Walczak Andrzej Augustyn
Faculty of Cybernetics, Military University of Technology, Gen. Kaliskiego St. 2, 00-908 Warsaw, Poland.
Entropy (Basel). 2022 Dec 6;24(12):1780. doi: 10.3390/e24121780.
The unexpectable variations of the diagnosed disease symptoms are quite often observed during medical diagnosis. In stochastics, such behavior is called "grey swan" or "black swan" as synonyms of sudden, unpredictable change. Evolution of the disease's symptoms is usually described by means of Markov processes, where dependency on process history is neglected. The common expectation is that such processes are Gaussian. It is demonstrated here that medical observation can be described as a Markov process and is non-Gaussian. Presented non-Gaussian processes have "fat tail" probability density distribution (pdf). "Fat tail" permits a slight change of probability density distribution and triggers an unexpectable big variation of the diagnosed parameter. Such "fat tail" solution is delivered by the anomalous diffusion model applied here to describe disease evolution and to explain the possible presence of "swans" mentioned above. The proposed model has been obtained as solution of the Fractal Fokker-Planck equation (FFPE). The paper shows a comparison of the results of the theoretical model of anomalous diffusion with experimental results of clinical studies using bioimpedance measurements in cardiology. This allows us to consider the practical usefulness of the proposed solutions.
在医学诊断过程中，经常会观察到已确诊疾病症状出现意想不到的变化。在随机过程中，这种行为被称为“灰天鹅”或“黑天鹅”，作为突然的、不可预测变化的同义词。疾病症状的演变通常用马尔可夫过程来描述，其中忽略了对过程历史的依赖性。通常的预期是这些过程是高斯分布的。本文证明医学观察可以描述为一个马尔可夫过程，并且是非高斯的。所提出的非高斯过程具有“肥尾”概率密度分布（pdf）。“肥尾”允许概率密度分布有轻微变化，并引发已诊断参数意想不到的大变化。这里应用反常扩散模型来描述疾病演变并解释上述“天鹅”可能的存在，从而给出这种“肥尾”解决方案。所提出的模型是作为分形福克 - 普朗克方程（FFPE）的解得到的。本文展示了反常扩散理论模型的结果与心脏病学中使用生物阻抗测量的临床研究实验结果的比较。这使我们能够考虑所提出解决方案的实际实用性。
