticos se recogieron en tiempo real, a la cabecera del paciente, una parte en hojas de recogida de datos, y otra de forma automatizada mediante el instrumento pH-Tono versión 1.1 (que originó la patente ES 2 379 817 B1). Análisis Estadístico Se utilizó el método de regresión lineal múltiple mediante el programa SPSS versión 15®, para obtener estimaciones útiles, válidas y fiables de diferentes parámetros deseados, a partir de indicadores clave realizando comparaciones entre dos parámetros. En la comparación de parámetros se obtuvo la correlación lineal de Pearson (r), significación estadística, tamaño del efecto (r2), ecuación de regresión y diagrama de dispersión. Para el estudio descriptivo se obtuvo la media, desviación estándar, rango y porcentajes. RESULTADOS PRINCIPALES • Descripción general de la serie La población de estudio incluyó a 21 pacientes (14 niñas y 7 niños), con edades entre 2 meses y 14 años. Los diagnósticos principales fueron: politraumatismo grave en 4, shock séptico en 9 (5 de ellos meningococo), IRA (insuficiencia respiratoria aguda grave) y SDRA (síndrome de distres respiratorio agudo) en 6 y control postquirúrgico en 2 pacientes. Seis de los pacientes presentaban antecedentes patológicos de interés. Se analizaron un total de 269 muestras. • Dudas metodológicas: ¿Qué parámetro/s son los idóneos para monitorizar la perfusión tisular esplácnica? Planteamos si las ecuaciones clásicas de pH pueden ser sustituidas por ecuaciones simplificadas. Tras sustituciones y simplificaciones matemáticas en las ecuaciones clásicas obtuvimos las ecuaciones simplificadas, que no precisan el uso de constantes ni de variables previamente calculadas Ecuación habitual de cálculo Ecuación simplificada pHi = 6.1 + log10 ([HCO3- / PgCO2 * 0,03) pHi = pHa – log PgCO2/PaCO2 pHgap = pHa–pHi pHgap = log PgCO2/PaCO2 pHis = 7.4 – pHgap pHis = 7.4 – log PgCO2/PaCO2 CO2gap ó P(g-a)CO2 = PgCO2 - PaCO2 CO2gapP= (PgCO2-PaCO2)*100/PgCO2 *[HCO3-] = 0.03 * PaCO2 * 10 (pHa-6.1) Donde 6.1 es pK del sistema HCO3- / CO2 en plasma a 37ºC; [HCO3- es la concentración arterial de bicarbonato (Mm/L); PgCO2 presión gástrica de CO2; 0.03 constante de solubilidad del CO2 en plasma a 37ºC; pHa, pH arterial; PaCO2, presión arterial de CO2; PCO2gap, diferencia gastro-arterial de CO2; pHgap diferencia pHa-pHi; pHis pHi estándar. Para demostrar su utilidad, se compararon ambos modos de cálculo, obteniendo correlaciones cercanas a 1. Por tanto, las ecuaciones simplificadas pueden sustituir a las clásicas, conservando la utilidad que éstas últimas puedan tener. A la vista de estas ecuaciones, podemos afirmar que sólo el pHi realiza una medición del pH de la mucosa intestinal al restar la diferencia sistémico-regional del pH arterial. El resto de parámetros sólo valoran diferencias sistémico-regionales de pH o CO2, lo que les confiere utilidad en situaciones de alcalosis o acidosis sistémica. Tienen por tanto un uso complementario al pHi. Parámetros que miden diferencias sistémico-regionales ¿Pero cuál o cuáles de estos parámetros deben utilizarse de forma complementaria con el pHi?, ¿tienen la misma utilidad?: el coeficiente de correlación del pHis (utilizando el cálculo clásico) fue muy alto con el CO2gap y CO2gapP (r>-0,88). Al repetir esta correlación con la fórmula simplificada del pHis, su correlación aumentó (r=-0,94 con el CO2gap), siendo la correlación con el CO2gapP casi perfecta (r>-0,99). Por otra parte, al realizar las correlaciones de estos parámetros, obtuvimos las ecuaciones de regresión que las relacionan y las utilizamos para calcular que valores de CO2gap y CO2gapP corresponderían a: 1) Un valor normal de pHis (7,40). 2) El valor de pHis considerado límite de normalidad (7,32) y 3) Un valor claramente patológico de pHis (7,10). Para ver si el valor de la PaCO2 (referencia sistémica) podía influenciar estos cálculos, los repetimos para las muestras con PaCO2 > de 50 mmHg. Los resultados son: pHis CO2gap (mmHg) CO2gapP(%) Serie completa (N = 269) 7,40 -1 1,2 Serie PaCO2> 50 mmHg (N = 145) 7,40 -0,67 0,4 Diferencia entre series 0 0,33 0,8 Serie completa (N = 269) 7,32 10,3 17 Serie PaCO2> 50 mmHg (N = 145) 7,32 12,5 16,2 Diferencia entre series 0 2,2 0,8 Serie completa (N = 269) 7,10 41,9 61,2 Serie PaCO2> 50 mmHg (N = 145) 7,10 49,3 60,4 Diferencia entre series 0 7,4 0,8 Obsérvese como para un mismo valor de pHis se obtienen valores de CO2gap diferentes según los niveles de PaCO2 de la muestra. Esto no ocurre con el CO2gapP. Por tanto, de acuerdo con nuestros resultados, "el CO2gap" tiene un grave inconveniente: la interpretación de sus valores depende del nivel de la PCO2 arterial. Así, no será posible establecer un rango de normalidad para este parámetro, ya que este rango variará con los cambios de la PaCO2. Para valorar estas diferencias sistémico-regionales deben utilizarse el pHis, pHgap o CO2gapP siendo este último parámetro, descrito por nosotros, el más adecuado para uso clínico. • Mejoras tecnológicas: ¿Puede realizarse medición en continuo y no invasiva de estos parámetros? Para ello, debemos sustituir la PaCO2 que es el parámetro de referencia sistémica (su medición es invasiva e intermitente). Con esta finalidad realizamos un estudio de correlaciones de este parámetro con sus tres modos de estimación en continuo existentes. Los resultados fueron los siguientes: - PaCO2 vs EtCO2 . Con la ER, en nuestra serie, a un valor de PaCO2 = 40 mmHg (PaCO2 normal en sangre), le corresponde un valor de EtCO2 de 31 mmHg. (Diferencia de 9). - PaCO2 vs PgCO2. Con la ER, a un valor de PaCO2 = 40 mmHg, le corresponde un valor de PgCO2 de 45,2 mmHg. (Diferencia de 5,2) - PaCO2 vs PtcCO2. Con la ER, a un valor de PaCO2 = 40 mmHg, le corresponde un valor de PtcCO2 de 41,4 mmHg. (Diferencia de 1,4) Por tanto, la sustitución de la PaCO2 por la PtcCO2 en los parámetros de referencia podría tener utilidad clínica para la valoración continua de la perfusión tisular esplácnica. Utilizando las ecuaciones de regresión obtuvimos los siguientes resultados: - CO2gap versus CO2gapTc: a un valor de CO2gap de 10,6 mmHg, le corresponde un valor de CO2gapTc de 8,4 mmHg. - CO2gapP versus CO2gapPTc (en porcentaje): a un valor de CO2gapP = 13,7 %, le corresponde un valor de CO2gapPTc de 10 %. - pHis versus pHisTc. ER a un valor de pHis = 7,321, le corresponde un valor de pHisTc de 7,341. - pHi versus pHiTc. ER a un valor de pHi = 7,31, le corresponde un valor de pHiTc de 7,326. Por todo lo expuesto, la sustitución de la PaCO2 por el PtcCO2 propuesta por nosotros para la valoración continua de la perfusión tisular esplácnica en el paciente crítico puede tener utilidad clínica.Gastric intramucosal pH (pHi) and systemic-regional gradient of CO2 in critical pediatric patient. Continuous monitoring of the splanchnic tissue perfusion. INTRODUCTION Compensated shock situations characterized by the presence of acidosis in the intestinal mucosa, which are identified by measuring the pHi (intramucosal pH), are extremely common in critically ill pediatric patients. These situations of intestinal ischemia are associated with multiple organ dysfunction syndrome (MODS). PHi can be measured indirectly by tonometry, using a modified version of the Henderson-Hasselbach formula. This technique is based on two assumptions: 1. PCO2 tonometrically measured approximates the intestinal mucosa CO2 concentration, 2. bicarbonate concentration in the intestinal mucosa is in balance with the intestinal capillary bed, and at the same time, with its concentration in arterial blood. The utility of pHi as a prognostic indicator in the critical patient has been demonstrated in numerous publications: a diminished pHi on admission at ICU is a sign of poor prognosis. However, there was some controversy about its usefulness to lead the therapy in a critical patient. This was probably related to technological limitations (measurements are intermittent, laborious and invasive). Moreover, there were methodological concerns about the use of pHi, thus another related parameter was proposed, the gastric-arterial CO2 gradient (CO2gap = PgCO2 - PaCO2) and in order to carry out this measurement in a noninvasive and continuous way, replacement of arterial CO2 by EtCO2 (end tidal CO2) was also proposed. Despite this, these contributions were not helpful, so the technique fell into disuse and the system stopped being commercialized in 2010. Interest in tonometry has reemerged in 2015, with the publication of a meta-analysis that concludes: "In intensive care patients, therapy guided by gastric tonometry can reduce overall mortality." In spite of this result, the authors recognize methodological drawbacks: "It is necessary to clarify the exact meaning of the physiology of pHi and PCO2gap". Overcoming these technical and methodological difficulties can be of great clinical interest. OBJECTIVES. 1. To clarify the methodological doubts about splanchnic tissue perfusion monitored by tonometry. 2. To provide technological improvements that simplify calculation of monitoring parameters of splanchnic tissue perfusion, decrease their invasiveness and enable continuous information gathering (according to the patent ES 2379817 B1). MATERIAL AND METHODS Prospective observational clinical study in critically ill children admitted to Section CIP (Pediatric Intensive Care) at Clínico University Hospital of Valencia, from October 2005 to April 2008. Following the initial stabilization, the patient was placed a tonometry catheter (8F) (TM Tonometrics Catheter) to determine the PgCO2 automatically, so we are able to calculate the pHi and other derived parameters. Patient was connected to the Tonometry Device using the module M-Tono de la Casa Datex-Ohmeda Instrumentarium Corp. (Helsinki. Finland) (currently General Electrics). Measurements of first hour were discarded. Other measurements recorded were: - PtCO2 (transcutaneous CO2 pressure) transcutaneous monitor 500. Tosca Radiometer (Copenhagen, Denmark). - EtCO2 with metabolic module M-COVX. - Arterial blood samples: pHa, PaCO2, PaO2, bicarbonate and lactate. A series of respiratory and hemodynamic variables were collected. All clinical and laboratory data were collected in real time, at the patient bedside, some of them in data collection sheets. The rest were automatically collected by the pH-tone instrument version 1.1 (which the patent ES 2,379,817 B1). Statistic Analysis Multiple lineal regression method was used with SPSS software (version 15®) to obtain useful, valid and reliable estimations of the selected parameters. Regarding the comparison of parameters, we obtained: the linear correlation of Pearson (r), statistical significance, the magnitude of the effect (r2), the regression equation and the scatter plot. Regarding the descriptive study, mean, standard deviation, range and percentages were obtained. MAIN RESULTS General Description of the series The study population included 21 patients (14 girls and 7 boys), aged 2 months to 14 years. The main diagnoses were: 4 severe multiple trauma, 9 septic shock (5 of them by meningococcus), 6 IRA (severe acute respiratory failure) or ARDS (acute respiratory distress syndrome) and 2 patients admitted to postoperative control. Six of the patients had pathological history of interest. A total of 269 samples were analyzed. Methodological concerns, What are the appropriate parameters to monitor the splanchnic tissue perfusion? We wonder whether the classical equations of pH can be replaced by simplified equations. After substitutions and mathematical simplifications in the classical equations we obtained the simplified equations, which do not require the use of constants or variables previously calculated (Table 1). Ecuación habitual de cálculo Ecuación simplificada pHi = 6.1 + log10 ([HCO3- / PgCO2 * 0,03) (6) pHi = pHa – log PgCO2/PaCO2 pHgap = pHa – pHi (7) pHgap = log PgCO2/PaCO2 pHis = 7.4 – pHgap (8) pHis = 7.4 – log PgCO2/PaCO2 CO2gap ó P(g-a)CO2 = PgCO2 - PaCO2 (5) CO2gapP= (PgCO2-PaCO2)*100/PgCO2 *[HCO3-] = 0.03 * PaCO2 * 10 (pHa-6.1) Table1. Equations to calculate the regional parameters. 6.1, plasmatic pK of HCO3- /CO2 system at 37ºC; [HCO3- arterial bicarbonate concentration (mM / L); PgCO2 gastric pressure of CO2; 0.03 plasmatic solubility constant of CO2 at 37 ° C; pHa, arterial pH; PaCO2, PaCO2; PCO2gap, gastro-arterial difference of CO2; pHgap difference Pha-pHi; pHis standard pHi. In order to demonstrate its utility, both calculation methods were compared, obtaining correlations close to 1. Therefore, the simplified equations can replace the classics (preserving their utility). In light of these equations, we can assert that only the pHi performs a measurement of pH of the intestinal mucosa, by subtracting the systemic-regional gradient of the arterial pH. The rest of parameters only evaluate the systemic-regional differences either the pH or CO2. This gives them utility in situations of systemic acidosis or alkalosis. Therefore, they have a complementary use to the pHi. Parameters that measure systemic-regional differences Which of these parameters should be used, in a complementary way, with the pHi?, Do they have the same utility ?: The pHis correlation coefficient (using the classical calculation) was very high with CO2gap and CO2gapP (r> -0 , 88). When repeating this correlation with the simplified formula of pHis, the correlation increased (r = -0.94 with CO2gap), resulting an almost perfect correlation with CO2gapP (r> -0.99). On the other hand, when making correlations of these parameters, we obtained the regression equations derived. Then, we used those equations to calculate the values of CO2gap and CO2gapP that would correspond to: 1) A normal value pHis (7.40). 2) The value of pHis considered limit of normality (7.32) and 3) A clearly pathological pHis value (7.10). To find out whether the value of PaCO2 (systemic reference) could influence these calculations, we repeated them for samples with PaCO2> 50 mmHg. The results are shown in Table 2. pHis CO2gap (mmHg) CO2gapP (%) Complete Series (N = 269) 7,40 -1 1,2 Series of PaCO2> 50 mmHg (N = 145) 7,40 -0,67 0,4 Difference between Series 0 0,33 0,8 Complete Series (N = 269) 7,32 10,3 17 Series of PaCO2> 50 mmHg (N = 145) 7,32 12,5 16,2 Difference between Series 0 2,2 0,8 Complete Series (N = 269) 7,10 41,9 61,2 Series of PaCO2> 50 mmHg (N = 145) 7,10 49,3 60,4 Difference between Series 0 7,4 0,8 Table 2. Values obtained from CO2gap and CO2gapP for different levels of pHis using the regression equations that relate them. Note as for the same value pHis, different values of CO2gap are obtained according to PaCO2 levels of the sample. This does not happen with CO2gapP. Consequently, according to our results, "the CO2gap" has a serious inconvenient: the interpretation of values depends on the level of arterial PCO2. So, it is not possible to establish a normal range for this parameter, since this range will vary with changes in PaCO2. To assess these systemic-regional differences, the pHis, pHgap or CO2gapP should be used, being CO2gapP (described by us), the most suitable for clinical use. Technological improvements: could it be possible to get a continuous and noninvasive measurement of these parameters? To achieve this, we must replace the PaCO2 as it is systemic reference of the parameter (its measurement is invasive and intermittent). For this purpose we conducted a correlation study of this parameter with its three existing modes of continuous estimation. The results of the study were the following: - PaCO2 and EtCO2. With the Regression equation (RE), in our series, a PaCO2 = 40 mmHg (normal blood PaCO2) corresponds to a value of 31 mmHg EtCO2. (difference of 9). - PaCO2 and PCO2. With the RE, a value of PaCO2 = 40 mmHg corresponds to a value of 45.2 mmHg PgCO2. (difference of 5.2). - PaCO2 vs PtcCO2. With the RE, a value of PaCO2 = 40 mmHg corresponds to a value of 41.4 mmHg PtcCO2. (difference of 1.4). Therefore, replacing the PaCO2 by the PtcCO2 in the reference parameters could have clinical utility for a continuous assessment of splanchnic tissue perfusion. Using the RE we obtained the following results: - CO2gap versus CO2gapTc: a value of 10.6 mmHg CO2gap corresponds to a value of 8.4 mmHg CO2gapTc. - CO2gapP versus CO2gapPTc (in percentage): a value of CO2gapP = 13,7 % corresponds to a value of 10 % CO2gapPTc. - pHis versus pHisT: a value of pHis = 7,321 corresponds to a value of pHisTc of 7,341. - pHi versus pHiTc: :a value of pHi = 7,31 corresponds to a value of pHiTc of 7,326. Our results suggest that the replacement of PaCO2 by the PtcCO2 proposed by us for a continuous assessment of splanchnic tissue perfusion in critically ill patients, may have clinical utility