Multi-fidelity modelling via recursive co-kriging and Gaussian-Markov random fields.

We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian-Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Radiofrequency hyperthermia as adjuvant therapy following surgical resection of an experimental malignant neoplasm.

Local recurrence after radical surgery is a major problem with many primary solid cancers. The use of radiofrequency hyperthermia (RFHT) as adjuvant therapy to surgery was explored in the Fischer bladder carcinoma (FBCa)/F344 rat tumor system. After subcutaneous innoculation of 34 rats with 10(6) FBCa cells in suspension, RFHT was administered to 17 animals on days 1, 5, 8, and 12. The development of palpable tumors was delayed but not prevented, and tumor growth was retarded in RFHT-treated animals. In another experiment 40 rats were innoculated by subcutaneous trocar injection with a 1 mm3 piece of FBCa. After tumor excision on day 17, adjuvant therapy (untreated control, mitomycin C, RFHT, or RFHT plus mitomycin C) was started on day 20 (10 rats/treatment). The 20 RFHT-treated rats had only 1 incisional recurrence as compared to 9 recurrences in sham-heated rats (P less than 0.005). The authors conclude that RFHT has considerable value as adjuvant therapy to surgery in these tumors. Additional studies of RFHT as adjuvant treatment after surgical excision of tumors are planned.

Further experience with regional radiofrequency hyperthermia and cytotoxic chemotherapy for unresectable hepatic neoplasia.

The authors report on 178 patients with unresectable hepatic tumors who have been treated with 1 to 25 (median, 6) courses of radiofrequency hyperthermia (RFHT) and chemotherapy. In 137 patients, the hepatic tumors consisted of metastases from colorectal adenocarcinomas. For patients who had no previous therapy and who had colorectal metastases with no extraheptic disease, cumulative survival at 52 weeks' follow-up was 80.5% and partial tumor regression was seen in 78.4%. Among the 69 patients who previously had conventional treatment for their hepatic disease, partial regression was seen in 43.5%. We are no longer monitoring tumor core temperature routinely, as the invasive methods currently in use yield irreproducible results; the risks to the patient cannot be justified in view of the questionable relevance of the data obtained. A prospective randomized study of systemic chemotherapy with or without RFHT in patients with colorectal hepatic metastases is in progress.

Reversal of lethal, chemotherapeutically induced acute hepatic necrosis in rats by regenerating liver cytosol.

In this report we further evaluate the role of regenerating liver cytosol (RLC) as a stimulator of hepatic regeneration by assessing its effect on survival, liver function, and hepatic regeneration in a model of in vivo isolated perfusion of the rat liver with high concentrations of cytotoxic drugs and regional hyperthermia. Isolated perfusion with 500 mg/kg of 5-fluorouracil (5-FU) and 2.5 mg/kg of mitomycin-C (Mit-C) resulted in 70% (n = 20) and 71% (n = 14) mortality, respectively, from 2 to 7 days after perfusion, with extensive, patchy necrosis and infarction seen on histologic examination and markedly elevated levels of serum glutamic oxaloacetic transaminase (SGOT) and serum glutamic pyruvic transaminase (SGPT) at 6 and 24 hours after perfusion. The intraperitoneal administration of RLC (80 mg total protein/rat) at the time of hepatic perfusion resulted in 70% (5-FU, n = 20, P less than 0.05) and 80% (Mit-C, n = 20, P less than 0.01) survival at 21 days post perfusion. RLC-treated rats demonstrated significantly lower SGOT and SGPT levels at 6 and 24 hours after perfusion and normal liver histologic appearance by 14 days after perfusion in surviving rats. Hepatic regenerative capacity following partial hepatectomy was severely inhibited (P less than 0.001) following isolated hepatic perfusion with sublethal doses of 5-FU (125 mg/kg, 250 mg/kg), Mit-C (1.5 mg/kg) and hyperthermia (41 degrees C and 43 degrees C X 5 minutes). The administration of RLC at the time of partial hepatectomy restored the DNA synthetic response in perfused rats to that seen in normal control rats after partial hepatectomy (P less than 0.05). These results demonstrate that the liver is the source of a factor (s) (RLC) that significantly improves survival after lethal chemotherapeutic injury to the liver by stimulating endogenous hepatic regeneration. A potential clinical application for a stimulator of hepatic regeneration in situations of deliberate, therapeutic insult to the liver is suggested.

The effect of liver cytosol on hepatic regeneration and tumor growth.

This report further evaluates the concept that the interaction of factors that originate within the liver can contribute, regulate or even initiate the actual development of hepatic regeneration after liver cell necrosis or partial hepatectomy. The effect of liver cytosol (100,000 g supernatant), both from intact adult rat liver (NLC) and from adult rat liver remnants that had been regenerating for 24 hours after 70% partial hepatectomy (PH) in posthepatectomy liver regeneration in the rat was studied. The specificity of the growth-controlling properties in liver cytosol was determined using tumor cells. The intraperitoneal administration of NLC after PH resulted in approximately 70-80% inhibition of the peak 3H-DNA specific activity seen in controls at 18 and 24 hours post-PH, with a significant increase in DNA synthesis at 31-40 hours post-PH. The intraperitoneal administration of RLC after PH, augmented the hepatic regenerative response normally produced. Autoradiographic determination of hepatic nuclear labeling confirmed the inhibitory and stimulatory properties of NLC and RLC respectively. Syngeneic NLC or RLC at six and 24 days after subcutaneous tumor inoculation resulted in significant inhibition of tumor growth for both a methylcholanthrene-induced bladder carcinoma (FBCa) and an HTC-hepatoma. The retardation of FBCa growth could be enhanced by administering NLC or RLC every three or seven days. Syngeneic and xenogeneic liver cytosol resulted in dose-dependent inhibition of P815 mastocytoma cell proliferation in vitro. It is apparent from these studies that both stimulatory and inhibitory factors can be extracted from liver tissue that not only influence liver cell regeneration, but also affect tumor growth. Further isolation and characterization of these factors may lead to an understanding of more fundamental problems such as the control of normal and malignant cell growth.

Protection of thermochemotherapeutic-induced lethal acute hepatic necrosis in the rat by 16,16-dimethyl prostaglandin E2.

These studies further evaluate the hepatocytoprotective properties of 16,16-dimethyl prostaglandin E2 (dmPGE2) by assessing its effect on survival, liver function, and hepatic regeneration in a model of in vivo isolated perfusion of the rat liver with high concentrations of cytotoxic drugs and regional hyperthermia. Isolated perfusion with 1.0 g/kg of 5-FU or hyperthermia of 41 degrees C X 10 min resulted in 90-100% mortality in control rats, with extensive, patchy necrosis and infarction on histologic examination, and markedly elevated levels of SGOT and SGPT at 24 hr after perfusion. Pretreatment with dmPGE2 (10 micrograms/kg sc) at 30 min before, and at 6 and 24 hr after hepatic perfusion significantly improved survival to 80% (P less than 0.01) following 5-FU perfusion and to 40% (P less than 0.05) following hyperthermic perfusion. Animals were followed for at least 21 days after perfusion and demonstrated normal liver histology, dmPGE2-treated rats demonstrated significantly lower SGOT and SGPT levels at 24 hr after perfusion. dmPGE2 (2 micrograms/kg sc) given as above improved the length of time of survival but eventual mortality was not significantly improved. Oral administration (50 micrograms/kg po at 30 min before, 6 and 24 hr after perfusion) and posttreatment (10 micrograms/kg sc at 1, 6, and 24 hr after perfusion) had no significant effect on survival. Hepatic regenerative capacity following partial hepatectomy was severely suppressed following isolated hyperthermochemotherapeutic hepatic perfusion. Pretreatment with dmPGE2 (10 micrograms/kg sc) restored the DNA synthetic response in perfused rats to that seen in normal control rats after partial hepatectomy (P less than 0.05 and P less than 0.01). The results from these studies further confirm the role of dmPGE2 as a hepatocytoprotective agent and suggest potential clinical application in situations where there has been deliberate, therapeutic insult to the liver.

Hyperthermochemotherapeutic in vivo isolated perfusion of the rat liver.

This report describes a system of in vivo isolated perfusion of the rat liver. The effects of perfusion with 5-fluorouracil (5-FU) (0.125-1.5 g/kg) on survival, liver function, and hepatic regeneration are studied. A dose of 0.125-0.25 g/kg of 5-FU produced acceptable toxicity with 0% and 25% mortality rate, but induced liver dysfunction indicated by abnormal biochemical values and severe inhibition of hepatic regeneration. Doses of 0.5 g/kg, 1.0 g/kg, and 1.5 g/kg produced a mortality of 60%, 100%, and 100%, respectively. Regional hyperthermia (37-43 degrees C) achieved by perfusion of the liver with heated saline produced an adverse effect on survival, liver function and hepatic regeneration, which are both temperature- and perfusion time-dependent. Hyperthermochemotherapy using in vivo isolated hepatic perfusion might be acceptable for the treatment of unresectable liver cancer, but should not be utilized as an adjuvant therapy prior to hepatic resection without the use of hepatic growth factors which could reverse the inhibitory effect of hepatic perfusion.

Hyperthermia as a treatment for neoplasia.

The use of hyperthermia to treat malignant neoplasms is currently a "hot" issue. It has been demonstrated that heating tumour cells to 42 degrees C or above leads to their self-destruction by decreased cellular metabolism and aerobic respiration. The selective accumulation of heat in the malignant tissue at 42 degrees to 44 degrees C, compared with the temperature of normal tissue, is probably related to the different blood supply within the tumour. The historical background and the experimental and clinical results of hyperthermia are reviewed. The advantages and disadvantages of the different thermotherapy techniques currently in use are discussed. Hyperthermia is probably more efficient if combined with other antitumour treatment modalities.