When the optimal is not the best: parameter estimation in complex biological models

Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values. Results: We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit. Conclusions: The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system, and point to the need of a theory that addresses this problem more generally

Direct intramyocardial transthoracic transplantation of bone marrow mononuclear cells for non-ischemic dilated cardiomyopathy: INTRACELL, a prospective randomized controlled trial

Objective: We tested the hypothesis that direct intramyocardial injection of bone marrow mononuclear cells in patients with non-ischemic dilated cardiomyopathy can improve left ventricular function and physical capacity. Methods: Thirty non-ischemic dilated cardiomyopathy patients with left ventricular ejection fraction <35% were randomized at a 1:2 ratio into two groups, control and treated. The bone marrow mononuclear cells group received 1.06&#177;108 bone marrow mononuclear cells through mini-thoracotomy. There was no intervention in the control group. Assessment was carried out through clinical evaluations as well as a 6-min walk test, nuclear magnectic resonance imaging and echocardiogram. Results: The bone marrow mononuclear cells group showed a trend toward left ventricular ejection fraction improvement, with magnectic resonance imaging - at 3 months, showing an increase from 27.80&#177;6.86% to 30.13&#177;9.06% (P=0.08) and returning to baseline at 9 months (28.78%, P=0.77). Magnectic resonance imaging showed no changes in left ventricular ejection fraction during follow-up of the control group (28.00&#177;4.32%, 27.42&#177;7.41%, and 29.57&#177;4.50%). Echocardiogram showed left ventricular ejection fraction improved in the bone marrow mononuclear cells group at 3 months, 25.09&#177;3.98 to 30.94&#177;9.16 (P=0.01), and one year, 30.07&#177;7.25% (P=0.001). The control group showed no change (26.1&#177;4.4 vs 26.5&#177;4.7 and 30.2&#177;7.39%, P=0.25 and 0.10, respectively). Bone marrow mononuclear cells group showed improvement in New York Heart Association functional class, from 3.40&#177;0.50 to 2.41&#177;0.79 (P=0.002); patients in the control group showed no change (3.37&#177;0.51 to 2.71&#177;0.95; P=0.17). Six-minute walk test improved in the bone marrow mononuclear cells group (348.00&#177;93.51m at baseline to 370.41&#177;91.56m at 12 months, P=0.66) and there was a non-significant decline in the control group (361.25&#177;90.78m to 330.00&#177;123.42m after 12 months, P=0.66). Group comparisons were non-significant. Conclusion: The trend of intragroup functional and subjective improvement was not confirmed when compared to the control group. Direct intramyocardial application of bone marrow mononuclear cells in non-ischemic dilated cardiomyopathy was not associated with significant changes in left ventricular function. Differences observed within the bone marrow mononuclear cells group could be due to placebo effect or low statistical power