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Model Combining Fluid Hemodynamics and Fractal Theory for Analysis of in vivo Peripheral Pulmonary and Systemic Vascular Resistance of Shunt Cardiac Defects

中村, 嘉宏 東京大学 DOI:10.15083/0002008268

2023.12.27

概要

審査の結果の要旨

⽒名 中村 嘉宏

本研究は左右短絡による⼆次性肺⾼⾎圧 (PH) を伴う先天性⼼疾患の治療指針に重要な要因と
なる末梢肺動脈の⾎管床変化の理論的解析を⽬的としている。フラクタル理論および fluid
hemodynamics に基づく⾎管樹数学モデルを⽤い、正常および様々な重症度の PH 症例の⼼臓カテ
ーテル検査データから肺体⾎管樹フラクタル次数 x、同フラクタル parameters, ⾎管抵抗構成要素
(⾎管⻑ l [mm], ⾎管半径 r [µm], ⾎管数 N) の算出を試み、下記の結果を得ている。
1. ⽣体の単位抵抗動脈⾎管樹の幾何学様式を n 世代の⾮対称分岐を繰り返すフラクタル構造と
仮定し、⾎流量 Q [L/min], 末梢⾎管抵抗 R [mmHg/L/min], 抵抗動脈圧格差 P [mmHg]および body
scale M を⽤いて導出された数式モデルに基づき、Q vs. R/M の臨床データによる両対数プロットで、
最⼩⼆乗法による回帰直線の傾きから⾎管樹のフラクタル次数 x が算出可能であることを⽰した。
2.本数式モデルを⽤いた体循環データの分析で、複数ある body scale の候補の中から⾝⻑ BL [m]
が最適であることを発⾒し、コントロール群および全症例で末梢体動脈フラクタル次数 xs が 2.9 ~
3.1 となることを⽰した。これは、⾎流量−⾎管半径関係における最適条件として有名な Murray
(1926)の法則や uniform shear-stress 論の根拠である cubic rule, x = 3 を良く説明した。
3.正常肺循環とみなされる control 群では肺動脈抵抗⾎管樹のフラクタル次数 xp は 2.2 と算出さ
れ、morphometry により報告されたヒトを始めとする哺乳動物の正常肺動脈⾎管樹の⽂献データと
⼀致した。また x および縦軸切⽚からフラクタル parameters を求め⽂献上報告された正常肺体動脈
樹データと良く⼀致した。
4.PH が進⾏するに伴い、xp は 2.2 から 3.0 に漸増することを予測した。フラクタル parameters の
変化は、重症 PH 群の肺動脈抵抗⾎管樹では 3 世代中枢から抵抗⾎管領域が開始し、control 群で半
径 100 µm と仮定した⾎管の半径は重症 PH 群では 22%の減少、また重症 PH 群では肺胞内動脈の
総数が平均でコントロール群の 1/9 となることを意味し、PH による vasoconstriction や肺胞内動脈
成⻑抑制を良く説明した。これらの結果は⽂献上の autopsy あるいは術中 biopsy による組織学的報
告と定量的に⽐較され compatible であった。
5.正常から重症 PH で xp が 2.2 → 3.0 へ変化することの考察として、1)⾼肺⾎流という側⾯
から Murray の cost function で⾎流を⾎管半径の関数とみなし⾎流最⼤条件から x = 3 を説明した。
また2)最⼩エネルギーの原理により、弾性動脈では中枢末梢とも結果的に x = 2.3 が導出され、剛
性動脈では x が Reynolds 数の連続関数として記述されることを⽰した。その結果、剛性動脈では

運動エネルギーが⼗分⼤きい上⾏⼤動脈の条件では x → 2.3、運動エネルギーが⼗分⼩さい末梢
循環では x → 3.0 になることが予測され、本来弾性である末梢肺動脈が PH 下で剛性となり x が
3.0 に推移することを理論的に初めて説明した。

以上、本論⽂は、フラクタル理論と fluid hemodynamics に基づく数式モデルを考案し、従来の
臨床的に測定可能な⾎管抵抗のデータから⾎管抵抗を構成する各要素のシミュレーションを可能
とした。また同数式モデルを臨床データの解析に応⽤し、⾼肺⾎流性⼆次性肺⾼⾎圧が惹起する末
梢肺動脈病変の幾何学的変化を予測、その結果が従来の組織学的知⾒を定量的に良く説明すること
を⽰した。臨床データから正常⾎管床のみならず病的⾎管床の幾何学的様式とその変化を推測する
⽅法論は未報告である。またフラクタル次数の変化を統計⼒学的な説明から可能とした理論的考察
も今までに類を⾒ない。本研究は今後の⽣体⾎管床変化の病態⽣理や過程の究明、また⼈⼯⾎管樹
や⼈⼯回路設計への応⽤が期待され重要な貢献を為すと考えられる。

よって本論⽂は博⼠( 医学 )の学位請求論⽂として合格と認められる。

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